Chapter LXIII. repeats the promise of freedom to the English church
and of their rights and liberties to all.
Magna Carta is an elaboration of the accession charter of Henry I., and is based upon the Articles of the Barons. It is, however, very much longer than the former charter and somewhat longer than the Articles. Moreover, it differs in several particulars from the Articles, these differences being doubtless the outcome of deliberation and of compromise. For instance, the provisions in Magna Carta concerning the freedom of the church find no place in the Articles, while a comparison between the two documents suggests that in other ways also influences favourable to the church and the clergy were at work while the famous charter was being framed. When one reflects how active and prominent Langton and other prelates were at Runnimede the change is not surprising. Another difference between the two documents concerns the towns and the trading classes. Certain privileges granted to them in the Articles are not found in Magna Carta, although, it must be noted, this document bestows exceptionally favoured treatment on the citizens of London. The conclusion is that the friends of the towns and the traders were less in evidence at Runnimede than they were at the earlier meetings of the barons, but that the neighbouring Londoners were strong enough to secure a good price for their support.
Magna Carta throws much light on the condition of England in the early 13th century. By denouncing the evil deeds of John and the innovations practised by him, it shows what these were and how they were hated; how money had been raised, how forest areas had been extended, how minors and widows had been cheated and oppressed. By declaring, as it does, what were the laws and customs of a past age wherein justice prevailed, it shows what was the ideal of good government formed by John's prelates and barons. Magna Carta can hardly be said to have introduced any new ideas. As Pollock and Maitland (_History of English Law_) say "on the whole the charter contains little that is absolutely new. It is restorative." But although mature study has established the truth of this proposition it was not always so. Statesmen and commentators alike professed to find in Magna Carta a number of political ideas which belonged to a later age, and which had no place in the minds of its framers. It was regarded as having conferred upon the nation nothing less than the English constitution in its perfect and completed form. Sir Edward Coke finds in Magna Carta a full and proper legal answer to every exaction of the Stuart kings, and a remedy for every evil suffered at the time. Sir William Blackstone is almost equally admiring. Edmund Burke says "Magna Carta, if it did not give us originally the House of Commons, gave us at least a House of Commons of weight and consequence." Lord Chatham used words equally superlative. "Magna Carta, the Petition of Rights and the Bill of Rights form that code, which I call the Bible of the English Constitution." Modern historians, although less rhetorical, speak in the highest terms of the importance of Magna Carta, the view of most of them being summed up in the words of Dr Stubbs: "The whole of the constitutional history of England is a commentary on this charter."
Many regard Magna Carta as giving equal rights to all Englishmen. J. R. Green says "The rights which the barons claimed for themselves they claimed for the nation at large." As a matter of fact this statement is only true with large limitations. The villains, who formed the majority of the population, got very little from it; in fact the only clauses which protect them do so because they are property--the property of their lords--and therefore valuable. They get neither political nor civil rights under Magna Carta. The traders, too, get little, while preferential treatment is meted out to the clergy and the barons. Its benefits are confined to freemen, and of the benefits the lion's share fell to the larger landholders; the smaller landholders getting, it is true, some crumbs from the table. It did not establish freedom from arbitrary arrest, or the right of the representatives of the people to control taxation, or trial by jury, or other conceptions of a later generation.
The story of Magna Carta after the death of John is soon told. On the 12th of November 1216 the regent William Marshal, earl of Pembroke, reissued the charter in the name of the young king Henry III. But important alterations were made. War was being waged against Louis of France, and the executive must not be hampered in the work of raising money; moreover the personal equation had disappeared, the barons did not need to protect themselves against John. Consequently the chapter limiting the power of the crown to raise scutages and aids without the consent of the council vanished, and with it the complementary one which determined the method of calling a council. Other provisions, the object of which had been to restrain John from demanding more money from various classes of his subjects, were also deleted, and the same fate befell such chapters as dealt with mere temporary matters. The most important of these was Chapter LXI., which provided for the appointment of 25 executors to compel John to observe the charter. The next year peace was made at Lambeth (Sept. 11, 1217) between Henry III. and Louis and another reissue of the charter was promised. This promise was carried out, but two charters appeared, one being a revised issue of Magna Carta proper, and the other a separate charter dealing with the forests, all references to which were omitted from the more important document. The date of this issue appears to have been the 6th of November 1217. The issue of a separate forest charter at this time led subsequently to some confusion. Roger of Wendover asserts that John issued a separate charter of this kind when Magna Carta appeared. This statement was believed by subsequent writers until the time of Blackstone, who was the first to discover the mistake.
As issued in 1217 Magna Carta consists of 47 chapters only. It declares that henceforward scutages shall be taken according to the precedents of Henry II.'s reign. New provisions were introduced for the preservation of the peace--unlawful castles were to be destroyed--while others were directed towards making the administration of justice by the visiting justices less burdensome. With regard to the land and the services due therefrom a beginning was made of the policy which culminated in the statutes of Mortmain and of Quia Emptores. The sheriffs were ordered to publish the revised charter on the 22nd of February 1218. Then in February 1225 Henry III. again issued the two charters with only two slight alterations, and this is the final form taken by Magna Carta, this text being the one referred to by Coke and the other early commentators. Subsequently the charters were confirmed several times by Henry III. and by Edward I., the most important occasion being their confirmation by Edward at Ghent in November 1297. On this occasion some supplementary articles were added to the charter; these were intended to limit the taxing power of the crown.
There are at present in existence four copies of Magna Carta, sealed with the great seal of King John, and several unsealed copies. Of the four two are in the British Museum. Both came into the possession of the Museum with the valuable collection of papers which had belonged to Sir Robert Cotton, who had obtained possession of both. One was found in Dover castle about 1630. This was damaged by fire in 1731; the other is undamaged. The two other sealed copies belong to the cathedrals of Lincoln and of Salisbury. Both were written evidently in a less hurried fashion than those in the British Museum, and the one at Lincoln was regarded as the most perfect by the commissioners who were responsible for the appearance of the _Statutes of the Realm_ 1810. The British Museum also contains the original parchment of the Articles of the Barons. Magna Carta was first printed by Richard Pynson in 1499. This, however, was not the original text, which was neglected until the time of Blackstone, who printed the various issues of the charter in his book _The Great Charter and the Charter of the Forest_ (1759). The earliest commentator of note was Sir Edward Coke, who published his _Second Institute_, which deals with Magna Carta, by order of the Long Parliament in 1642. Modern commentators, who also print the various texts of the charter, are Richard Thomson, _An Historical Essay on the Magna Carta of King John_ (1829); C. Bémont, in his _Chartes des libertés anglaises_ (1892); and W. Stubbs in his _Select Charters_ (1895). A more recent book and one embodying the results of the latest research is W. S. McKechnie, _Magna Carta_ (1905). The text of Magna Carta is also printed in the _Statutes of the Realm_ (1810-1828), and in T. Rymer's _Foedera_ (1816-1869). In addition to Blackstone, Coke and these later writers, the following works may also be consulted: John Reeves, _History of English Law_ (1783-1784); L. O. Pike, _A Constitutional History of the House of Lords_ (1894); W. Stubbs, _Constitutional History of England_ (1897); Sir F. Pollock and F. W. Maitland, _The History of English Law_ (1895); W. S. Holdsworth, _A History of English Law_ (1903), and Kate Norgate, _John Lackland_ (1902). (A. W. H.*)
MAGNA GRAECIA ([Greek: he megale Hellas]), the name given (first, apparently, in the 6th century B.C.) to the group of Greek cities along the coast of the "toe" of South Italy (or more strictly those only from Tarentum to Locri, along the east coast), while the people were called Italiotes ([Greek: Italiôtai]). The interior, which the Greeks never subdued, continued to be in the hands of the Bruttii, the native mountaineers, from whom the district was named in Roman times ([Greek: Brettia] also in Greek writers). The Greek colonies were established first as trading stations, which grew into independent cities. At an early time a trade in copper was carried on between Greece and Temesa (Homer, _Od._ i. 181).[1] The trade for a long time was chiefly in the hands of the Euboeans; and Cyme (Cumae) in Campania was founded in the 8th century B.C., when the Euboean Cyme was still a great city. After this the energy of Chalcis went onward to Sicily, and the states of the Corinthian Gulf carried out the colonization of Italy, Rhegium having been founded, it is true, by Chalcis, but after Messana (Zancle), and at the request of the inhabitants of the latter. Sybaris (721) and Crotona (703) were Achaean settlements; Locri Epizephyrii (about 710) was settled by Ozolian Locrians, so that, had it not been for the Dorian colony of Tarentum, the southern coast of Italy would have been entirely occupied by a group of Achaean cities. Tarentum (whether or no founded by pre-Dorian Greeks--its founders bore the unexplained name of Partheniae) became a Laconian colony at some unknown date, whence a legend grew up connecting the Partheniae with Sparta, and 707 B.C. was assigned as its traditional date. Tarentum is remarkable as the only foreign settlement made by the Spartans. It was industrial, depending largely on the purple and pottery trade. Ionian Greeks fleeing from foreign invasion founded Siris about 650 B.C., and, much later, Elea (540).
The Italian colonies were planted among friendly, almost kindred, races, and grew much more rapidly than the Sicilian Greek states, which had to contend against the power of Carthage. After the Achaean cities had combined to destroy the Ionic Siris, and had founded Metapontum as a counterpoise to the Dorian Tarentum, there seems to have been little strife among the Italiotes. An amphictyonic league, meeting in common rites at the temple of Hera on the Lacinian promontory, fostered a feeling of unity among them. The Pythagorean and Eleatic systems of philosophy had their chief seat in Magna Graecia. Other departments of literature do not seem to have been so much cultivated among them. The poet Ibycus, though a native of Rhegium, led a very wandering life. They sent competitors to the Olympic games (among them the famous Milo of Croton); and the physicians of Croton early in the 6th century (especially in the person of Democedes) were reputed the best in Greece; but politically they appear to have generally kept themselves separate. One ship of Croton, however, fought at Salamis, though it is not recorded that Greece asked the Italiotes for help when it sent ambassadors to Gelon of Syracuse. Mutual discord first sapped the prosperity of Magna Graecia. In 510 Croton, having defeated the Sybarites in a great battle, totally destroyed their city. Croton maintained alone the leading position which had belonged jointly to the Achaean cities (Diod. xiv. 103); but from that time Magna Graecia steadily declined. In the war between Athens and Syracuse Magna Graecia took comparatively little part; Locri was strongly anti-Athenian, but Rhegium, though it was the headquarters of the Athenians in 427, remained neutral in 415. Foreign enemies pressed heavily on it. The Lucanians and Bruttians on the north captured one town after another. Dionysius of Syracuse attacked them from the south; and after he defeated the Crotoniate league and destroyed Caulonia (389 B.C.), Tarentum remained the only powerful city. Henceforth the history of Magna Graecia is only a record of the vicissitudes of Tarentum (q.v.). Repeated expeditions from Sparta and Epirus tried in vain to prop up the decaying Greek states against the Lucanians and Bruttians; and when in 282 the Romans appeared in the Tarentine Gulf the end was close at hand. The aid which Pyrrhus brought did little good to the Tarentines, and his final departure in 274 left them defenceless. During these constant wars the Greek cities had been steadily decaying; and in the second Punic war, when most of them seized the opportunity of revolting from Rome, their very existence was in some cases annihilated. Malaria increased in strength as the population diminished. We are told by Cicero (_De am._ 4), _Magna Graecia nunc quidem deleta est_. Many of the cities completely disappeared, and hardly any of them were of great importance under the Roman empire; some, like Tarentum, maintained their existence into modern times, and in these only (except at Locri) have archaeological investigations of any importance been carried on; so that there still remains a considerable field for investigation. (T. As.)
FOOTNOTE:
[1] This passage should perhaps be referred to the 8th century B.C. It is the first mention of an Italian place in a literary record.
MAGNATE (Late Lat. _magnas_, a great man), a noble, a man in high position, by birth, wealth or other qualities. The term is specifically applied to the members of the Upper House in Hungary, the _Förendihaz_ or House of Magnates (see HUNGARY).
MAGNES (_c._ 460 B.C.), Athenian writer of the Old Comedy, a native of the deme of Icaria in Attica. His death is alluded to by Aristophanes (_Equites_, 518-523, which was brought out in 424 B.C.), who states that in his old age Magnes had lost the popularity which he had formerly enjoyed. The few titles of his plays that remain, such as the _Frogs_, the _Birds_, the _Gall-flies_, indicate that he anticipated Aristophanes in introducing grotesque costumes for the chorus.
See T. Kock, _Comicorum atticorum fragmenta_, i. (1880); G. H. Bode, _Geschichte der hellenischen Dichtkunst_, iii. pt. 2 (1840).
MAGNESIA, in ancient geography the name of two cities in Asia Minor and of a district in eastern Thessaly, lying between the Vale of Tempe and the Pagasaean Gulf.
(1) MAGNESIA AD MAEANDRUM, a city of Ionia, situated on a small stream flowing into the Maeander, 15 Roman miles from Miletus and rather less from Ephesus. According to tradition, reinforced by the similarity of names, it was founded by colonists from the Thessalian tribe of the Magnetes, with whom were associated, according to Strabo, some Cretan settlers (Magnesia retained a connexion with Crete, as inscriptions found there attest). It was thus not properly an Ionic city, and for this reason, apparently, was not included in the Ionian league, though superior in wealth and prosperity to most of the members except Ephesus and Miletus. It was destroyed by the Cimmerii in their irruption into Asia Minor, but was soon after rebuilt, and gradually recovered its former prosperity. It was one of the towns assigned by Artaxerxes to Themistocles for support in his exile, and there the latter ended his days. His statue stood in its market-place. Thibron, the Spartan, persuaded the Magnesians to leave their indefensible and mutinous city in 399 B.C. and build afresh at Leucophrys, an hour distant, noted for its temple of Artemis Leucophryne, which, according to Strabo, surpassed that at Ephesus in the beauty of its architecture, though inferior in size and wealth. Its ruins were excavated by Dr K. Humann for the Constantinople Museum in 1891-1893; but most of the frieze of the temple of Artemis Leucophryne, representing an Amazon battle, had already been carried off by Texier (1843) to the Louvre. It was an octostyle, pseudo-dipteral temple of highly ornate Ionic order, built on older foundations by Hermogenes of Alabanda at the end of the 3rd century B.C. The platform has been greatly overgrown since the excavation, but many bases, capitals, and other architectural members are visible. In front of the west façade stood a great altar. An immense _peribolus_ wall is still standing (20 ft. high), but its Doric colonnade has vanished. The railway runs right through the precinct, and much of Magnesia has gone into its bridges and embankments. South and west of the temple are many other remains of the Roman city, including a fairly perfect theatre excavated by Hiller von Gärtringen, and the shell of a large gymnasium. Part of the Agora was laid open to Humann, but his trenches have fallen in. The site is so unhealthy that even the Circassians who settled there twenty years ago have almost all died off or emigrated. Magnesia continued under the kings of Pergamum to be one of the most flourishing cities in this part of Asia; it resisted Mithradates in 87 B.C., and was rewarded with civic freedom by Sulla; but it appears to have greatly declined under the Roman empire, and its name disappears from history, though on coins of the time of Gordian it still claimed to be the seventh city of Asia.
See K. Haumann, _Magnesia am Maeander_ (1904).
(2) MAGNESIA AD SIPYLUM (mod. _Manisa_, q.v.), a city of Lydia about 40 m. N.E. of Smyrna on the river Hermus at the foot of Mt Sipylus. No mention of the town is found till 190 B.C., when Antiochus the Great was defeated under its walls by the Roman consul L. Scipio Asiaticus. It became a city of importance under the Roman dominion and, though nearly destroyed by an earthquake in the reign of Tiberius, was restored by that emperor and flourished through the Roman empire. It was one of the few towns in this part of Asia Minor which remained prosperous under the Turkish rule. The most famous relic of antiquity is the "Niobe of Sipylus" (_Suratlu Tash_) on the lowest slopes of the mountain about 4 m. east of the town. This is a colossal seated image cut in a niche of the rock, of "Hittite" origin, and perhaps that called by Pausanias the "very ancient statue of the Mother of the Gods," carved by Broteas, son of Tantalus, and sung by Homer. Near it lie many remains of a primitive city, and about half a mile east is the rock-seat conjecturally identified with Pausanias' "Throne of Pelops." There are also hot springs and a sacred grotto of Apollo. The whole site seems to be that of the early "Tantalus" city. (D. G. H.)
MAGNESITE, a mineral consisting of magnesium carbonate, MgCO3, and belonging to the calcite group of rhombohedral carbonates. It is rarely found in crystals or crystalline masses, being usually compact or earthy and intermixed with more or less hydrous magnesium silicate (meerschaum). The compact material has the appearance of unglazed porcelain, and the earthy that of chalk. In colour it is usually dead white, sometimes yellowish. The hardness of the crystallized mineral is 4; sp. gr. 3.1. The name magnesite as originally applied by J. C. Delamétherie in 1797 included several minerals containing magnesium, and at the present day it is used by French writers for meerschaum. The mineral has also been called baudisserite from the locality Baudissero near Ivrea in Piedmont. Breunnerite is a ferriferous variety.
Magnesite is a product of alteration of magnesium silicates, and occurs as veins and patches in serpentine, talc-schist or dolomite-rock. It is extensively mined in the island of Euboea in the Grecian Archipelago, near Salem in Madras, and in California, U.S.A. It is principally used for the manufacture of highly refractory fire-bricks for lining steel furnaces and electric furnaces; also for making plaster, tiles and artificial stone; for the preparation of magnesium salts (Epsom salts, &c.); for whitening; paper-pulp and wool; and as a paint.
MAGNESIUM [symbol Mg, atomic weight 24.32 (O = 16)], a metallic chemical element. The sulphate or "Epsom salts" (q.v.) was isolated in 1695 by N. Grew, while in 1707 M. B. Valentin prepared _magnesia alba_ from the mother liquors obtained in the manufacture of nitre. Magnesia was confounded with lime until 1755, when J. Black showed that the two substances were entirely different; and in 1808 Davy pointed out that it was the oxide of a metal, which, however, he was not able to isolate. Magnesium is found widely distributed in nature, chiefly in the forms of silicate, carbonate and chloride, and occurring in the minerals olivine, hornblende, talc, asbestos, meerschaum, augite, dolomite, magnesite, carnallite, kieserite and kainite. The metal was prepared (in a state approximating to purity) by A. A. B. Bussy (_Jour. de pharm._ 1829, 15, p. 30; 1830, 16, p. 142), who fused the anhydrous chloride with potassium; H. Sainte Claire Deville's process, which used to be employed commercially, was essentially the same, except that sodium was substituted for potassium (_Comptes rendus_, 1857, 44, p. 394), the product being further purified by redistillation. It may also be prepared by heating a mixture of carbon, oxide of iron and magnesite to bright redness; and by heating a mixture of magnesium ferrocyanide and sodium carbonate, the double cyanide formed being then decomposed by heating it with metallic zinc. Electrolytic methods have entirely superseded the older methods. The problem of magnesium reduction is in many respects similar to that of aluminium extraction, but the lightness of the metal as compared, bulk for bulk, with its fused salts, and the readiness with which it burns when exposed to air at high temperatures, render the problem somewhat more difficult.
Moissan found that the oxide resisted reduction by carbon in the electric furnace, so that electrolysis of a fusible salt of the metal must be resorted to. Bunsen, in 1852, electrolysed fused magnesium chloride in a porcelain crucible. In later processes, carnallite (a natural double chloride of magnesium and potassium) has commonly, after careful dehydration, been substituted for the single chloride. Graetzel's process, which was at one time employed, consisted in electrolysing the chloride in a metal crucible heated externally, the crucible itself forming the cathode, and the magnesium being deposited upon its inner surface. W. Borchers also used an externally heated metal vessel as the cathode; it is provided with a supporting collar or flange a little below the top, so that the upper part of the vessel is exposed to the cooling influence of the air, in order that a crust of solidified salt may there be formed, and so prevent the creeping of the electrolyte over the top. The carbon anode passes through the cover of a porcelain cylinder, open at the bottom, and provided with a side-tube at the top to remove the chlorine formed during electrolysis. The operation is conducted at a dull red heat (about 760° C. or 1400° F.), the current density being about 0.64 amperes per sq. in. of cathode surface, and the pressure about 7 volts. The fusing-point of the metal is about 730° C. (1350° F.), and the magnesium is therefore reduced in the form of melted globules which gradually accumulate. At intervals the current is interrupted, the cover removed, and the temperature of the vessel raised considerably above the melting-point of magnesium. The metal is then removed from the walls with the aid of an iron scraper, and the whole mass poured into a sheet-iron tray, where it solidifies. The solidified chloride is then broken up, the shots and fused masses of magnesium are picked out, run together in a plumbago crucible without flux, and poured into a suitable mould. Smaller pieces are thrown into a bath of melted carnallite and pressed together with an iron rod, the bath being then heated until the globules of metal float to the top, when they may be removed in perforated iron ladles, through the holes in which the fused chloride can drain away, but through which the melted magnesium cannot pass by reason of its high surface tension. The globules are then re-melted. F. Oettel (_Zeit. f. Elektrochem._, 1895, 2, p. 394) recommends the electrolytic preparation from carnallite; the mineral should be freed from water and sulphates.
Magnesium is a silvery white metal possessing a high lustre. It is malleable and ductile. Sp. gr. 1.75. It preserves its lustre in dry air, but in moist air it becomes tarnished by the formation of a film of oxide. It melts at 632.7° C. (C. T. Heycock and F. H. Neville), and boils at about 1100°C. Magnesium and its salts are diamagnetic. It burns brilliantly when heated in air or oxygen, or even in carbon dioxide, emitting a brilliant white light and leaving a residue of magnesia, MgO. The light is rich in the violet and ultra-violet rays, and consequently is employed in photography. The metal is also used in pyrotechny. It also burns when heated in a current of steam, which it decomposes with the liberation of hydrogen and the formation of magnesia. At high temperatures it acts as a reducing agent, reducing silica to silicon, boric acid to boron, &c. (H. Moissan, _Comptes rendus_, 1892, 114, p. 392). It combines directly with nitrogen, when heated in the gas, to form the nitride Mg3N2 (see ARGON). It is rapidly dissolved by dilute acids, with the evolution of hydrogen and the formation of magnesium salts. It precipitates many metals from solutions of their salts.
_Magnesium Oxide_, magnesia, MgO, occurs native as the mineral periclase, and is formed when magnesium burns in air; it may also be prepared by the gentle ignition of the hydroxide or carbonate. It is a non-volatile and almost infusible white powder, which slowly absorbs moisture and carbon dioxide from air, and is readily soluble in dilute acids. On account of its refractory nature, it is employed in the manufacture of crucibles, furnace linings, &c. It is also used in making hydraulic cements. A crystalline form was obtained by M. Houdard (_Abst. J. C. S._, 1907, ii. p. 621) by fusing the oxide and sulphide in the electric furnace. _Magnesium hydroxide_ Mg(OH)2, occurs native as the minerals brucite and némalite, and is prepared by precipitating solutions of magnesium salts by means of caustic soda or potash. An artificial brucite was prepared by A. de Schulten (_Comptes rendus_, 1885, 101, p. 72) by boiling magnesium chloride with caustic potash and allowing the solution to cool. Magnesium hydroxide is a white amorphous solid which is only slightly soluble in water; the solubility is, however, greatly increased by ammonium salts. It possesses an alkaline reaction and absorbs carbon dioxide. It is employed in the manufacture of cements.
When magnesium is heated in fluorine or chlorine or in the vapour of bromine or iodine there is a violent reaction, and the corresponding halide compounds are formed. With the exception of the fluoride, these substances are readily soluble in water and are deliquescent. The fluoride is found native as sellaïte, and the bromide and iodide occur in sea water and in many mineral springs. The most important of the halide salts is the _chloride_ which, in the hydrated form, has the formula MgCl2·6H2O. It may be prepared by dissolving the metal, its oxide, hydroxide, or carbonate in dilute hydrochloric acid, or by mixing concentrated solutions of magnesium sulphate and common salt, and cooling the mixture rapidly, when the less soluble sodium sulphate separates first. It is also formed as a by-product in the manufacture of potassium chloride from carnallite. The hydrated salt loses water on heating, and partially decomposes into hydrochloric acid and magnesium oxychlorides. To obtain the anhydrous salt, the double magnesium ammonium chloride, MgCl2·NH4Cl·6H2O, is prepared by adding ammonium chloride to a solution of magnesium chloride. The solution is evaporated, and the residue strongly heated, when water and ammonium chloride are expelled, and anhydrous magnesium chloride remains. Magnesium chloride readily forms double salts with the alkaline chlorides. A strong solution of the chloride made into a thick paste with calcined magnesia sets in a few hours to a hard, stone-like mass, which contains an oxychloride of varying composition. Magnesium oxychloride when heated to redness in a current of air evolves a mixture of hydrochloric acid and chlorine and leaves a residue of magnesia, a reaction which is employed in the Weldon-Pechiney and Mond processes for the manufacture of chlorine.
_Magnesium Carbonate,_ MgCO3.--The normal salt is found native as the mineral magnesite, and in combination with calcium carbonate as dolomite, whilst hydromagnesite is a basic carbonate. It is not possible to prepare the normal carbonate by precipitating magnesium salts with sodium carbonate. C. Marignac has prepared it by the action of calcium carbonate on magnesium chloride. A salt MgCO3·3H2O or Mg(CO3H)(OH)·2H2O may be prepared from the carbonate by dissolving it in water charged with carbon dioxide, and then reducing the pressure (W. A. Davis, _Jour. Soc. Chem. Ind._ 1906, 25, p. 788). The carbonate is not easily soluble in dilute acids, but is readily soluble in water containing carbon dioxide. _Magnesia alba_, a white bulky precipitate obtained by adding sodium carbonate to Epsom salts, is a mixture of Mg(CO3H)(OH)·2H2O, Mg(CO3H)(OH) and Mg(OH)2. It is almost insoluble in water, but readily dissolves in ammonium salts.
_Magnesium Phosphates._--By adding sodium phosphate to magnesium sulphate and allowing the mixture to stand, hexagonal needles of MgHPO4·7H2O are deposited. The _normal phosphate_, Mg3P2O8, is found in some guanos, and as the mineral wagnerite. It may be prepared by adding normal sodium phosphate to a magnesium salt and boiling the precipitate with a solution of magnesium sulphate. It is a white amorphous powder, readily soluble in acids. _Magnesium ammonium phosphate_, MgNH4PO4·6H2O, is found as the mineral struvite and in some guanos; it occurs also in urinary calculi and is formed in the putrefaction of urine. It is prepared by adding sodium phosphate to magnesium sulphate in the presence of ammonia and ammonium chloride. When heated to 100° C., it loses five molecules of water of crystallization, and at a higher temperature loses the remainder of the water and also ammonia, leaving a residue of magnesium pyrophosphate, Mg2P2O7. _Magnesium Nitrate_, Mg(NO3)2·6H2O, is a colourless, deliquescent, crystalline solid obtained by dissolving magnesium or its carbonate in nitric acid, and concentrating the solution. The crystals melt at 90° C. _Magnesium Nitride_, Mg3N2, is obtained as a greenish-yellow amorphous mass by passing a current of nitrogen or ammonia over heated magnesium (F. Briegleb and A. Geuther, _Ann._, 1862, 123, p. 228; see also W. Eidmann and L. Moeser, _Ber._, 1901, 34, p. 390). When heated in dry oxygen it becomes incandescent, forming magnesia. Water decomposes it with liberation of ammonia and formation of magnesium hydroxide. The chlorides of nickel, cobalt, chromium, iron and mercury are converted into nitrides when heated with it, whilst the chlorides of copper and platinum are reduced to the metals (A. Smits, _Rec. Pays Bas_, 1896, 15, p. 135). _Magnesium sulphide_, MgS, may be obtained, mixed with some unaltered metal and some magnesia, as a hard brown mass by heating magnesia, in sulphur vapour. It slowly decomposes in moist air. _Magnesium sulphate_, MgSO4, occurs (with IH2O) as Kieserite. A hexahydrate is also known. The salt may be obtained from Kieserite: formerly it was prepared by treating magnesite or dolomite with sulphuric acid.
Grignard Reagent.
_Organic Compounds._--By heating magnesium filings with methyl and ethyl iodides A. Cahours (_Ann. chim. phys._, 1860, 58, pp. 5, 19) obtained magnesium methyl, Mg(CH3)2, and magnesium ethyl, Mg(C2H5)2, as colourless, strongly smelling, mobile liquids, which are spontaneously inflammable and are readily decomposed by water. The compounds formed by the action of magnesium on alkyl iodides in the cold have been largely used in synthetic organic chemistry since V. Grignard (_Comptes rendus_, 1900 et seq.) observed that magnesium and alkyl or aryl halides combined together in presence of anhydrous ether at ordinary temperatures (with the appearance of brisk boiling) to form compounds of the type RMgX(R = an alkyl or aryl group and X = halogen). These compounds are insoluble in ether, are non-inflammable and exceedingly reactive. A. V. Baeyer (_Ber._, 1902, 35, p. 1201) regards them as oxonium salts containing tetravalent oxygen (C2H5)2:O:(MgR) (X), whilst W. Tschelinzeff (_Ber._, 1906, 39, p. 773) considers that they contain two molecules of ether. In preparing the Grignard reagent the commencement of the reaction is accelerated by a trace of iodine. W. Tschelinzeff (_Ber._, 1904, 37, p. 4534) showed that the ether may be replaced by benzene containing a small quantity of ether or anisole, or a few drops of a tertiary amine. With unsaturated alkyl halides the products are only slightly soluble in ether, and two molecules of the alkyl compound are brought into the reaction. They are very unstable, and do not react in the normal manner. (V. Grignard and L. Tissier, _Comptes rendus_, 1901, 132, p. 558).
The products formed by the action of the Grignard reagent with the various types of organic compounds are usually thrown out of solution in the form of crystalline precipitates or as thick oils, and are then decomposed by ice-cold dilute sulphuric or acetic acids, the magnesium being removed as a basic halide salt.
_Applications._--For the formation of primary and secondary alcohols see ALDEHYDES and KETONES. Formaldehyde behaves abnormally with magnesium benzyl bromide (M. Tiffeneau, _Comptes rendus_, 1903, 137, p. 573). forming ortho-tolylcarbinol, CH3·C6H4·CH2OH, and not benzylcarbinol, C6H5CH2·CH2OH (cf. the reaction of formaldehyde on phenols: O. Manasse, _Ber._ 1894, 27, p. 2904). Acid esters yield carbinols, many of which are unstable and readily pass over into unsaturated compounds, especially when warmed with acetic anhydride: R·CO2R´(R´´)2·R·:C·OMgX -> (R´´)2R·:C·OH.
Formic ester yields a secondary alcohol under similar conditions. Acid chlorides behave in an analogous manner to esters (Grignard and Tissier, _Comptes rendus_, 1901, 132, p. 683). Nitriles yield ketones (the nitrogen being eliminated as ammonia), the best yields being given by the aromatic nitriles (E. Blaise, ibid., 1901, 133, p. 1217): R·CN -> RR´:C:NMgI -> R·CO·R´. Acid amides also react to form ketones (C. Béis, ibid., 1903, 137, 575):
R·CONH2 -> RR´:C(OMgX)·NHMgX + R´H -> R·CO·R´;
the yield increases with the complexity of the organic residue of the acid amide. On passing a current of dry carbon dioxide over the reagent, the gas is absorbed and the resulting compound, when decomposed by dilute acids, yields an organic acid, and similarly with carbon oxysulphide a thio-acid is obtained:
RMgX -> R·CO2MgX -> R·CO2H; COS -> CS(OMgX)·R -> R·CSOH.
A. Klages (_Ber._, 1902, 35, pp. 2633 et seq.) has shown that if one uses an excess of magnesium and of an alkyl halide with a ketone, an ethylene derivative is formed. The reaction appears to be perfectly general unless the ketone contains two ortho-substituent groups. Organo-metallic compounds can also be prepared, for example
SnBr4 + 4MgBrC6H5 = 4MgBr2 + Sn(C6H5)4.
For a summary see A. McKenzie, _B. A. Rep._ 1907.
_Detection._--The magnesium salts may be detected by the white precipitate formed by adding sodium phosphate (in the presence of ammonia and ammonium chloride) to their solutions. The same reaction is made use of in the quantitative determination of magnesium, the white precipitate of magnesium ammonium phosphate being converted by ignition into magnesium pyrophosphate and weighed as such. The atomic weight of magnesium has been determined by many observers. J. Berzelius (_Ann. chim. phys._, 1820, 14, p. 375), by converting the oxide into the sulphate, obtained the value 12.62 for the equivalent. R. F. Marchand and T. Scheerer (_Jour. prakt. Chem._, 1850, 50, p. 358), by ignition of the carbonate, obtained the value 24.00 for the atomic weight, whilst C. Marignac, by converting the oxide into the sulphate, obtained the value 24.37. T. W. Richards and H. G. Parker (_Zeit. anorg. Chem._, 1897, 13, p. 81) have obtained the value 24.365 (O = 16).
_Medicine._--These salts of magnesium may be regarded as the typical _saline purgatives_. Their aperient action is dependent upon the minimum of irritation of the bowel, and is exercised by their abstraction from the blood of water, which passes into the bowel to act as a diluent of the salt. The stronger the solution administered, the greater is the quantity of water that passes into the bowel, a fact to be borne in mind when the salt is administered for the purpose of draining superfluous fluid from the system, as in dropsy. The oxide and carbonate of magnesium are also invaluable as antidotes, since they form insoluble compounds with oxalic acid and salts of mercury, arsenic, and copper. The result is to prevent the local corrosive action of the poison and to prevent absorption of the metals. As alkaloids are insoluble in alkaline solutions, the oxide and carbonate--especially the former--may be given in alkaloidal poisoning. The compounds of magnesium are not absorbed into the blood in any appreciable quantity, and therefore exert no remote actions upon other functions. This is fortunate, as the result of injecting a solution of a magnesium salt into a vein is rapid poisoning. Hence it is of the utmost importance to avoid the use of salts of this metal whenever it is necessary--as in diabetic coma--to increase the alkalinity of the blood rapidly. The usual doses of the oxide and carbonate of magnesium are from half a drachm to a drachm.
MAGNETISM. The present article is a digest, mainly from an experimental standpoint, of the leading facts and principles of magnetic science. It is divided into the following sections:
1. General Phenomena.
2. Terminology and Elementary Principles.
3. Magnetic Measurements.
4. Magnetization in Strong Fields.
5. Magnetization in Weak Fields.
6. Changes of Dimensions attending Magnetization.
7. Effects of Mechanical Stress on Magnetization.
8. Effects of Temperature on Magnetism.
9. Magnetic Properties of Alloys and Compounds of Iron.
10. Miscellaneous Effects of Magnetization:--Electric Conductivity--Hall Effect--Electro-Thermal Relations--Thermo-electric Quality--Elasticity--Chemical and Voltaic Effects.
11. Feebly Susceptible Substances.
12. Molecular Theory of Magnetism.
13. Historical and Chronological Notes.
Of these thirteen sections, the first contains a simple description of the more prominent phenomena, without mathematical symbols or numerical data. The second includes definitions of technical terms in common use, together with so much of the elementary theory as is necessary for understanding the experimental work described in subsequent portions of the article; a number of formulae and results are given for purposes of reference, but the mathematical reasoning by which they are obtained is not generally detailed, authorities being cited whenever the demonstrations are not likely to be found in ordinary textbooks. The subjects discussed in the remaining sections are sufficiently indicated by their respective headings. (See also ELECTROMAGNETISM, TERRESTRIAL MAGNETISM, MAGNETO-OPTICS and UNITS.)
1. GENERAL PHENOMENA
Pieces of a certain highly esteemed iron ore, which consists mainly of the oxide Fe3O4, are sometimes found to possess the power of attracting small fragments of iron or steel. Ore endowed with this curious property was well known to the ancient Greeks and Romans, who, because it occurred plentifully in the district of Magnesia near the Aegean coast, gave it the name of _magnes_, or the _Magnesian stone_. In English-speaking countries the ore is commonly known as _magnetite_, and pieces which exhibit attraction as _magnets_; the cause to which the attractive property is attributed is called _magnetism_, a name also applied to the important branch of science which has been evolved from the study of phenomena associated with the magnet.
If a magnet is dipped into a mass of iron filings and withdrawn, filings cling to certain parts of the stone in moss-like tufts, other parts remaining bare. There are generally two regions where the tufts are thickest, and the attraction therefore greatest, and between them is a zone in which no attraction is evidenced. The regions of greatest attraction have received the name of _poles_, and the line joining them is called the _axis_ of the magnet; the space around a magnet in which magnetic effects are exhibited is called the _field of magnetic force_, or the _magnetic field_.
Up to the end of the 15th century only two magnetic phenomena of importance, besides that of attraction, had been observed. Upon one of these is based the principle of the mariner's compass, which is said to have been known to the Chinese as early as 1100 B.C., though it was not introduced into Europe until more than 2000 years later; a magnet supported so that its axis is free to turn in a horizontal plane will come to rest with its poles pointing approximately north and south. The other phenomenon is mentioned by Greek and Roman writers of the 1st century: a piece of iron, when brought into contact with a magnet, or even held near one, itself becomes "inductively" magnetized, and acquires the power of lifting iron. If the iron is soft and fairly pure, it loses its attractive property when removed from the neighbourhood of the magnet; if it is hard, some of the induced magnetism is permanently retained, and the piece becomes an artificial magnet. Steel is much more retentive of magnetism than any ordinary iron, and some form of steel is now always used for making artificial magnets. Magnetism may be imparted to a bar of hardened steel by stroking it several times from end to end, always in the same direction, with one of the poles of a magnet. Until 1820 all the artificial magnets in practical use derived their virtue, directly or indirectly, from the natural magnets found in the earth: it is now recognized that the source of all magnetism, not excepting that of the magnetic ore itself, is electricity, and it is usual to have direct recourse to electricity for producing magnetization, without the intermediary of the magnetic ore. A wire carrying an electric current is surrounded by a magnetic field, and if the wire is bent into the form of an elongated coil or spiral, a field having certain very useful qualities is generated in the interior. A bar of soft iron introduced into the coil is at once magnetized, the magnetism, however, disappearing almost completely as soon as the current ceases to flow. Such a combination constitutes an _electromagnet_, a valuable device by means of which a magnet can be instantly made and unmade at will. With suitable arrangements of iron and coil and a sufficiently strong current, the intensity of the temporary magnetization may be very high, and electromagnets capable of lifting weights of several tons are in daily use in engineering works (see ELECTROMAGNETISM). If the bar inserted into the coil is of hardened steel instead of iron, the magnetism will be less intense, but a larger proportion of it will be retained after the current has been cut off. Steel magnets of great strength and of any convenient form may be prepared either in this manner or by treatment with an electromagnet; hence the natural magnet, or _lodestone_ as it is commonly called, is no longer of any interest except as a scientific curiosity.
Some of the principal phenomena of magnetism may be demonstrated with very little apparatus; much may be done with a small bar-magnet, a pocket compass and a few ounces of iron filings. Steel articles, such as knitting or sewing needles and pieces of flat spring, may be readily magnetized by stroking them with the bar-magnet; after having produced magnetism in any number of other bodies, the magnet will have lost nothing of its own virtue. The compass needle is a little steel magnet balanced upon a pivot; one end of the needle, which always bears a distinguishing mark, points approximately, but not in general exactly, to the north,[1] the vertical plane through the direction of the needle being termed the _magnetic meridian_. The bar-magnet, if suspended horizontally in a paper stirrup by a thread of unspun silk, will also come to rest in the magnetic meridian with its marked end pointing northwards. The north-seeking end of a magnet is in English-speaking countries called the _north pole_ and the other end the _south pole_; in France the names are interchanged. If one pole of the bar-magnet is brought near the compass, it will attract the opposite pole of the compass-needle; and the magnetic action will not be sensibly affected by the interposition between the bar and the compass of any substance whatever except iron or other magnetizable metal. The poles of a piece of magnetized steel may be at once distinguished if the two ends are successively presented to the compass; that end which attracts the south pole of the compass needle (and is therefore north) may be marked for easy identification.
Similar magnetic poles are not merely indifferent to each other, but exhibit actual repulsion. This can be more easily shown if the compass is replaced by a magnetized knitting needle, supported horizontally by a thread. The north pole of the bar-magnet will repel the north pole of the suspended needle, and there will likewise be repulsion between the two south poles. Such experiments as these demonstrate the fundamental law that _like poles repel each other_; _unlike poles attract_. It follows that between two neighbouring magnets, the poles of which are regarded as centres of force, there must always be four forces in action. Denoting the two pairs of magnetic poles by N, S and N´, S´, there is attraction between N and S´, and between S and N´; repulsion between N and N´, and between S and S´. Hence it is not very easy to determine experimentally the law of magnetic force between poles. The difficulty was overcome by C. A. Coulomb, who by using very long and thin magnets, so arranged that the action of their distant poles was negligible, succeeded in establishing the law, which has since been confirmed by more accurate methods, that _the force of attraction or repulsion exerted between two magnetic poles varies inversely as the square of the distance between them_. Since the poles of different magnets differ in strength, it is important to agree upon a definite unit or standard of reference in terms of which the strength of a pole may be numerically specified. According to the recognized convention, the unit pole is that which acts upon an equal pole at unit distance with unit force: a north pole is reckoned as positive (+) and a south pole as negative (-). Other conditions remaining unchanged, the force between two poles is proportional to the product of their strengths; it is repulsive or attractive according as the signs of the poles are like or unlike.
If a wire of soft iron is substituted for the suspended magnetic needle, either pole of the bar-magnet will attract either end of the wire indifferently. The wire will in fact become temporarily magnetized by induction, that end of it which is nearest to the pole of the magnet acquiring opposite polarity, and behaving as if it were the pole of a permanent magnet. Even a permanent magnet is susceptible of induction, its polarity becoming thereby strengthened, weakened, or possibly reversed. If one pole of a strong magnet is presented to the like pole of a weaker one, there will be repulsion so long as the two are separated by a certain minimum distance. At shorter distances the magnetism induced in the weaker magnet will be stronger than its permanent magnetism, and there will be attraction; two magnets with their like poles in actual contact will always cling together unless the like poles are of exactly equal strength. Induction is an effect of the field of force associated with a magnet. Magnetic force has not merely the property of acting upon magnetic poles, it has the additional property of producing a phenomenon known as _magnetic induction_, or _magnetic flux_, a physical condition which is of the nature of a flow continuously circulating through the magnet and the space outside it. Inside the magnet the course of the flow is from the south pole to the north pole; thence it diverges through the surrounding space, and again converging, re-enters the magnet at the south pole. When the magnetic induction flows through a piece of iron or other magnetizable substance placed near the magnet, a south pole is developed where the flux enters and a north pole where it leaves the substance. Outside the magnet the direction of the magnetic induction is generally the same as that of the magnetic force. A map indicating the direction of the force in different parts of the field due to a magnet may be constructed in a very simple manner. A sheet of cardboard is placed above the magnet, and some iron filings are sifted thinly and evenly over the surface: if the cardboard is gently tapped, the filings will arrange themselves in a series of curves, as shown in fig. 1. This experiment suggested to Faraday the conception of "lines of force," of which the curves formed by the filings afford a rough indication; Faraday's lines are however not confined to the plane of the cardboard, but occur in the whole of the space around the magnet. A _line of force_ may be defined as an imaginary line so drawn that its direction at every point of its course coincides with the direction of the magnetic force at that point. Through any point in the field one such line can be drawn, but not more than one, for the force obviously cannot have more than one direction; the lines therefore never intersect. A line of force is regarded as proceeding from the north pole towards the south pole of the magnet, its direction being that in which an isolated north pole would be urged along it. A south pole would be urged oppositely to the conventional "direction" of the line; hence it follows that a very small magnetic needle, if placed in the field, would tend to set itself along or tangentially to the line of force passing through its centre, as may be approximately verified if the compass be placed among the filings on the cardboard. In the internal field of a long coil of wire carrying an electric current, the lines of force are, except near the ends, parallel to the axis of the coil, and it is chiefly for this reason that the field due to a coil is particularly well adapted for inductively magnetizing iron and steel. The older operation of magnetizing a steel bar by drawing a magnetic pole along it merely consists in exposing successive portions of the bar to the action of the strong field near the pole.
Faraday's lines not only show the direction of the magnetic force, but also serve to indicate its magnitude or strength in different parts of the field. Where the lines are crowded together, as in the neighbourhood of the poles, the force is greater (or the field is stronger) than where they are more widely separated; hence the strength of a field at any point can be accurately specified by reference to the concentration of the lines. The lines presented to the eye by the scattered filings are too vague and ill-defined to give a satisfactory indication of the field-strength (see Faraday, _Experimental Researches_, § 3237) though they show its direction clearly enough. It is however easy to demonstrate by means of the compass that the force is much greater in some parts of the field than in others. Lay the compass upon the cardboard, and observe the rate at which its needle vibrates after being displaced from its position of equilibrium; this will vary greatly in different regions. When the compass is far from the magnet, the vibrations will be comparatively slow; when it is near a pole, they will be exceedingly rapid, the frequency of the vibrations varying as the square root of the magnetic force at the spot. In a refined form this method is often employed for measuring the intensity of a magnetic field at a given place, just as the intensity of gravity at different parts of the earth is deduced from observations of the rate at which a pendulum of known length vibrates.
It is to the non-uniformity of the field surrounding a magnet that the apparent attraction between a magnet and a magnetizable body such as iron is ultimately due. This was pointed out by W. Thomson (afterwards Lord Kelvin) in 1847, as the result of a mathematical investigation undertaken to explain Faraday's experimental observations. If the inductively magnetized body lies in a part of the field which happens to be uniform there will be no resulting force tending to move the body, and it will not be "attracted." If however there is a small variation of the force in the space occupied by the body, it can be shown that the body will be urged, not necessarily towards a magnetic pole, but _towards places of stronger magnetic force_. It will not in general move along a line of force, as would an isolated pole, but will follow the direction in which the magnetic force increases most rapidly, and in so doing it may cross the lines of force obliquely or even at right angles.
If a magnetized needle were supported so that it could move freely about its centre of gravity it would not generally settle with its axis in a horizontal position, but would come to rest with its north-seeking pole either higher or lower than its centre. For the practical observation of this phenomenon it is usual to employ a needle which can turn freely in the plane of the magnetic meridian upon a horizontal axis passing through the centre of gravity of the needle. The angle which the magnetic axis makes with the plane of the horizon is called the _inclination_ or _dip._ Along an irregular line encircling the earth in the neighbourhood of the geographical equator the needle takes up a horizontal position, and the dip is zero. At places north of this line, which is called the _magnetic equator_, the north end of the needle points downwards, the inclination generally becoming greater with increased distance from the equator. Within a certain small area in the Arctic Circle (about 97° W. long., 70° N. lat.) the north pole of the needle points vertically downwards, the dip being 90°. South of the magnetic equator the south end of the needle is always inclined downwards, and there is a spot within the Antarctic Circle (148° E. long., 74° S. lat.) where the needle again stands vertically, but with its north end directed upwards. All these observations may be accounted for by the fact first recognized by W. Gilbert in 1600, that the earth itself is a great magnet, having its poles at the two places where the dipping needle is vertical. To be consistent with the terminology adopted in Britain, it is necessary to regard the pole which is geographically north as being the south pole of the terrestrial magnet, and that which is geographically south as the north pole; in practice however the names assigned to the terrestrial magnetic poles correspond with their geographical situations. Within a limited space, such as that contained in a room, the field due to the earth's magnetism is sensibly uniform, the lines of force being parallel straight lines inclined to the horizon at the angle of dip, which at Greenwich in 1910 was about 67°. It is by the horizontal component of the earth's total force that the compass-needle is directed.
The magnets hitherto considered have been assumed to have each two poles, the one north and the other south. It is possible that there may be more than two. If, for example, a knitting needle is stroked with the south pole of a magnet, the strokes being directed from the middle of the needle towards the two extremities alternately, the needle will acquire a north pole at each end and a south pole in the middle. By suitably modifying the manipulation a further number of _consequent poles_, as they are called, may be developed. It is also possible that a magnet may have no poles at all. Let a magnetic pole be drawn several times around a uniform steel ring, so that every part of the ring may be successively subjected to the magnetic force. If the operation has been skilfully performed the ring will have no poles and will not attract iron filings. Yet it will be magnetized; for if it is cut through and the cut ends are drawn apart, each end will be found to exhibit polarity. Again, a steel wire through which an electric current has been passed will be magnetized, but so long as it is free from stress it will give no evidence of magnetization; if, however, the wire is twisted, poles will be developed at the two ends, for reasons which will be explained later. A wire or rod in this condition is said to be _circularly magnetized_; it may be regarded as consisting of an indefinite number of elementary ring-magnets, having their axes coincident with the axis of the wire and their planes at right angles to it. But no magnet can have a single pole; if there is one, there must also be at least a second, of the opposite sign and of exactly equal strength. Let a magnetized knitting needle, having north and south poles at the two ends respectively, be broken in the middle; each half will be found to possess a north and a south pole, the appropriate supplementary poles appearing at the broken ends. One of the fragments may again be broken, and again two bipolar magnets will be produced; and the operation may be repeated, at least in imagination, till we arrive at molecular magnitudes and can go no farther. This experiment proves that the condition of magnetization is not confined to those parts where polar phenomena are exhibited, but exists throughout the whole body of the magnet; it also suggests the idea of _molecular magnetism_, upon which the accepted theory of magnetization is based. According to this theory the molecules of any magnetizable substance are little permanent magnets the axes of which are, under ordinary conditions, disposed in all possible directions indifferently. The process of magnetization consists in turning round the molecules by the application of magnetic force, so that their north poles may all point more or less approximately in the direction of the force; thus the body as a whole becomes a magnet which is merely the resultant of an immense number of molecular magnets.
In every magnet the strength of the south pole is exactly equal to that of the north pole, the action of the same magnetic force upon the two poles being equal and oppositely directed. This may be shown by means of the uniform field of force due to the earth's magnetism. A magnet attached to a cork and floated upon water will set itself with its axis in the magnetic meridian, but it will be drawn neither northward nor southward; the forces acting upon the two poles have therefore no horizontal resultant. And again if a piece of steel is weighed in a delicate balance before and after magnetization, no change whatever in its weight can be detected; there is consequently no upward or downward resultant force due to magnetization; the contrary parallel forces acting upon the poles of the magnet are equal, constituting a couple, which may tend to turn the body, but not to propel it.
Iron and its alloys, including the various kinds of steel, though exhibiting magnetic phenomena in a pre-eminent degree, are not the only substances capable of magnetization. Nickel and cobalt are also strongly magnetic, and in 1903 the interesting discovery was made by F. Heusler that an alloy consisting of copper, aluminium and manganese (Heusler's alloy), possesses magnetic qualities comparable with those of iron. Practically the metals iron, nickel and cobalt, and some of their alloys and compounds constitute a class by themselves and are called _ferromagnetic_ substances. But it was discovered by Faraday in 1845 that all substances, including even gases, are either attracted or repelled by a sufficiently powerful magnetic pole. Those substances which are attracted, or rather which tend, like iron, to move from weaker to stronger parts of the magnetic field, are termed _paramagnetic_; those which are repelled, or tend to move from stronger to weaker parts of the field, are termed diamagnetic. Between the ferromagnetics and the paramagnetics there is an enormous gap. The maximum magnetic susceptibility of iron is half a million times greater than that of liquid oxygen, one of the strongest paramagnetic substances known. Bismuth, the strongest of the diamagnetics, has a negative susceptibility which is numerically 20 times less than that of liquid oxygen.
Many of the physical properties of a metal are affected by magnetization. The dimensions of a piece of iron, for example, its elasticity, its thermo-electric power and its electric conductivity are all changed under the influence of magnetism. On the other hand, the magnetic properties of a substance are affected by such causes as mechanical stress and changes of temperature. An account of some of these effects will be found in another section.[2]
2. TERMINOLOGY AND ELEMENTARY PRINCIPLES
In what follows the C.G.S. electromagnetic system of units will be generally adopted, and, unless otherwise stated, magnetic substances will be assumed to be _isotropic_, or to have the same physical properties in all directions.
_Vectors._--Physical quantities such as magnetic force, magnetic induction and magnetization, which have direction as well as magnitude, are termed vectors; they are compounded and resolved in the same manner as mechanical force, which is itself a vector. When the direction of any vector quantity denoted by a symbol is to be attended to, it is usual to employ for the symbol either a block letter, as H, I, B, or a German capital, as [H], [F], [B].[3]
_Magnetic Poles and Magnetic Axis._--A _unit magnetic pole_ is that which acts on an equal pole at a distance of one centimetre with a force of one dyne. A pole which points north is reckoned positive, one which points south negative. The action between any two magnetic poles is mutual. If m1 and m2 are the strengths of two poles, d the distance between them expressed in centimetres, and f the force in dynes,
[f] = m1m2/d² (1).
The force is one of attraction or repulsion, according as the sign of the product m1m2 is negative or positive. The poles at the ends of an infinitely thin uniform magnet, or _magnetic filament_, would act as definite centres of force. An actual magnet may generally be regarded as a bundle of magnetic filaments, and those portions of the surface of the magnet where the filaments terminate, and so-called "free magnetism" appears, may be conveniently called poles or polar regions. A more precise definition is the following: When the magnet is placed in a uniform field, the parallel forces acting on the positive poles of the constituent filaments, whether the filaments terminate outside the magnet or inside, have a resultant, equal to the sum of the forces and parallel to their direction, acting at a certain point N. The point N, which is the centre of the parallel forces, is called the _north_ or _positive pole_ of the magnet. Similarly, the forces acting in the opposite direction on the negative poles of the filaments have a resultant at another point S, which is called the _south_ or _negative pole_. The opposite and parallel forces acting on the poles are always equal, a fact which is sometimes expressed by the statement that the total magnetism of a magnet is zero. The line joining the two poles is called the _axis of the magnet_.
_Magnetic Field._--Any space at every point of which there is a finite magnetic force is called a _field of magnetic force_, or a _magnetic field_. The _strength_ or _intensity_ of a magnetic field at any point is measured by the force in dynes which a unit pole will experience when placed at that point, the _direction_ of the field being the direction in which a positive pole is urged. The field-strength at any point is also called the _magnetic force_ at that point; it is denoted by H, or, when it is desired to draw attention to the fact that it is a vector quantity, by the block letter H, or the German character [H]. Magnetic force is sometimes, and perhaps more suitably, termed _magnetic intensity_; it corresponds to the intensity of gravity g in the theory of heavy bodies (see Maxwell, _Electricity and Magnetism_, § 12 and § 68, footnote). A _line of force_ is a line drawn through a magnetic field in the direction of the force at each point through which it passes. A _uniform magnetic field_ is one in which H has everywhere the same value and the same direction, the lines of force being, therefore, straight and parallel. A magnetic field is generally due either to a conductor carrying an electric current or to the poles of a magnet. The magnetic field due to a long straight wire in which a current of electricity is flowing is at every point at right angles to the plane passing through it and through the wire; its strength at any point distant r centimetres from the wire is
H = 2i/r, (2)
i being the current in C.G.S. units.[4] The lines of force are evidently circles concentric with the wire and at right angles to it; their direction is related to that of the current in the same manner as the rotation of a corkscrew is related to its thrust. The field at the centre of a circular conductor of radius r through which current is passing is
H = 2[pi]i/r, (3)
the direction of the force being along the axis and related to the direction of the current as the thrust of a corkscrew to its rotation. The field strength in the interior of a long uniformly wound coil containing n turns of wire and having a length of l centimetres is (except near the ends)
H = 4[pi]in/l. (4)
In the middle portion of the coil the strength of the field is very nearly uniform, but towards the end it diminishes, and at the ends is reduced to one-half. The direction of the force is parallel to the axis of the coil, and related to the direction of the current as the thrust of a corkscrew to its rotation. If the coil has the form of a ring of mean radius r, the length will be 2[pi]r, and the field inside the coil may be expressed as
H = 2ni/r. (5)
The uniformity of the field is not in this case disturbed by the influence of ends, but its strength at any point varies inversely as the distance from the axis of the ring. When therefore sensible uniformity is desired, the radius of the ring should be large in relation to that of the convolutions, or the ring should have the form of a short cylinder with thin walls. The strongest magnetic fields employed for experimental purposes are obtained by the use of electromagnets. For many experiments the field due to the earth's magnetism is sufficient; this is practically quite uniform throughout considerable spaces, but its total intensity is less than half a unit.
_Magnetic Moment and Magnetization._--The moment, M, M or [M], of a uniformly and longitudinally magnetized bar-magnet is the product of its length into the strength of one of its poles; it is the moment of the couple acting on the magnet when placed in a field of unit intensity with its axis perpendicular to the direction of the field. If l is the length of the magnet, M = ml. The action of a magnet at a distance which is great compared with the length of the magnet depends solely upon its moment; so also does the action which the magnet experiences when placed in a uniform field. The moment of a small magnet may be resolved like a force. The _intensity of magnetization_, or, more shortly, the _magnetization_ of a uniformly magnetized body is defined as the magnetic moment per unit of volume, and is denoted by I, I, or [I]. Hence
I = M/v = ml/v = m/a,
v being the volume and a the sectional area. If the magnet is not uniform, the magnetization at any point is the ratio of the moment of an element of volume at that point to the volume itself, or I = m·ds/dv. where ds is the length of the element. The direction of the magnetization is that of the magnetic axis of the element; in isotropic substances it coincides with the direction of the magnetic force at the point. If the direction of the magnetization at the surface of a magnet makes an angle [epsilon] with the normal, the normal component of the magnetization, I cos [epsilon], is called the _surface density_ of the magnetism, and is generally denoted by [sigma].
_Potential and Magnetic Force._--The _magnetic potential_ at any point in a magnetic field is the work which would be done against the magnetic forces in bringing a unit pole to that point from the boundary of the field. The line through the given point along which the potential decreases most rapidly is the direction of the resultant magnetic force, and the rate of decrease of the potential in any direction is equal to the component of the force in that direction. If V denote the potential, F the resultant force, X, Y, Z, its components parallel to the co-ordinate axes and n the line along which the force is directed, then
[delta]V [delta]V [delta]V/ [delta]V - -------- = F, - -------- = X, - --------- = Y, - -------- = Z. (6) [delta]n [delta]x [delta]y [delta]z
Surfaces for which the potential is constant are called _equipotential surfaces_. The resultant magnetic force at every point of such a surface is in the direction of the normal (n) to the surface; every line of force therefore cuts the equipotential surfaces at right angles. The potential due to a single pole of strength m at the distance r from the pole is
V = m/r, (7)
the equipotential surfaces being spheres of which the pole is the centre and the lines of force radii. The potential due to a thin magnet at a point whose distance from the two poles respectively is r and r´ is
V = m(l/r = l/r´). (8)
When V is constant, this equation represents an equipotential surface.
The equipotential surfaces are two series of ovoids surrounding the two poles respectively, and separated by a plane at zero potential passing perpendicularly through the middle of the axis. If r and r´ make angles [theta] and [theta]´ with the axis, it is easily shown that the equation to a line of force is
cos [theta] - cos [theta]´ = constant. (9)
At the point where a line of force intersects the perpendicular bisector of the axis r = r´ = r0, say, and cos [theta] - cos [theta]´ obviously = l/r0, l being the distance between the poles; l/r0 is therefore the value of the constant in (9) for the line in question. Fig. 2 shows the lines of force and the plane sections of the equipotential surfaces for a thin magnet with poles concentrated at its ends. The potential due to a small magnet of moment M, at a point whose distance from the centre of the magnet is r, is
V = M cos [theta]/r², (10)
where [theta] is the angle between r and the axis of the magnet. Denoting the force at P (see fig. 3) by F, and its components parallel to the co-ordinate axes by X and Y, we have
[delta]V M X = - -------- = --- (3 cos² [theta] - 1), [delta]x r³
[delta]V M Y = - -------- = --- (3 sin [theta] cos [theta]). (11) [delta]y r³
If F_r is the force along r and F_t that along t at right angles to r,
M F_r = X cos [theta] + Y sin [theta] = --- 2 cos [theta], (12) r³
M F_t = -X sin [theta] + Y cos [theta] = --- sin [theta], (13) r³ For the resultant force at P,
M F = [root](F_r² + F_t²) = --- [root](3 cos² [theta] + 1). (14) r³
The direction of F is given by the following construction: Trisect OP at C, so that OC = OP/3; draw CD at right angles to OP, to cut the axis produced in D; then DP will be the direction of the force at P. For a point in the axis OX, [theta] = 0; therefore cos [theta] = 1, and the point D coincides with C; the magnitude of the force is, from (14),
F_x = 2M/r³, (15)
its direction being along the axis OX. For a point in the line OY bisecting the magnet perpendicularly, [theta] = [pi]/2 therefore cos [theta] = 0, and the point D is at an infinite distance. The magnitude of the force is in this case
F_y = M/r³, (16)
and its direction is parallel to the axis of the magnet. Although the above useful formulae, (10) to (15), are true only for an infinitely small magnet, they may be practically applied whenever the distance r is considerable compared with the length of the magnet.
_Couples and Forces between Magnets._--If a small magnet of moment M is placed in the sensibly uniform field H due to a distant magnet, the couple tending to turn the small magnet upon an axis at right angles to the magnet and to the force is
MH sin [theta], (17)
where [theta] is the angle between the axis of the magnet and the direction of the force. In fig. 4 S´N´ is a small magnet of moment M´, and SN a distant fixed magnet of moment M; the axes of SN and S´N´ make angles of [theta] and [phi] respectively with the line through their middle points. It can be deduced from (17), (12) and (13) that the couple on S´N´ due to SN, and tending to increase [phi], is
MM´(sin [theta] cos [phi] - 2 sin [phi] cos [theta])/r³. (18)
This vanishes if sin [theta] cos [phi] = 2 sin [phi] cos [theta], i.e. if tan [phi] = ½ tan [theta], S´N´ being then along a line of force, a result which explains the construction given above for finding the direction of the force F in (14). If the axis of SN produced passes through the centre of S´N´, [theta] = 0, and the couple becomes
2MM´ sin [phi]/r³, (19)
tending to diminish [phi]; this is called the "end on" position. If the centre of S´N´ is on the perpendicular bisector of SN, [theta] = ½[pi], and the couple will be
MM´ cos [phi]/r³, (20)
tending to increase [phi]; this is the "broadside on" position. These two positions are sometimes called the first and second (or A and B) principal positions of Gauss. The components X, Y, parallel and perpendicular to r, of the force between the two magnets SN and S´N´ are
X = 3MM´(sin [theta] sin [phi] - 2 cos [theta] cos [phi])/r^4, (21) Y = 3MM´(sin [theta] cos [phi] + sin [phi] cos [theta])/r^4. (22)
It will be seen that, whereas the couple varies inversely as the cube of the distance, the force varies inversely as the fourth power.
_Distributions of Magnetism._--A magnet may be regarded as consisting of an infinite number of elementary magnets, each having a pair of poles and a definite magnetic moment. If a series of such elements, all equally and longitudinally magnetized, were placed end to end with their unlike poles in contact, the external action of the filament thus formed would be reduced to that of the two extreme poles. The same would be the case if the magnetization of the filament varied inversely as the area of its cross-section a in different parts. Such a filament is called a _simple magnetic solenoid_, and the product aI is called the _strength_ of the solenoid. A magnet which consists entirely of such solenoids, having their ends either upon the surface or closed upon themselves, is called a _solenoidal magnet_, and the magnetism is said to be distributed solenoidally; there is no free magnetism in its interior. If the constituent solenoids are parallel and of equal strength, the magnet is also uniformly magnetized. A thin sheet of magnetic matter magnetized normally to its surface in such a manner that the magnetization at any place is inversely proportional to the thickness h of the sheet at that place is called a _magnetic shell_; the constant product hI is the _strength_ of the shell and is generally denoted by [Phi] or [phi]. The potential at any point due to a magnetic shell is the product of its strength into the solid angle [omega] subtended by its edge at the given point, or V = [Phi][omega]. For a given strength, therefore, the potential depends solely upon the boundary of the shell, and the potential outside a closed shell is everywhere zero. A magnet which can be divided into simple magnetic shells, either closed or having their edges on the surface of the magnet, is called a _lamellar magnet_, and the magnetism is said to be distributed lamellarly. A magnet consisting of a series of plane shells of equal strength arranged at right angles to the direction of magnetization will be uniformly magnetized.
It can be shown that uniform magnetization is possible only when the form of the body is ellipsoidal. (Maxwell, _Electricity and Magnetism_, II., § 437). The cases of greatest practical importance are those of a sphere (which is an ellipsoid with three equal axes) and an ovoid or prolate ellipsoid of revolution. The potential due to a uniformly magnetized sphere of radius a for an external point at a distance r from the centre is
V = (4/3)[pi] a³I cos [theta]/r², (23)
[theta] being the inclination of r to the magnetic axis. Since (4/3)[pi]a³I is the moment of the sphere (= volume × magnetization), it appears from (10) that the magnetized sphere produces the same external effect as a very small magnet of equal moment placed at its centre and magnetized in the same direction; the resultant force therefore is the same as in (14). The force in the interior is uniform, opposite to the direction of magnetization, and equal to (4/3)[pi]I. When it is desired to have a uniform magnet with definitely situated poles, it it usual to employ one having the form of an ovoid, or elongated ellipsoid of revolution, instead of a rectangular or cylindrical bar. If the magnetization is parallel to the major axis, and the lengths of the major and minor axes are 2a and 2c, the poles are situated at a distance equal to (2/3)a from the centre, and the magnet will behave externally like a simple solenoid of length (4/3)a. The internal force F is opposite to the direction of the magnetization, and equal to NI, where N is a coefficient depending only on the ratio of the axes. The moment = (4/3)[pi] ac²I = -(4/3)[pi] ac²FN.
The distribution of magnetism and the position of the poles in magnets of other shapes, such as cylindrical or rectangular bars, cannot be specified by any general statement, though approximate determinations may be obtained experimentally in individual cases.[5] According to F. W. G. Kohlrausch[6] the distance between the poles of a cylindrical magnet the length of which is from 10 to 30 times the diameter, is sensibly equal to five-sixths of the length of the bar. This statement, however, is only approximately correct, the distance between the poles depending upon the intensity of the magnetization.[7] In general, the greater the ratio of length to section, the more nearly will the poles approach the end of the bar, and the more nearly uniform will be the magnetization. For most practical purpose a knowledge of the exact position of the poles is of no importance; the magnetic moment, and therefore the mean magnetization, can always be determined with accuracy.
_Magnetic Induction or Magnetic Flux._--When magnetic force acts on any medium, whether magnetic, diamagnetic or neutral, it produces within it a phenomenon of the nature of a flux or flow called _magnetic induction_ (Maxwell, _loc. cit._, § 428). Magnetic induction, like other fluxes such as electrical, thermal or fluid currents, is defined with reference to an area; it satisfies the same conditions of continuity as the electric current does, and in isotropic media it depends on the magnetic force just as the electric current depends on the electromotive force. The magnitude of the flux produced by a given magnetic force differs in different media. In a uniform magnetic field of unit intensity formed in empty space the induction or magnetic flux across an area of 1 square centimetre normal to the direction of the field is arbitrarily taken as the unit of induction. Hence if the induction per square centimetre at any point is denoted by B, then in empty space B is numerically equal to H; moreover in isotropic media both have the same direction, and for these reasons it is often said that in empty space (and practically in air and other non-magnetic substances) B and H are identical. Inside a magnetized body, B is the force that would be exerted on a unit pole if placed in a narrow crevasse cut in the body, the walls of the crevasse being perpendicular to the direction of the magnetization (Maxwell, § § 399, 604); and its numerical value, being partly due to the free magnetism on the walls, is generally very different from that of H. In the case of a straight uniformly magnetized bar the direction of the magnetic force due to the poles of the magnet is from the north to the south pole outside the magnet, and from the south to the north inside. The magnetic flux per square centimetre at any point (B, B, or [B]) is briefly called the _induction_, or, especially by electrical engineers, the _flux-density_. The direction of magnetic induction may be indicated by _lines of induction_; a line of induction is always a closed curve, though it may possibly extend to and return from infinity. Lines of induction drawn through every point in the contour of a small surface form a re-entrant tube bounded by lines of induction; such a tube is called a _tube of induction_. The cross-section of a tube of induction may vary in different parts, but the total induction across any section is everywhere the same. A special meaning has been assigned to the term "lines of induction." Suppose the whole space in which induction exists to be divided up into _unit tubes_, such that the surface integral of the induction over any cross-section of a tube is equal to unity, and along the axis of each tube let a line of induction be drawn. These axial lines constitute the system of lines of induction which are so often referred to in the specification of a field. Where the induction is high the lines will be crowded together; where it is weak they will be widely separated, the number per square centimetre crossing a normal surface at any point being always equal to the numerical value of B. The induction may therefore be specified as B lines per square centimetre. The direction of the induction is also of course indicated by the direction of the lines, which thus serve to map out space in a convenient manner. Lines of induction are frequently but inaccurately spoken of as lines of force.
When induction or magnetic flux takes place in a ferromagnetic metal, the metal becomes magnetized, but the magnetization at any point is proportional not to B, but to B - H. The factor of proportionality will be 1-4[pi], so that
I = (B - H)/4[pi], (24)
or
B = H + 4[pi] I. (25)
Unless the path of the induction is entirely inside the metal, free magnetic poles are developed at those parts of the metal where induction enters and leaves, the polarity being south at the entry and north at the exit of the flux. These free poles produce a magnetic field which is superposed upon that arising from other sources. The _resultant magnetic field_, therefore, is compounded of two fields, the one being due to the poles, and the other to the external causes which would be operative in the absence of the magnetized metal. The intensity (at any point) of the field due to the magnetization may be denoted by H_i, that of the external field by H0, and that of the resultant field by H. In certain cases, as, for instance, in an iron ring wrapped uniformly round with a coil of wire through which a current is passing, the induction is entirely within the metal; there are, consequently, no free poles, and the ring, though magnetized, constitutes a poleless magnet. Magnetization is usually regarded as the direct effect of the resultant magnetic force, which is therefore often termed the _magnetizing force_.
_Permeability and Susceptibility._--The ratio B/H is called the _permeability_ of the medium in which the induction is taking place, and is denoted by µ. The ratio I/H is called the _susceptibility_ of the magnetized substance, and is denoted by [kappa]. Hence
B = µH and I = [kappa]H. (26)
Also
B H + 4[pi]I µ = --- = ---------- = 1 + 4[pi][kappa], (27) H H
and
µ - 1 [kappa] = ----- (28) 4[pi]
Since in empty space B has been assumed to be numerically equal to H, it follows that the permeability of a vacuum is equal to 1. The permeability of most material substances differs very slightly from unity, being a little greater than 1 in paramagnetic and a little less in diamagnetic substances. In the case of the ferromagnetic metals and some of their alloys and compounds, the permeability has generally a much higher value. Moreover, it is not constant, being an apparently arbitrary function of H or of B; in the same specimen its value may, under different conditions, vary from less than 2 to upwards of 5000. The magnetic susceptibility [kappa] expresses the numerical relation of the magnetization to the magnetizing force. From the equation [kappa] = (µ - 1)/4[pi], it follows that the magnetic susceptibility of a vacuum (where µ = l) is 0, that of a diamagnetic substance (where µ < l) has a negative value, while the susceptibility of paramagnetic and ferromagnetic substances (for which µ > 1) is positive. No substance has yet been discovered having a negative susceptibility sufficiently great to render the permeability (= 1 + 4[pi][kappa]) negative.
_Magnetic Circuit._--The circulation of magnetic induction or flux through magnetic and non-magnetic substances, such as iron and air, is in many respects analogous to that of an electric current through good and bad conductors. Just as the lines of flow of an electric current all pass in closed curves through the battery or other generator, so do all the lines of induction pass in closed curves through the magnet or magnetizing coil. The total magnetic induction or flux corresponds to the current of electricity (practically measured in amperes); the induction or flux density B to the density of the current (number of amperes to the square centimetre of section); the magnetic permeability to the specific electric conductivity; and the line integral of the magnetic force, sometimes called the magneto-motive force, to the electromotive force in the circuit. The principal points of difference are that (1) the magnetic permeability, unlike the electric conductivity, which is independent of the strength of the current, is not in general constant; (2) there is no perfect insulator for magnetic induction, which will pass more or less freely through all known substances. Nevertheless, many important problems relating to the distribution of magnetic induction may be solved by methods similar to those employed for the solution of analogous problems in electricity. For the elementary theory of the magnetic circuit see ELECTRO-MAGNETISM.
_Hysteresis, Coercive Force, Retentiveness._--It is found that when a piece of ferromagnetic metal, such as iron, is subjected to a magnetic field of changing intensity, the changes which take place in the induced magnetization of the iron exhibit a tendency to lag behind those which occur in the intensity of the field--a phenomenon to which J. A. Ewing (_Phil. Trans._ clxxvi. 524) has given the name of _hysteresis_ (Gr. [Greek: hystereô], to lag behind). Thus it happens that there is no definite relation between the magnetization of a piece of metal which has been previously magnetized and the strength of the field in which it is placed. Much depends upon its antecedent magnetic condition, and indeed upon its whole magnetic history. A well-known example of hysteresis is presented by the case of permanent magnets. If a bar of hard steel is placed in a strong magnetic field, a certain intensity of magnetization is induced in the bar; but when the strength of the field is afterwards reduced to zero, the magnetization does not entirely disappear. That portion which is permanently retained, and which may amount to considerably more than one-half, is called the _residual magnetization_. The ratio of the residual magnetization to its previous maximum value measures the _retentiveness_, or _retentivity_, of the metal.[8] Steel, which is well suited for the construction of permanent magnets, is said to possess great "coercive force." To this term, which had long been used in a loose and indefinite manner, J. Hopkinson supplied a precise meaning (_Phil. Trans._ clxxvi. 460). The _coercive force_, or _coercivity_, of a material is that reversed magnetic force which, while it is acting, just suffices to reduce the residual induction to nothing after the material has been temporarily submitted to any great magnetizing force. A metal which has great retentiveness may at the same time have small coercive force, and it is the latter quality which is of chief importance in permanent magnets.
_Demagnetizing Force._--It has already been mentioned that when a ferromagnetic body is placed in a magnetic field, the resultant magnetic force H, at a point within the body, is compounded of the force H0, due to the external field, and of another force, H_i, arising from the induced magnetization of the body. Since H_i generally tends to oppose the external force, thus making H less than H0, it may be called the _demagnetizing force_. Except in the few special cases when a uniform external field produces uniform magnetization, the value of the demagnetizing force cannot be calculated, and an exact determination of the actual magnetic force within the body is therefore impossible. An important instance in which the calculation can be made is that of an elongated _ellipsoid of revolution_ placed in a uniform field H0, with its axis of revolution parallel to the lines of force. The magnetization at any point inside the ellipsoid will then be
[kappa]H0 I = ------------ (29) 1 + [kappa]N
where
/ 1 \ / 1 1 + e \ N = 4[pi]( --- - 1 ) ( --- log ----- ), \ e2 / \ 2e 1 - e /
e being the eccentricity (see Maxwell's _Treatise_, § 438). Since I = [kappa]H, we have
[kappa]H + [kappa]NI = [kappa]H0, (30)
or
H = H0 - NI,
NI being the demagnetizing force H_i. N may be called, after H. du Bois (_Magnetic Circuit_, p. 33), the _demagnetizing factor_, and the ratio of the length of the ellipsoid 2c to its equatorial diameter 2a (= c/a), the _dimensional ratio_, denoted by the symbol [m].
Since e = [root](1 - a²/c²) = [root](1 - 1/[m]²),
the above expression for N may be written
4[pi] / [m] [m] + [root]([m]² - 1) \ N = -------- ( ------------------ log ---------------------- - 1 ) [m]² - 1 \ 2 [root]([m]² - 1) [m] - [root]([m]² - 1) / _ _ 4[pi] | [m] / \ | = -------- | ---------------- log ( [m] + [root]([m]² - 1) ) - 1 |, [m]² - 1 |_ [root]([m]² - 1) \ / _|
from which the value of N for a given dimensional ratio can be calculated. When the ellipsoid is so much elongated that 1 is negligible in relation to [m]², the expression approximates to the simpler form
4[pi] N = ----- (log 2[m] - 1). (31) [m]²
In the case of a _sphere_, e = O and N = (4/3)[pi]; therefore from (29)
[kappa]H0 3[kappa] I = [kappa]H = -------------------- = ---------------- H0, (32) 1 + (4/3)[pi][kappa] 3 + 4[pi][kappa]
Whence
3 3 H = ---------------- H0 = ----- H0, (33) 3 + 4[pi][kappa] µ + 2
and
3µ B = µH = ----- H0. (34) µ + 2
Equations (33) and (34) show that when, as is generally the case with ferromagnetic substances, the value of µ is considerable, the resultant magnetic force is only a small fraction of the external force, while the numerical value of the induction is approximately three times that of the external force, and nearly independent of the permeability. The demagnetizing force inside a _cylindrical rod_ placed longitudinally in a uniform field H0 is not uniform, being greatest at the ends and least in the middle part. Denoting its mean value by [H]_i, and that of the demagnetizing factor by [N], we have
H = H0 - [H]_i = H0 - [N]I. (35)
Du Bois has shown that when the dimensional ratio [m] (= length/diameter) exceeds 100, [N][m]² = constant = 45, and hence for long thin rods
[N] = 45/[m]². (36)
From an analysis of a number of experiments made with rods of different dimensions H. du Bois has deduced the corresponding mean demagnetizing factors. These, together with values of [m]²[N] for cylindrical rods, and of N and [m]²N for ellipsoids of revolution, are given in the following useful table (_loc. cit._ p. 41):--
_Demagnetizing Factors._
+------+--------------------+-------------------+ | | Cylinder. | Ellipsoid. | | [m]. +----------+---------+----------+--------+ | | [N]. | [m]²[N].| N. | [m]²N. | +------+----------+---------+----------+--------+ | 0 | 12.5664 | 0 | 12.5664 | 0 | | 0.5 | -- | -- | 6.5864 | -- | | 1 | -- | -- | 4.1888 | -- | | 5 | -- | -- | 0.7015 | -- | | 10 | 0.2160 | 21.6 | 0.2549 | 25.5 | | 15 | 0.1206 | 27.1 | 0.1350 | 30.5 | | 20 | 0.0775 | 31.0 | 0.0848 | 34.0 | | 25 | 0.0533 | 33.4 | 0.0579 | 36.2 | | 30 | 0.0393 | 35.4 | 0.0432 | 38.8 | | 40 | 0.0238 | 38.7 | 0.0266 | 42.5 | | 50 | 0.0162 | 40.5 | 0.0181 | 45.3 | | 60 | 0.0118 | 42.4 | 0.0132 | 47.5 | | 70 | 0.0089 | 43.7 | 0.0101 | 49.5 | | 80 | 0.0069 | 44.4 | 0.0080 | 51.2 | | 90 | 0.0055 | 44.8 | 0.0065 | 52.5 | | 100 | 0.0045 | 45.0 | 0.0054 | 54.0 | | 150 | 0.0020 | 45.0 | 0.0026 | 58.3 | | 200 | 0.0011 | 45.0 | 0.0016 | 64.0 | | 300 | 0.00050 | 45.0 | 0.00075 | 67.5 | | 400 | 0.00028 | 45.0 | 0.00045 | 72.0 | | 500 | 0.00018 | 45.0 | 0.00030 | 75.0 | | 1000 | 0.00005 | 45.0 | 0.00008 | 80.0 | +------+--------------------+-------------------+
In the middle part of a rod which has a length of 400 or 500 diameters the effect of the ends is insensible; but for many experiments the condition of endlessness may be best secured by giving the metal the shape of a ring of uniform section, the magnetic field being produced by an electric current through a coil of wire evenly wound round the ring. In such cases H_i = 0 and H = H0.
The residual magnetization I_r retained by a bar of ferromagnetic metal after it has been removed from the influence of an external field produces a demagnetizing force [N]I_r, which is greater the smaller the dimensional ratio. Hence the difficulty of imparting any considerable permanent magnetization to a short thick bar not possessed of great coercive force. The magnetization retained by a long thin rod, even when its coercive force is small, is sometimes little less than that which was produced by the direct action of the field.
_Demagnetization by Reversals._--In the course of an experiment it is often desired to eliminate the effects of previous magnetization, and, as far as possible, wipe out the magnetic history of a specimen. In order to attain this result it was formerly the practice to raise the metal to a bright red heat, and allow it to cool while carefully guarded from magnetic influence. This operation, besides being very troublesome, was open to the objection that it was almost sure to produce a material but uncertain change in the physical constitution of the metal, so that, in fact, the results of experiments made before and after the treatment were not comparable. Ewing introduced the method (_Phil. Trans._ clxxvi. 539) of demagnetizing a specimen by subjecting it to a succession of magnetic forces which alternated in direction and gradually diminished in strength from a high value to zero. By means of a simple arrangement, which will be described farther on, this process can be carried out in a few seconds, and the metal can be brought as often as desired to a definite condition, which, if not quite identical with the virgin state, at least closely approximates to it.
_Forces acting on a Small Body in the Magnetic Field._--If a small magnet of length ds and pole-strength m is brought into a magnetic field such that the values of the magnetic potential at the negative and positive poles respectively are V1 and V2, the work done upon the magnet, and therefore its potential energy, will be
W = m(V2 - V1) = m dV,
which may be written
dV dV W = m ds -- = M -- = -MH0 = -vIH0, ds ds
where M is the moment of the magnet, v the volume, I the magnetization, and H0 the magnetic force along _ds_. The small magnet may be a sphere rigidly magnetized in the direction of H0; if this is replaced by an isotropic sphere inductively magnetized by the field, then, for a displacement so small that the magnetization of the sphere may be regarded as unchanged, we shall have
[kappa] dW = -vI dH0 = -v -------------------- H0 dH0; 1 + (4/3)[pi][kappa]
whence
v [kappa] W = - --- -------------------- H^2_0. (37) 2 1 + (4/3)[pi][kappa]
The mechanical force acting on the sphere in the direction of displacement x is
dW [kappa] dH^2_0 F = - -- = v -------------------- ------. (38) dx 1 + (4/3)[pi][kappa] dx
If H0 is constant, the force will be zero; if H0 is variable, the sphere will tend to move in the direction in which H0 varies most rapidly. The coefficient [kappa]/(1 + (4/3)[pi][kappa]) is positive for ferromagnetic and paramagnetic substances, which will therefore tend to move from weaker to stronger parts of the field; for all known diamagnetic substances it is negative, and these will tend to move from stronger to weaker parts. For small bodies other than spheres the coefficient will be different, but its sign will always be negative for diamagnetic substances and positive for others;[9] hence the forces acting on any small body will be in the same directions as in the case of a sphere.[10]
_Directing Couple acting on an Elongated Body._--In a non-uniform field every volume-element of the body tends to move towards regions of greater or less force according as the substance is paramagnetic or diamagnetic, and the behaviour of the whole mass will be determined chiefly by the tendency of its constituent elements. For this reason a thin bar suspended at its centre of gravity between a pair of magnetic poles will, if paramagnetic, set itself along the line joining the poles, where the field is strongest, and if diamagnetic, transversely to the line. These are the "axial" and "equatorial" positions of Faraday. It can be shown[11] that in a uniform field an elongated piece of any non-crystalline material is in stable equilibrium only when its length is parallel to the lines of force; for diamagnetic substances, however, the directing couple is exceedingly small, and it would hardly be possible to obtain a uniform field of sufficient strength to show the effect experimentally.
_Relative Magnetization._--A substance of which the real susceptibility is [kappa] will, when surrounded by a medium having the susceptibility [kappa]´, behave towards a magnet as if its susceptibility were [kappa]_a = ([kappa] - [kappa]´)/(1 + 4[pi][kappa]´). Since 1 + 4[pi][kappa]´ can never be negative, the apparent susceptibility [kappa]_a will be positive or negative according as [kappa] is greater or less than [kappa]´. Thus, for example, a tube containing a weak solution of an iron salt will appear to be diamagnetic if it is immersed in a stronger solution of iron, though in air it is paramagnetic.[12]
_Circular Magnetization._--An electric current i flowing uniformly through a cylindrical wire whose radius is a produces inside the wire a magnetic field of which the lines of force are concentric circles around the axis of the wire. At a point whose distance from the axis of the wire is r the tangential magnetic force is
H = 2ir/a² (39)
it therefore varies directly as the distance from the axis, where it is zero.[13] If the wire consists of a ferromagnetic metal, it will become "circularly" magnetized by the field, the lines of magnetization being, like the lines of force, concentric circles. So long as the wire (supposed isotropic) is free from torsional stress, there will be no external evidence of magnetism.
_Magnetic Shielding._--The action of a hollow magnetized shell on a point inside it is always opposed to that of the external magnetizing force,[14] the resultant interior field being therefore weaker than the field outside. Hence any apparatus, such as a galvanometer, may be partially shielded from extraneous magnetic action by enclosing it in an iron case. If a hollow sphere[15] of which the outer radius is R and the inner radius r is placed in a uniform field H0, the field inside will also be uniform and in the same direction as H0, and its value will be approximately
H0 H_i = ---------------------------- (40) 1 + (2/9)(µ - 2) (1 - r³/R³)
For a cylinder placed with its axis at right angles to the lines of force,
H0 H_i = ------------------------ (41) 1 + ¼(µ - 2) (1 - r²/R²)
These expressions show that the thicker the screen and the greater its permeability µ, the more effectual will be the shielding action. Since µ can never be infinite, complete shielding is not possible.
_Magneto-Crystallic Phenomenon._--In anisotropic bodies, such as crystals, the direction of the magnetization does not in general coincide with that of the magnetic force. There are, however, always three _principal axes_ at right angles to one another along which the magnetization and the force have the same direction. If each of these axes successively is placed parallel to the lines of force in a uniform field H, we shall have
I1 = [kappa]1H, I2 = [kappa]2H, I3 = [kappa]3H,
the three susceptibilities [kappa] being in general unequal, though in some cases two of them may have the same value. For crystalline bodies the value of [kappa] (+ or -) is nearly always small and constant, the magnetization being therefore independent of the form of the body and proportional to the force. Hence, whatever the position of the body, if the field be resolved into three components parallel to the principal axes of the crystal, the actual magnetization will be the resultant of the three magnetizations along the axes. The body (or each element of it) will tend to set itself with its axis of greatest susceptibility parallel to the lines of force, while, if the field is not uniform, each volume-element will also tend to move towards places of greater or smaller force (according as the substance is paramagnetic or diamagnetic), the tendency being a maximum when the axis of greatest susceptibility is parallel to the field, and a minimum when it is perpendicular to it. The phenomena may therefore be exceedingly complicated.[16]
3. MAGNETIC MEASUREMENTS
_Magnetic Moment._--The moment M of a magnet may be determined in many ways,[17] the most accurate being that of C. F. Gauss, which gives the value not only of M, but also that of H, the horizontal component of the earth's force. The product MH is first determined by suspending the magnet horizontally, and causing it to vibrate in small arcs. If A is the moment of inertia of the magnet, and t the time of a complete vibration, MH = 4[pi]²A/t² (torsion being neglected). The ratio M/H is then found by one of the magnetometric methods which in their simplest forms are described below. Equation (44) shows that as a first approximation.
M/H = (d² - l²) tan [theta]/2d,
where l is half the length of the magnet, which is placed in the "broadside-on" position as regards a small suspended magnetic needle, d the distance between the centre of the magnet and the needle, and [theta] the angle through which the needle is deflected by the magnet. We get therefore
M² = MH × M/H = 2[pi]²A(d² - l²)² tan [theta]/t²d (42)
H² = MH × H/M = 8[pi]²Ad/{t²(d² - l²)² tan [theta]} (43)
When a high degree of accuracy is required, the experiments and calculations are less simple, and various corrections are applied. The moment of a magnet may also be deduced from a measurement of the couple exerted on the magnet by a uniform field H. Thus if the magnet is suspended horizontally by a fine wire, which, when the magnetic axis points north and south, is free from torsion, and if [theta] is the angle through which the upper end of the wire must be twisted to make the magnet point east and west, then MH = C[theta], or M = C[theta]/H, where C is the torsional couple for 1°. A bifilar suspension is sometimes used instead of a single wire. If P is the weight of the magnet, l the length of each of the two threads, 2a the distance between their upper points of attachment, and 2b that between the lower points, then, approximately, MH = P(ab/l) sin [theta]. It is often sufficient to find the ratio of the moment of one magnet to that of another. If two magnets having moments M, M´ are arranged at right angles to each other upon a horizontal support which is free to rotate, their resultant R will set itself in the magnetic meridian. Let [theta] be the angle which the standard magnet M makes with the meridian, then M´/R = sin [theta], and M/R = cos [theta], whence M´ = M tan [theta].
A convenient and rapid method of estimating a magnetic moment has been devised by H. Armagnat.[18] The magnet is laid on a table with its north pole pointing northwards, A compass having a very short needle is placed on the line which bisects the axis of the magnet at right angles, and is moved until a neutral point is found where the force due to the earth's field H is balanced by that due to the magnet. If 2l is the distance between the poles m and -m, d the distance from either pole to a point P on the line AB (fig. 5), we have for the resultant force at P
R = -2 cos [theta] × m/d² = -2lm/d³ = -M/d³.
When P is the neutral point, H is equal and opposite to R; therefore M = Hd³, or the moment is numerically equal to the cube of the distance from the neutral point to a pole, multiplied by the horizontal intensity of the earth's force. The distance between the poles may with sufficient accuracy for a rough determination be assumed to be equal to five-sixths of the length of the magnet.
_Measurement of Magnetization and Induction._--The magnetic condition assumed by a piece of ferromagnetic metal in different circumstances is determinable by various modes of experiment which may be classed as magnetometric, ballistic, and traction methods. When either the magnetization I or the induction B corresponding to a given magnetizing force H is known, the other may be found by means of the formula B = 4[pi]I + H.
_Magnetometric Methods._--Intensity of magnetization is most directly measured by observing the action which a magnetized body, generally a long straight rod, exerts upon a small magnetic needle placed near it. The magnetic needle may be cemented horizontally across the back of a little plane or concave mirror, about ¼ or 3/8 in. in diameter, which is suspended by a single fibre of unspun silk; this arrangement, when enclosed in a case with a glazed front to protect it from currents of air, constitutes a simple but efficient magnetometer. Deflections of the suspended needle are indicated by the movement of a narrow beam of light which the mirror reflects from a lamp and focusses upon a graduated cardboard scale placed at a distance of a few feet; the angular deflection of the beam of light is, of course, twice that of the needle. The suspended needle is, in the absence of disturbing causes, directed solely by the horizontal component of the earth's field of magnetic force H_E, and therefore sets itself approximately north and south. The magnetized body which is to be tested should be placed in such a position that the force H_P due to its poles may, at the spot occupied by the suspended needle, act in a direction at right angles to that due to the earth--that is, east and west. The direction of the resultant field of force will then make, with that of H_E, an angle [theta], such that H_p/H_E = tan [theta], and the suspended needle will be deflected through the same angle. We have therefore
H_P = H_E tan [theta].
The angle [theta] is indicated by the position of the spot of light upon the scale, and the horizontal intensity of the earth's field H_E is known; thus we can at once determine the value of H_P, from which the magnetization I of the body under test may be calculated.
In order to fulfil the requirement that the field which a magnetized rod produces at the magnetometer shall be at right angles to that of the earth, the rod may be conveniently placed in any one of three different positions with regard to the suspended needle.
(1) The rod is set in a horizontal position level with the suspended needle, its axis being in a line which is perpendicular to the magnetic meridian, and which passes through the centre of suspension of the needle. This is called the "end-on" position, and is indicated in fig. 6. AB is the rod and C the middle point of its axis; NS is the magnetometer needle; AM bisects the undeflected needle NS at right angles. Let 2l = the length of the rod (or, more accurately, the distance between its poles), v = its volume, m and -m the strength of its poles, and let d = the distance CM. For most ordinary purposes the length of the needle may be assumed to be negligible in comparison with the distance between the needle and the rod. We then have approximately for the field at M due to the rod
m m 4dl H_P = -------- - -------- = m ----------. (d - l)² (d + l)² (d² - l²)²
Therefore
(d² - l²)²H_P (d² - l²)² H_E tan [theta] 2ml = M = ------------- = --------------------------. (44) 2d 2d
And
M (d² - l²)²H_E I = --- = ------------- tan [theta], (45) v 2dv
whence we can find the values of I which correspond to different angles of deflection.
(2) The rod may be placed horizontally east and west in such a position that the direction of the undeflected suspended needle bisects it at right angles. This is known as the "broadside-on" position, and is represented in fig. 7. Let the distance of each pole of the rod AB from the centre of the magnetometer needle = d. Then, since H_P, the force at M due to m and -m, is the resultant of m/d² and -m/d², we have
H_P 2l --- = --- m d
or
2ml H_P = ---, d³
the direction being parallel to AB.
And
d³ H_P d³ H_E I = ------ = ------ tan [theta]. (46) v v
(3) In the third position the test rod is placed vertically with one of its poles at the level of the magnetometer needle, and in the line drawn perpendicularly to the undeflected needle from its centre of suspension. The arrangement is shown in fig. 8, where AB is the vertical rod and M indicates the position of the magnetometer needle, which is supposed to be perpendicular to the plane of the paper. Denoting the distance AM by d1, BM by d2, and AB by l, we have for the force at M due to the magnetism of the rod
m m H_P = --- - horizontal component of --- d1² d2²
/ 1 d1 \ = m ( --- - --- ). \ d1² d2³ /
Therefore
H_P d1² H_E m = --------- = ------------ tan [theta], 1 d1 / d1 \³ --- - --- 1 - ( ---- ) d1² d2³ \ d2 /
and
ld1²H_E I = ------------------ tan [theta]. (47) { / d1 \³ } v { 1 - ( ---- ) } { \ d2 / }
This last method of arrangement is called by Ewing the "one-pole" method, because the magnetometer deflection is mainly caused by the upper pole of the rod (_Magnetic Induction_, p. 40). For experiments with long thin rods or wires it has an advantage over the other arrangements in that the position of the poles need not be known with great accuracy, a small upward or downward displacement having little effect upon the magnetometer deflection. On the other hand, a vertically placed rod is subject to the inconvenience that it is influenced by the earth's magnetic field, which is not the case when the rod is horizontal and at right angles to the magnetic meridian. This extraneous influence may, however, be eliminated by surrounding the rod with a coil of wire carrying a current such as will produce in the interior a magnetic field equal and opposite to the vertical component of the earth's field.
If the cardboard scale upon which the beam of light is reflected by the magnetometer mirror is a flat one, the deflections as indicated by the movement of the spot of light are related to the actual deflections of the needle in the ratio of tan 2[theta] to [theta]. Since [theta] is always small, sufficiently accurate results may generally be obtained if we assume that tan 2[theta] = 2 tan [theta]. If the distance of the mirror from the scale is equal to n scale divisions, and if a deflection [theta] of the needle causes the reflected spot of light to move over s scale divisions, we shall have
s/n = tan 2[theta] exactly,
s/2n = tan [theta] approximately.
We may therefore generally substitute s/2n for tan [theta] in the various expressions which have been given for I.
Of the three methods which have been described, the first two are generally the most suitable for determining the moment or the magnetization of a permanent magnet, and the last for studying the changes which occur in the magnetization of a long rod or wire when subjected to various external magnetic forces, or, in other words, for determining the relation of I to H. A plan of the apparatus as arranged by Ewing for the latter purpose is shown diagrammatically in fig. 9. The cardboard scale SS is placed above a wooden screen, having in it a narrow vertical slit which permits a beam of light from the lamp L to reach the mirror of the magnetometer M, whence it is reflected upon the scale. A is the upper end of a glass tube, half a metre or so in length, which is clamped in a vertical position behind the magnetometer. The tube is wound over its whole length with two separate coils of insulated wire, the one being outside the other. The inner coil is supplied, through the intervening apparatus, with current from the battery of secondary cells B1; this produces the desired magnetic field inside the tube. The outer coil derives current, through an adjustable resistance R, from a constant cell B2; its object is to produce inside the tube a magnetic field equal and opposite to that due to the earth's magnetism. C is a "compensating coil" consisting of a few turns of wire through which the magnetizing current passes; it serves to neutralize the effect produced upon the magnetometer by the magnetizing coil, and its distance from the magnetometer is so adjusted that when the circuit is closed, no ferromagnetic metal being inside the magnetizing coil, the magnetometer needle undergoes no deflection. K is a commutator for reversing the direction of the magnetizing current, and G a galvanometer for measuring it. The strength of the magnetizing current is regulated by adjusting the position of the sliding contact E upon the resistance DF. The current increases to a maximum as E approaches F, and diminishes to almost nothing when E is brought up to D; it can be completely interrupted by means of the switch H.
The specimen upon which an experiment is to be made generally consists of a wire having a "dimensional ratio" of at least 300 or 400; its length should be rather less than that of the magnetizing coil, in order that the field H0, to which it is subjected, may be approximately uniform from end to end. The wire is supported inside the glass tube A with its upper pole at the same height as the magnetometer needle. Various currents are then passed through the magnetizing coil, the galvanometer readings and the simultaneous magnetometer deflections being noted. From the former we deduce H0, and from the latter the corresponding value of I, using the formulae H0 = 4[pi]in/l and
d1² H_E I = ----------------------- × s, (48) 2n[pi]r² {1 - (d1/d2)³}
where s is the deflection in scale-divisions, n the distance in scale-divisions between the scale and the mirror, and r the radius of the wire.
The curve, fig. 10, shows the result of a typical experiment made upon a piece of soft iron (Ewing, _Phil. Trans._ vol. clxxvi. Plate 59), the magnetizing field H0 being first gradually increased and then diminished to zero. When the length of the wire exceeds 400 diameters, or thereabouts, H0 may generally be considered as equivalent to H, the actual strength of the field as modified by the magnetization of the wire; but if greater accuracy is desired, the value of H_i (= NI) may be found by the help of du Bois's table and subtracted from H0. For a dimensional ratio of 400, N =0.00028, and therefore H = H0 - 0.00028I. This correction may be indicated in the diagram by a straight line drawn from 0 through the point at which the line of I = 1000 intersects that of H = 0.28 (Rayleigh, Phil. Mag. xxii. 175), the true value of H for any point on the curve being that measured from the sloping line instead of from the vertical axis. The effect of the ends of the wire is, as Ewing remarks, to shear the diagram in the horizontal direction through the angle which the sloping line makes with the vertical.
Since the induction B is equal to H + 4[pi]I, it is easy from the results of experiments such as that just described to deduce the relation between B and H; a curve indicating such relation is called a curve of induction. The general character of curves of magnetization and of induction will be discussed later. A notable feature in both classes of curves is that, owing to hysteresis, the ascending and descending limbs do not coincide, but follow very different courses. If it is desired to annihilate the hysteretic effects of previous magnetization and restore the metal to its original condition, it may be demagnetized by reversals. This is effected by slowly moving the sliding contact E (fig. 9) from F to D, while at the same time the commutator K is rapidly worked, a series of alternating currents of gradually diminishing strength being thus caused to pass through the magnetizing coil.
The magnetometric method, except when employed in connexion with ellipsoids, for which the demagnetizing factors are accurately known, is generally less satisfactory for the exact determination of induction or magnetization than the ballistic method. But for much important experimental work it is better adapted than any other, and is indeed sometimes the only method possible.[19]
_Ballistic Methods._--The so-called "ballistic" method of measuring induction is based upon the fact that a change of the induction through a closed linear conductor sets up in the conductor an electromotive force which is proportional to the rate of change. If the conductor consists of a coil of wire the ends of which are connected with a suitable galvanometer, the integral electromotive force due to a sudden increase or decrease of the induction through the coil displaces in the circuit a quantity of electricity Q = [delta]BnsR, where [delta]B is the increment or decrement of induction per square centimetre, s is the area of the coil, n the number of turns of wire, and R the resistance of the circuit. Under the influence of the transient current, the galvanometer needle undergoes a momentary deflection, or "throw," which is proportional to Q, and therefore to [delta]B, and thus, if we know the deflection produced by the discharge through the galvanometer of a given quantity of electricity, we have the means of determining the value of [delta]B.
The galvanometer which is used for ballistic observations should have a somewhat heavy needle with a period of vibration of not less than five seconds, so that the transient current may have ceased before the swing has well begun; an instrument of the d'Arsonval form is recommended, not only because it is unaffected by outside magnetic influence, but also because the moving part can be instantly brought to rest by means of a short-circuit key, thus effecting a great saving of time when a series of observations is being made. In practice it is usual to standardize or "calibrate" the galvanometer by causing a known change of induction to take place within a standard coil connected with it, and noting the corresponding deflection on the galvanometer scale. Let s be the area of a single turn of the standard coil, n the number of its turns, and r the resistance of the circuit of which the coil forms part; and let S, N and R be the corresponding constants for a coil which is to be used in an experiment. Then if a known change of induction [delta]B_a inside the standard coil is found to cause a throw of d scale-divisions, any change of induction [delta]B through the experimental coil will be numerically equal to the corresponding throw D multiplied by snRB_a/SNrd. For a series of experiments made with the same coil this fraction is constant, and we may write [delta]B = kD. Rowland and others have used an earth coil for calibrating the galvanometer, a known change of induction through the coil being produced by turning it over in the earth's magnetic field, but for several reasons it is preferable to employ an electric current as the source of a known induction. A primary coil of length l, having n turns, is wound upon a cylinder made of non-conducting and non-magnetic material, and upon the middle of the primary a secondary or induction coil is closely fitted. When a current of strength i is suddenly interrupted in the primary, the increment of induction through the secondary is sensibly equal to 4[pi]in/l units. All the data required for standardizing the galvanometer can in this way be determined with accuracy.
The ballistic method is largely employed for determining the relation of induction to magnetizing force in samples of the iron and steel used in the manufacture of electrical machinery, and especially for the observation of hysteresis effects. The sample may have the form of a closed ring, upon which are wound the induction coil and another coil for taking the magnetizing current; or it may consist of a long straight rod or wire which can be slipped into a magnetizing coil such as is used in magnetometric experiments, the induction coil being wound upon the middle of the wire. With these arrangements there is no demagnetizing force to be considered, for the ring has not any ends to produce one, and the force due to the ends of a rod 400 or 500 diameters in length is quite insensible at the middle portion; H therefore is equal to H0.
E. Grassot has devised a galvanometer, or "fluxmeter," which greatly alleviates the tedious operation of taking ballistic readings.[20] The instrument is of the d'Arsonval type; its coil turns in a strong uniform field, and is suspended in such a manner that torsion is practically negligible, the swings of the coil being limited by damping influences, chiefly electromagnetic. The index therefore remains almost stationary at the limit of its deflection, and the deflection is approximately the same whether the change of induction occurs suddenly or gradually.
_Induction and Hysteresis Curves._--Some typical induction curves, copied from a paper by Ewing (_Proc. Inst. C.E._ vol. cxxvi.), are given in figs. 11, 12 and 13. Fig. 11 shows the relation of B to H in a specimen which has never before been magnetized. The experiment may be made in two different ways: (1) the magnetizing current is increased by a series of sudden steps, each of which produces a ballistic throw, the value of B after any one throw being proportional to the sum of that and all the previous throws; (2) the magnetizing current having been brought to any desired value, is suddenly reversed, and the observed throw taken as measuring twice the actual induction. Fig. 12 shows the nature of the course taken by the curve when the magnetizing current, after having been raised to the value corresponding to the point a, is diminished by steps until it is nothing, and then gradually increased in the reverse direction. The downward course of the curve is, owing to hysteresis, strikingly different from its upward course, and when the magnetizing force has been reduced to zero, there is still remaining an induction of 7500 units. If the operation is again reversed, the upward course will be nearly, but not exactly, of the form shown by the line d e a, fig. 13. After a few repetitions of the reversal, the process becomes strictly cyclic, the upward and downward curves always following with precision the paths indicated in the figure. In order to establish the cyclic condition, it is sufficient to apply alternately the greatest positive and negative forces employed in the test (greatest H = about ±5 C.G.S. units in the case illustrated in the figure), an operation which is performed by simply reversing the direction of the maximum magnetizing current a few times.
The closed figure a c d e a is variously called a _hysteresis curve_ or _diagram_ or _loop_. The area [int] H dB enclosed by it represents the work done in carrying a cubic centimetre of the iron through the corresponding magnetic cycle; expressed in ergs this work is (1/4)[pi] [int] H dB.[21] To quote an example given by J. A. Fleming, it requires about 18 foot-pounds of work to make a complete magnetic cycle in a cubic foot of wrought iron, strongly magnetized first one way and then the other, the work so expended taking the form of heat in the mass.
Fig. 14 shows diagrammatically a convenient arrangement described by Ewing (see _Proc. Inst. C.E._ vol. cxxvi., and _Phil. Trans._, 1893A, p. 987) for carrying out ballistic tests by which either the simple B-H curve (fig. 11) or the hysteresis curve (figs. 12 and 13) can be determined. The sample under test is prepared in the form of a ring A, upon which are wound the induction and the magnetizing coils; the latter should be wound evenly over the whole ring, though for the sake of clearness only part of the winding is indicated in the diagram. The magnetizing current, which is derived from the storage battery B, is regulated by the adjustable resistance R and measured by the galvanometer G. The current passes through the rocking key K, which, when thrown over to the right, places a in contact with c and b with d, and when thrown over to the left, places a in contact with e and b with f. When the switch S is closed, K acts simply as a commutator or current-reverser, but if K is thrown over from right to left while S is opened, not only is the current reversed, but its strength is at the same time diminished by the interposition of the adjustable resistance R2. The induction coil wound upon the ring is connected to the ballistic galvanometer G2 in series with a large permanent resistance R3. In the same circuit is also included the induction coil E, which is used for standardizing the galvanometer; this secondary coil is represented in the diagram by three turns of wire wound over a much longer primary coil. The short-circuit key F is kept closed except when an observation is about to be made; its object is to arrest the swing of the d'Arsonval galvanometer G2. By means of the three-way switch C the battery current may be sent either into the primary of E, for the purpose of calibrating the galvanometer, or into the magnetizing coil of the ring under test. When it is desired to obtain a simple curve of induction, such as that in fig. 11, S is kept permanently closed, and corresponding values of H and B are determined by one of the two methods already described, the strength of the battery-current being varied by means of the adjustable resistance R. When a hysteresis curve is to be obtained, the procedure is as follows: The current is first adjusted by means of R to such a strength as will fit it to produce the greatest + and - values of the magnetizing force which it is intended to apply in the course of the cycle; then it is reversed several times, and when the range of the galvanometer throws has become constant, half the extent of an excursion indicates the induction corresponding to the extreme value of H, and gives the point a in the curve fig. 12. The reversing key K having been put over to the left side, the short-circuit key S is suddenly opened; this inserts the resistance R, which has been suitably adjusted beforehand, and thus reduces the current and therefore the magnetizing force to a known value. The galvanometer throw which results from the change of current measures the amount by which the induction is reduced, and thus a second point on the curve is found. In a similar manner, by giving different values to the resistance R, any desired number of points between a and c in the curve can be determined. To continue the process, the key K is turned over to the right-hand side, and then, while S is open, is turned back, thereby not only reversing the direction of the current, but diminishing its strength by an amount depending upon the previous adjustment of R2. In this way points can be found lying anywhere between c and d of fig. 12, and the determination of the downward limb of the curve is therefore completed. As the return curve, shown in fig. 13, is merely an inverted copy of the other, no separate determination of it is necessary.
In fig. 15 (J. A. Fleming, _Magnets and Electric Currents_, p. 193) are shown three very different types of hysteresis curves, characteristic of the special qualities of the metals from which they were respectively obtained. The distinguishing feature of the first is the steepness of its outlines; this indicates that the induction increases rapidly in relation to the magnetic force, and hence the metal is well suited for the construction of dynamo magnets. The second has a very small area, showing that the work done in reversing the magnetization is small; the metal is therefore adapted for use in alternating current transformers. On the other hand, the form of the third curve, with its large intercepts on the axes of H and B, denotes that the specimen to which it relates possesses both retentiveness and coercive force in a high degree; such a metal would be chosen for making good permanent magnets.
Several arrangements have been devised for determining hysteresis more easily and expeditiously than is possible by the ballistic method. The best known is J. A. Ewing's hysteresis-tester,[22] which is specially intended for testing the sheet iron used in transformers. The sample, arranged as a bundle of rectangular strips, is caused to rotate about a central horizontal axis between the poles of an upright C-shaped magnet, which is supported near its middle upon knife-edges in such a manner that it can oscillate about an axis in a line with that about which the specimen rotates; the lower side of the magnet is weighted, to give it some stability. When the specimen rotates, the magnet is deflected from its upright position by an amount which depends upon the work done in a single complete rotation, and therefore upon the hysteresis. The deflection is indicated by a pointer upon a graduated scale, the readings being interpreted by comparison with two standard specimens supplied with the instrument. G. F. Searle and T. G. Bedford[23] have introduced the method of measuring hysteresis by means of an electro-dynamometer used ballistically. The fixed and suspended coils of the dynamometer are respectively connected in series with the magnetizing solenoid and with a secondary wound upon the specimen. When the magnetizing current is twice reversed, so as to complete a cycle, the sum of the two deflections, multiplied by a factor depending upon the sectional area of the specimen and upon the constants of the apparatus, gives the hysteresis for a complete cycle in ergs per cubic centimetre. For specimens of large sectional area it is necessary to apply corrections in respect of the energy dissipated by eddy currents and in heating the secondary circuit. The method has been employed by the authors themselves in studying the effects of tension, torsion and circular magnetization, while R. L. Wills[24] has made successful use of it in a research on the effects of temperature, a matter of great industrial importance.
C. P. Steinmetz (_Electrician_, 1891, 26, p. 261; 1892, 28, pp. 384, 408, 425) has called attention to a simple relation which appears to exist between the amount of energy dissipated in carrying a piece of iron or steel through a magnetic cycle and the limiting value of the induction reached in the cycle. Denoting by W the work in ergs done upon a cubic centimetre of the metal ( = 1/4[pi] [int] H dB or [int] H dI), he finds W = [eta]B^(1.6) approximately, where [eta] is a number, called the hysteretic constant, depending upon the metal, and B is the maximum induction. The value of the constant [eta] ranges in different metals from about 0.001 to 0.04; in soft iron and steel it is said to be generally not far from 0.002. Steinmetz's formula may be tested by taking a series of hysteresis curves between different limits of B, measuring their areas by a planimeter, and plotting the logarithms of these divided by 4[pi] as ordinates against logarithms of the corresponding maximum values of B as abscissae. The curve thus constructed should be a straight line inclined to the horizontal axis at an angle [theta], the tangent of which is 1.6. Ewing and H. G. Klaassen (_Phil. Trans._, 1893, 184, 1017) have in this manner examined how nearly and within what range a formula of the type W = [eta]B^[epsilon] may be taken to represent the facts. The results of an example which they quote in detail may be briefly summarized as follows:--
+-----------------+------------+-----------------+-----------+ | | Hysteretic | Index. | Degrees. | | Limits of B. | Constant. | [epsilon] | [theta] | | | [eta] | (= tan [theta]) | | +-----------------+------------+-----------------+-----------+ | 200 to 500 | ... | 1.9 | 62.25 | | 500 to 1,000 | ... | 1.68 | 59.25 | | 1,000 to 2,000 | ... | 1.55 | 57.25 | | 2,000 to 8,000 | 0.01 | 1.475 | 55.75 | | 8,000 to 14,000 | 0.00134 | 1.70 | 59.50 | +-----------------+------------+-----------------+-----------+
It is remarked by the experimenters that the value of the index [epsilon] is by no means constant, but changes in correspondence with the successive well-marked stages in the process of magnetization. But though a formula of this type has no physical significance, and cannot be accepted as an equation to the actual curve of W and B, it is, nevertheless, the case that by making the index [epsilon] = 1.6, and assigning a suitable value to [eta], a formula may be obtained giving an approximation to the truth which is sufficiently close for the ordinary purposes of electrical engineers, especially when the limiting value of B is neither very great nor very small. Alexander Siemens (_Journ. Inst. Eng._, 1894, 23, 229) states that in the hundreds of comparisons of test pieces which have been made at the works of his firm, Steinmetz's law has been found to be practically correct.[25] An interesting collection of W-B curves embodying the results of actual experiments by Ewing and Klaassen on different specimens of metal is given in fig. 16. It has been shown by Kennelly (_Electrician_, 1892, 28, 666) that Steinmetz's formula gives approximately correct results in the case of nickel. Working with two different specimens, he found that the hysteresis loss in ergs per cubic centimetre (W) was fairly represented by 0.00125B^(1.6) and 0.00101B^(1.6) respectively, the maximum induction ranging from about 300 to 3000. The applicability of the law to cobalt has been investigated by Fleming (_Phil. Mag._, 1899, 48, 271), who used a ring of cast cobalt containing about 96% of the pure metal. The logarithmic curves which accompany his paper demonstrate that within wide ranges of maximum induction W = 0.01B^(1.6) = 0.527I^(1.62) very nearly. Fleming rightly regards it as not a little curious that for materials differing so much as this cast cobalt and soft annealed iron the hysteretic exponent should in both cases be so near to 1.6. After pointing out that, since the magnetization of the metal is the quantity really concerned, W is more appropriately expressed in terms of I, the magnetic moment per unit of volume, than of B, he suggests an experiment to determine whether the mechanical work required to effect the complete magnetic reversal of a crowd of small compass needles (representative of magnetic molecules) is proportional to the 1.6th power of the aggregate maximum magnetic moment before or after completion of the cycle.
The experiments of K. Honda and S. Shimizu[26] indicate that Steinmetz's formula holds for nickel and annealed cobalt up to B = 3000, for cast cobalt and tungsten steel up to B = 8000, and for Swedish iron up to B = 18,000, the range being in all cases extended at the temperature of liquid air.
The diagram, fig. 17, contains examples of ascending induction curves characteristic of wrought iron, cast iron, cobalt and nickel. These are to be regarded merely as typical specimens, for the details of a curve depend largely upon the physical condition and purity of the material; but they show at a glance how far the several metals differ from and resemble one another as regards their magnetic properties. Curves of magnetization (which express the relation of I to H) have a close resemblance to those of induction; and, indeed, since B = H + 4[pi]I, and 4[pi]I (except in extreme fields) greatly exceeds H in numerical value, we may generally, without serious error, put I = B/4[pi], and transform curves of induction into curves of magnetization by merely altering the scale to which the ordinates are referred. A scale for the approximate transformation for the curves in fig. 12 is given at the right-hand side of the diagram, the greatest error introduced by neglecting H/4[pi] not exceeding 0.6%. A study of such curves as these reveals the fact that there are three distinct stages in the process of magnetization. During the first stage, when the magnetizing force is small, the magnetization (or the induction) increases rather slowly with increasing force; this is well shown by the nickel curve in the diagram, but the effect would be no less conspicuous in the iron curve if the abscissae were plotted to a larger scale. During the second stage small increments of magnetizing force are attended by relatively large increments of magnetization, as is indicated by the steep ascent of the curve. Then the curve bends over, forming what is often called a "knee," and a third stage is entered upon, during which a considerable increase of magnetizing force has little further effect upon the magnetization. When in this condition the metal is popularly said to be "saturated." Under increasing magnetizing forces, greatly exceeding those comprised within the limits of the diagram, the magnetization does practically reach a limit, the maximum value being attained with a magnetizing force of less than 2000 for wrought iron and nickel, and less than 4000 for cast iron and cobalt. The induction, however, continues to increase indefinitely, though very slowly. These observations have an important bearing upon the molecular theory of magnetism, which will be referred to later.
The magnetic quality of a sample of iron depends very largely upon the purity and physical condition of the metal. The presence of ordinary impurities usually tends to diminish the permeability, though, as will appear later, the addition of small quantities of certain other substances is sometimes advantageous. A very pure form of iron, which from the method of its manufacture is called "steel," is now extensively used for the construction of dynamo magnets; this metal sometimes contains not more than 0.3% of foreign substances, including carbon, and is magnetically superior to the best commercial wrought iron. The results of some comparative tests published by Ewing (_Proc. Inst. C.E._, 1896) are given in the accompanying table. Those in the second column are quoted from a paper by F. Lydall and A. W. Pocklington (_Proc. Roy. Soc._, 1892, 52, 228) and relate to an exceptional specimen containing nearly 99.9% of the pure metal.
+----------+-----------------------------------------+ | | Magnetic Induction. | | Magnetic +--------+----------+----------+----------+ | Force. | Pure | Low Moor | Steel | Steel | | | Iron. | Iron. | Forging. | Casting. | +----------+--------+----------+----------+----------+ | 5 | 12,700 | 10,900 | 12,300 | 9,600 | | 10 | 14,980 | 13,120 | 14,920 | 13,050 | | 15 | 15,800 | 14,010 | 15,800 | 14,600 | | 20 | 16,300 | 14,580 | 16,280 | 15,310 | | 30 | 16,950 | 15,280 | 16,810 | 16,000 | | 40 | 17,350 | 15,760 | 17,190 | 16,510 | | 50 | .. | 16,060 | 17,500 | 16,900 | | 60 | .. | 16,340 | 17,750 | 17,180 | | 70 | .. | 16,580 | 17,970 | 17,400 | | 80 | .. | 16,800 | 18,180 | 17,620 | | 90 | .. | 17,000 | 18,390 | 17,830 | | 100 | .. | 17,200 | 18,600 | 18,030 | +----------+--------+----------+----------+----------+
To secure the highest possible permeability it is essential that the iron should be softened by careful annealing. When it is mechanically hardened by hammering, rolling or wire-drawing its permeability may be greatly diminished, especially under a moderate magnetizing force. An experiment by Ewing showed that by the operation of stretching an annealed iron wire beyond the limits of elasticity the permeability under a magnetizing force of about 3 units was reduced by as much as 75%. Ewing has also studied the effect of vibration in conferring upon iron an apparent or spurious permeability of high value; this effort also is most conspicuous when the magnetizing force is weak. The permeability of a soft iron wire, which was tapped while subjected to a very small magnetizing force, rose to the enormous value of about 80,000 (_Magnetic Induction_, § 85). It follows that in testing iron for magnetic quality the greatest care must be exercised to guard the specimen against any accidental vibration.
Low hysteresis is the chief requisite for iron which is to be used for transformer cores, and it does not necessarily accompany high permeability. In response to the demand, manufacturers have succeeded in producing transformer plate in which the loss of energy due to hysteresis is exceedingly small. Tests of a sample supplied by Messrs. Sankey were found by Ewing to give the following results, which, however, are regarded as being unusually favourable. In a valuable collection of magnetic data (_Proc. Inst. C.E._, cxxvi.) H. F. Parshall quotes tests of six samples of iron, described as of good quality, which showed an average hysteresis loss of 3070 ergs per c.cm. per cycle at an induction of 8000, being 1.6 times the loss shown by Ewing's specimen at the same induction.
+------------+----------------+-----------------+ | Limits of | Ergs per c.cm. | Watts per lb. | | Induction. | per cycle. | Frequency, 100. | +------------+----------------+-----------------+ | 2000 | 220 | 0.129 | | 3000 | 410 | 0.242 | | 4000 | 640 | 0.376 | | 5000 | 910 | 0.535 | | 6000 | 1200 | 0.710 | | 7000 | 1520 | 0.890 | | 8000 | 1900 | 1.120 | | 9000 | 2310 | 1.360 | +------------+----------------+-----------------+
The standard induction in reference to determinations of hysteresis is generally taken as 2500, while the loss is expressed in watts per lb. at a frequency of 100 double reversals, or cycles, per second. In many experiments, however, different inductions and frequencies are employed, and the hysteresis-loss is often expressed as ergs per cubic centimetre per cycle and sometimes as horse-power per ton. In order to save arithmetical labour it is convenient to be provided with conversion factors for reducing variously expressed results to the standard form. The rate at which energy is lost being proportional to the frequency, it is obvious that the loss at frequency 100 may be deduced from that at any other frequency n by simply multiplying by 100/n. Taking the density of iron to be 7.7, the factor for reducing the loss in ergs per c.cm. to watts per lb. with a frequency of 100 is 0.000589 (Ewing). Since 1 horse-power = 746 watts, and 1 ton = 2240 lb., the factor for reducing horse-power per ton to watts per lb. is 746/2240, or just 1/3. The loss for any induction B within the range for which Steinmetz's law holds may be converted into that for the standard induction 2500 by dividing it by B^(1.6)/2500^(1.6). The values of this ratio for different values of B, as given by Fleming (_Phil. Mag._, 1897), are contained in the second column of the annexed table. The third column shows the relative amount of hysteresis deduced by Ewing as a general mean from actual tests of many samples (_Journ. Inst. Elec. Eng._, 1895). Incidentally, these two columns furnish an undesigned test of the accuracy of Steinmetz's law: the greatest difference is little more than 1%.
+-----------+------------+-------------+ | Induction | B^(1.6) | Observed | | B. | ---------- | relative | | | 2500^(1.6) | Hysteresis. | +-----------+------------+-------------+ | 2000 | 0.700 | 0.702 | | 2500 | 1.000 | 1.000 | | 3000 | 1.338 | 1.340 | | 4000 | 2.118 | 2.128 | | 5000 | 3.031 | 3.000 | | 6000 | 4.058 | 4.022 | | 7000 | 5.193 | 5.129 | | 8000 | 6.430 | 6.384 | +-----------+------------+-------------+
_Curves of Permeability and Susceptibility._--The relations of µ (= B/H) to B, and of [kappa] (= I/H) to I may be instructively exhibited by means of curves, a method first employed by H. A. Rowland.[27] The dotted curve for µ and B in fig. 18 is copied from Rowland's paper. The actual experiment to which it relates was carried only as the point marked X, corresponding to a magnetizing force of 65, and an induction of nearly 17,000. Rowland, believing that the curve would continue to fall in a straight line meeting the horizontal axis, inferred that the induction corresponding to the point B--about 17,500--was the highest that could be produced by any magnetizing force, however great. It has, however, been shown that, if the magnetizing force is carried far enough, the curve always becomes convex to the axis instead of meeting it. The full line shows the result of an experiment in which the magnetizing force was carried up to 585,[28] but though the force was thus increased ninefold, the induction only reached 19,800, and the ultimate value of the permeability was still as much as 33.9.
_Ballistic Method with Yoke._--J. Hopkinson (_Phil. Trans._, 1885, 176, 455) introduced a modification of the usual ballistic arrangement which presents the following advantages; (1) very considerable magnetizing forces can be applied with ordinary means; (2) the samples to be tested, having the form of cylindrical bars, are more easily prepared than rings or wires; (3) the actual induction at any time can be measured, and not only changes of induction. On the other hand, a very high degree of accuracy is not claimed for the results. Fig. 19 shows the apparatus by which the ends of the bar are prevented from exerting any material demagnetizing force, while the permeance of the magnetic circuit is at the same time increased. A A, called the "yoke," is a block of annealed wrought iron about 18 in. long, 6½ in. wide and 2 in. thick, through which is cut a rectangular opening to receive the two magnetizing coils B B. The test bar C C, which slides through holes bored in the yoke, is divided near the middle into two parts, the ends which come into contact being faced true and square. Between the magnetizing coils is a small induction coil D, which is connected with a ballistic galvanometer. The induction coil is carried upon the end of one portion of the test bar, and when this portion is suddenly drawn back the coil slips off and is pulled out of the field by an india-rubber spring. This causes a ballistic throw proportional to the induction through the bar at the moment when the two portions were separated. With such an arrangement it is possible to submit the sample to any series of magnetic forces, and to measure its magnetic state at the end. The uncertainty with which the results are affected depends chiefly upon the imperfect contact between the bar and the yoke and also between the ends of the divided bar. It is probable that Hopkinson did not attach sufficient importance to the demagnetizing action of the cut (cf. Ewing, _Phil. Mag._, Sept. 1888, p. 274), and that the values which he assigned to H are consequently somewhat too high. He applied his method with good effect, however, in testing a large number of commercial specimens of iron and steel, the magnetic constants of which are given in a table accompanying his paper. When it is not required to determine the residual magnetization there is no necessity to divide the sample bar, and ballistic tests may be made in the ordinary way--by steps or by reversals--the source of error due to the transverse cut thus being avoided. Ewing (_Magnetic Induction_, § 194) has devised an arrangement in which two similar test bars are placed side by side; each bar is surrounded by a magnetizing coil, the two coils being connected to give opposite directions of magnetization, and each pair of ends is connected by a short massive block of soft iron having holes bored through it to fit the bars, which are clamped in position by set-screws. Induction coils are wound on the middle parts of both bars, and are connected in series. With this arrangement it is possible to find the actual value of the magnetizing force, corrected for the effects of joints and other sources of error. Two sets of observations are taken, one when the blocks are fixed at the ends of the bars, and another when they are nearer together, the clear length of the bars between them and of the magnetizing coils being reduced to one-half. If H1 and H2 be the values of 4[pi]in/l and 4[pi]i´[(n/2) / (l/2)] for the same induction B, it can be shown that the true magnetizing force is H = H1 - (H2 - H1). The method, though tedious in operation, is very accurate, and is largely employed for determining the magnetic quality of bars intended to serve as standards.
_Traction Methods._--The induction of the magnetization may be measured by observing the force required to draw apart the two portions of a divided rod or ring when held together by their mutual attraction. If a transverse cut is made through a bar whose magnetization is I and the two ends are placed in contact, it can be shown that this force is 2[pi]I² dynes per unit of area (Mascart and Joubert, _Electricity and Magnetism_, § 322); and if the magnetization of the bar is due to an external field H produced by a magnetizing coil or otherwise, there is an additional force equal to HI. Thus the whole force, when the two portions of the bar are surrounded by a loosely-fitting magnetizing coil, is
F = 2[pi]I² + HI
expressed as dynes per square centimetre. If each portion of the bar has an independent magnetizing coil wound tightly upon it, we have further to take into account the force due to the mutual action of the two magnetizing coils, which assists the forces already considered. This is equal to H²8[pi] per unit of sectional area. In the case supposed therefore the total force per square centimetre is
H² F = 2[pi]I² + HI + ----- 8[pi]
(4[pi]I + H)³ = ------------- 8[pi]
B² = -----. 8[pi]
The equation F = B²/8[pi] is often said to express "Maxwell's law of magnetic traction" (Maxwell, _Electricity and Magnetism_, §§ 642-646). It is, of course, true for permanent magnets, where H = 0, since then F = 2[pi]I²; but if the magnetization is due to electric currents, the formula is only applicable in the special case when the mutual action of the two magnets upon one another is supplemented by the electromagnetic attraction between separate magnetizing coils rigidly attached to them.[29]
The traction method was first employed by S. Bidwell (_Proc. Roy. Soc._, 1886, 40, 486), who in 1886 published an account of some experiments in which the relation of magnetization to magnetic field was deduced from observations of the force in grammes weight which just sufficed to tear asunder the two halves of a divided ring electromagnet when known currents were passing through the coils. He made use of the expression
F = Wg = 2[pi]I² + HI,
where W is the weight in grammes per square centimetre of sectional area, and g is the intensity of gravity which was taken as 981. The term for the attraction between the coils was omitted as negligibly small (see _Phil. Mag._, 1890, 29, 440). The values assigned to H were calculated from H = 2ni/r, and ranged from 3.9 to 585, but inasmuch as no account was taken of any demagnetizing action which might be due to the two transverse cuts, it is probable that they are somewhat too high. The results, nevertheless, agree very well with those for annealed wrought iron obtained by other methods. Below is given a selection from Bidwell's tables, showing corresponding values of magnetizing force, weight supported, magnetization, induction, susceptibility and permeability:--
+--------+---------+-------+--------+----------+--------+ | H. | W. | I. | B. | [kappa]. | µ. | +--------+---------+-------+--------+----------+--------+ | 3.9 | 2,210 | 587 | 7,390 | 151.0 | 1889.1 | | 5.7 | 3,460 | 735 | 9,240 | 128.9 | 1621.3 | | 10.3 | 5,400 | 918 | 11,550 | 89.1 | 1121.4 | | 22.2 | 8,440 | 1147 | 14,450 | 51.7 | 650.9 | | 40 | 9,680 | 1226 | 15,460 | 30.7 | 386.4 | | 115 | 12,170 | 1370 | 17,330 | 11.9 | 150.7 | | 208 | 13,810 | 1452 | 18,470 | 7.0 | 88.8 | | 362 | 14,740 | 1489 | 19,080 | 4.1 | 52.7 | | 465 | 15,275 | 1508 | 19,420 | 3.2 | 41.8 | | 585 | 15,905 | 1530 | 19,820 | 2.6 | 33.9 | +--------+---------+-------+--------+----------+--------+
A few months later R. H. M. Bosanquet (_Phil. Mag._, 1886, 22, 535) experimented on the relation of tractive force to magnetic induction. Instead of a divided ring he employed a divided straight bar, each half of which was provided with a magnetizing coil. The joint was surrounded by an induction coil connected with a ballistic galvanometer, an arrangement which enabled him to make an independent measurement of the induction at the moment when the two portions of the bar were separated. He showed that there was, on the whole, a fair agreement between the values determined ballistically and those given by the formula B = [root](8[pi]F). The greatest weight supported in the experiments was 14,600 grammes per square cm., and the corresponding induction 18,500 units. Taylor Jones subsequently found a good agreement between the theoretical and the observed values of the tractive force in fields ranging up to very high intensities (_Phil. Mag._, 1895, 39, 254, and 1896, 41, 153).
_Permeameters._--Several instruments in which the traction method is applied have been devised for the rapid measurement of induction or of magnetization in commercial samples of iron and steel. The earliest of these is S. P. Thompson's _permeameter_ (_Journ. Sci. Arts_, 1890, 38, 885), which consists of a rectangular block of iron shaped like Hopkinson's yoke, and slotted out in the same way to receive a magnetizing coil (fig. 20); the block is bored through at the upper end only, and its inner face opposite the hole is made quite flat and smooth. The sample has the form of a thin rod, one end of which is faced true; it is slipped into the magnetizing coil from above, and when the current is turned on its smooth end adheres tightly to the surface of the yoke. The force required to detach it is measured by a registering spring balance, which is clamped to the upper end of the rod, and thence the induction or the magnetization is deduced by applying the formula
(B - H)²/8[pi] = 2[pi]I² = Pg/S,
where P is the pull in grammes weight, S the sectional area of the rod in square cm., and g = 981. If the pull is measured in pounds and the area in square inches, the formula may be written B = 1317 × [root](P/S) + H. The instrument exhibited by Thompson would, without undue heating, take a current of 30 amperes, which was sufficient to produce a magnetizing force of 1000 units. A testing apparatus of a similar type devised by Gisbert Kapp (_Journ. Inst. Elec. Eng._ xxiii. 199) differs only in a few details from Thompson's permeameter. Ewing has described an arrangement in which the test bar has a soft-iron pole piece clamped to each of its ends; the pole pieces are joined by a long well-fitting block of iron, which is placed upon them (like the "keeper" of a magnet), and the induction is measured by the force required to detach the block. In all such measurements a correction should be made in respect of the demagnetizing force due to the joint, and unless the fit is very accurate the demagnetizing action will be variable. In the _magnetic balance_ of du Bois (_Magnetic Circuit_, p. 346) the uncertainty arising from the presence of a joint is avoided, the force measured being that exerted between two pieces of iron separated from each other by a narrow air-gap of known width. The instrument is represented diagrammatically in fig. 21. The test-piece A, surrounded by a magnetizing coil, is clamped between two soft-iron blocks B, B´. Y Y´ is a soft iron yoke, which rocks upon knife-edges K and constitutes the beam of the balance. The yoke has two projecting pieces C, C´ at unequal distances from the knife-edges, and separated from the blocks B, B´ by narrow air-gaps. The play of the beam is limited by a stop S and a screw R, the latter being so adjusted that when the end Y of the beam is held down the two air-gaps are of equal width. W is a weight capable of sliding from end to end of the yoke along a graduated scale. When there is no magnetization, the yoke is in equilibrium; but as soon as the current is turned on the block C is drawn downwards as far as the screw R will allow, for, though the attractive forces F between B and C and between B´ and C´ are equal, the former has a greater moment. The weight W is moved along the scale until the yoke just tilts over upon the stop S; the distance of W from its zero position is then, as can easily be shown, proportional to F, and therefore to B², and approximately to I². The scale is graduated in such a manner that by multiplying the reading by a simple factor (generally 10 or 2) the absolute value of the magnetization is obtained. The actual magnetizing force H is of course less than that due to the coil; the corrections required are effected automatically by the use of a set of demagnetization lines drawn on a sheet of celluloid which is supplied with the instrument. The celluloid sheet is laid upon the squared paper, and in plotting a curve horizontal distances are reckoned from the proper demagnetization line instead of from the vertical axis. An improved but somewhat more complex form of the instrument is described in _Ann. d. Phys._, 1900, 2, 317.
In Ewing's _magnetic balance_ (_Journ. Inst. Elec. Eng._ 1898, 27, 526), the value of the magnetic induction corresponding to a single stated magnetizing force is directly read off on a divided scale. The specimen, which has the form of a turned rod, 4 in. long and ¼ in. in diameter, is laid across the poles of a horseshoe electromagnet, excited by a current of such strength as to produce in the rod a magnetizing force H = 20. One pole has a V-shaped notch for the rod to rest in; the surface of the other is slightly rounded, forming a portion of a cylinder, the axis of which is perpendicular to the direction of the length of the rod. The rod touches this pole at a single point, and is pulled away from it by the action of a lever, the long arm of which is graduated and carries a sliding weight. The position of the weight at the moment when contact is broken indicates the induction in the rod. The standard force H = 20 was selected as being sufficiently low to distinguish between good and bad specimens, and at the same time sufficiently high to make the order of merit the same as it would be under stronger forces.
_Permeability Bridges._--Several pieces of apparatus have been invented for comparing the magnetic quality of a sample with that of a standard iron rod by a zero method, such as is employed in the comparison of electrical resistances by the Wheatstone bridge. An excellent instrument of the class is Ewing's _permeability bridge_. The standard rod and the test specimen, which must be of the same dimensions, are placed side by side within two magnetizing coils, and each pair of adjacent ends is joined by a short rectangular block or "yoke" of soft iron. An iron bar shaped like an inverted L projects upwards from each of the yokes, the horizontal portions of the bars being parallel to the rods, and nearly meeting at a height of about 8 in. above them (thus [symbol]). A compass needle placed in the gap serves to detect any flow of induction that may exist between the bent bars. For simplicity of calculation, the clear length of each rod between the yokes is made 12.56 (= 4[pi]) centimetres, while the coil surrounding the standard bar contains 100 turns; hence the magnetizing force due to a current of n amperes will be 10n C.G.S. units. The effective number of turns in the coil surrounding the test rod can be varied by means of three dial switches (for hundreds, tens and units), which also introduce compensating resistances as the number of effective turns in the coil is reduced, thus keeping the total resistance of the circuit constant. The two coils are connected in series, the same current passing through both. Suppose the switches to be adjusted so that the effective number of turns in the variable coil is 100; the magnetizing forces in the two coils will then be equal, and if the test rod is of the same quality as the standard, the flow of induction will be confined entirely to the iron circuit, the two yokes will be at the same magnetic potential, and the compass needle will not be affected. If, however, the permeability of the test rod differs from that of the standard, the number of lines of induction flowing in opposite directions through the two rods will differ, and the excess will flow from one yoke to the other, partly through the air, and partly along the path provided by the bent bars, deflecting the compass needle. But a balance may still be obtained by altering the effective number of turns in the test coil, and thus increasing or decreasing the magnetizing force acting on the test rod, till the induction in the two rods is the same, a condition which is fulfilled when reversal of the current has no effect on the compass needle. Let m be the number of turns in use, and H1 and H2 the magnetizing forces which produce the same induction B in the test and the standard rods respectively; then H1 = H2 × m/100. The value of B which corresponds to H2m/100 can be found from the (B, H) curve for the standard, which is assumed to have been determined; and this same value corresponds to the force H in the case of the test bar. Thus any desired number of corresponding values of H and B can be easily and quickly found.
_Measurement of Field Strength. Exploring Coil._--Since in air B = H, the ballistic method of measuring induction described above is also available for determining the strength of a magnetic field, and is more often employed than any other. A small coil of fine wire, connected in series with a ballistic galvanometer, is placed in the field, with its windings perpendicular to the lines of force, and then suddenly reversed or withdrawn from the field, the integral electromotive force being twice as great in the first case as in the second. The strength of the field is proportional to the swing of the galvanometer-needle, and, when the galvanometer is calibrated, can be expressed in C.G.S. units. Convenient arrangements have been introduced whereby the coil is reversed or withdrawn from the field by the action of a spring.
_Bismuth Resistance._--The fact, which will be referred to later, that the electrical resistance of bismuth is very greatly affected by a magnetic field has been applied in the construction of apparatus for measuring field intensity. A little instrument, supplied by Hartmann and Braun, contains a short length of fine bismuth wire wound into a flat double spiral, half an inch or thereabouts in diameter, and attached to a long ebonite handle. Unfortunately the effects of magnetization upon the specific resistance of bismuth vary enormously with changes of temperature; it is therefore necessary to take two readings of the resistance, one when the spiral is in the magnetic field, the other when it is outside.
_Electric Circuit._--If a coil of insulated wire is suspended so that it is in stable equilibrium when its plane is parallel to the direction of a magnetic field, the transmission of a known electric current through the coil will cause it to be deflected through an angle which is a function of the field intensity.
One of the neatest applications of this principle is that described by Edser and Stansfield (_Phil. Mag._, 1893, 34, 186), and used by them to test the stray fields of dynamos. An oblong coil about an inch in length is suspended from each end by thin strips of rolled German silver wire, one of which is connected with a spiral spring for regulating the tension, the other being attached to a torsion-head. Inside the torsion-head is a commutator for automatically reversing the current, so that readings may be taken on each side of zero, and the arrangement is such that when the torsion-head is exactly at zero the current is interrupted. To take a reading the torsion-head is turned until an aluminium pointer attached to the coil is brought to the zero position on a small scale; the strength of the field is then proportional to the angular torsion. The small current required is supplied to the coil from a single dry cell. The advantages of portability, very considerable range (from H = 1 upwards), and fair accuracy are claimed for the instrument.
_Polarized Light._--The intensity of a field may be measured by the rotation of the plane of polarization of light passing in the direction of the magnetic force through a transparent substance. If the field is uniform, H = [theta]/[omega]d, where [theta] is the rotation, d the thickness of the substance arranged as a plate at right angles to the direction of the field, and [omega] Verdet's constant for the substance.
For the practical measurement of field intensity du Bois has used plates of the densest Jena flint glass. These are preferably made slightly wedge-shape, to avoid the inconvenience resulting from multiple internal reflections, and they must necessarily be rather thin, so that double refractions due to internal strain may not exert a disturbing influence. Since Verdet's constant is somewhat uncertain for different batches of glass even of the same quality, each plate should be standardized in a field of known intensity. As the source of monochromatic light a bright sodium burner is used, and the rotation, which is exactly proportional to H, is measured by an accurate polarimeter. Such a plate about 1 mm. in thickness is said to be adapted for measuring fields of the order of 1000 units. A part of one surface of the plate may be silvered, so that the polarized ray, after having once traversed the glass, is reflected back again; the rotation is thus doubled, and moreover, the arrangement is, for certain experiments, more convenient than the other.
4. MAGNETIZATION IN STRONG FIELDS
_Fields due to Coils._--The most generally convenient arrangement for producing such magnetic fields as are required for experimental purposes is undoubtedly a coil of wire through which an electric current can be caused to flow. The field due to a coil can be made as nearly uniform as we please throughout a considerable space; its intensity, when the constants of the coil are known, can be calculated with ease and certainty and may be varied at will through wide ranges, while the apparatus required is of the simplest character and can be readily constructed to suit special purposes. But when exceptionally strong fields are desired, the use of a coil is limited by the heating effect of the magnetizing current, the quantity of heat generated per unit of time in a coil of given dimensions increasing as the square of the magnetic field produced in its interior. In experiments on magnetic strains carried out by H. Nagaoka and K. Honda (_Phil. Mag._, 1900, 49, 329) the intensity of the highest field reached in the interior of a coil was 2200 units; this is probably the strongest field produced by a coil which has hitherto been employed in experimental work. In 1890 some experiments in which a coil was used were made by du Bois (_Phil. Mag._, 1890, 29, 253, 293) on the magnetization of iron, nickel, and cobalt under forces ranging from about 100 to 1250 units. Since the demagnetizing factor was 0.052, the strongest field due to the coil was about 1340; but though arrangements were provided for cooling the apparatus by means of ice, great difficulty was experienced owing to heating. Du Bois's results, which, as given in his papers, show the relation of H to the magnetic moment per unit of mass, have been reduced by Ewing to the usual form, and are indicated in fig. 22, the earlier portions of the curves being sketched in from other data.
_Fields due to Electromagnets._--The problem of determining the magnetization of iron and other metals in the strong fields formed between the poles of an electromagnet was first attacked by J. A. Ewing and W. Low. An account of their preliminary experiments by what they call the _isthmus method_ was published in 1887 (_Proc. Roy. Soc._ 42, 200), and in the following year they described a more complete and perfect series (_Phil. Trans._, 1889, 180, 221).
The sample to be inserted between the magnet poles was prepared in the form of a bobbin resembling an ordinary cotton reel, with a short narrow neck (constituting the "isthmus") and conical ends. Upon the central neck was wound a coil consisting of one or two layers of very fine wire, which was connected with a ballistic galvanometer for measuring the induction in the iron; outside this coil, and separated from it by a small and accurately determined distance, a second coil was wound, serving to measure the induction in the iron, together with that in a small space surrounding it. The difference of the ballastic throws taken with the two coils measured the intensity of the field in the space around the iron, and it also enabled a correction to be made for the non-ferrous space between the iron neck and the centre of the thickness of the inner coil. The pole pieces of the electromagnet (see fig. 23) were furnished with a pair of truncated cones _b b_, of soft iron forming an extension of the conical ends of the bobbin c. The most suitable form for the pole faces is investigated in the paper, and the conclusion arrived at is that to produce the greatest concentration of force upon the central neck, the cones should have a common vertex in the middle of the neck with a semi-vertical angle of 54° 44´, while the condition for a uniform field is satisfied when the cones have a semi-vertical angle of 39° 14´; in the latter case the magnetic force in the air just outside is sensibly equal to that within the neck. A pair of cones having a semi-vertical angle of 45° were considered to combine high concentrative power with a sufficient approximation to uniformity of field. In most of the experiments the measurements were made by suddenly withdrawing the bobbin from its place between the pole pieces. Two groups of observations were recorded, one giving the induction in the inner coil and the other that in the outer coil. The value of the residual induction which persisted when the bobbin was drawn out was added to that of the induction measured, and thus the total induction in the iron was determined. The highest induction reached in these experiments was 45,350 units, more than twice the value of any previously recorded. The corresponding intensity of the outside field was 24,500, but, owing to the wide angle of the cones used (about 2 × 63°), this was probably greater than the value of the magnetic force within the metal. The following table shows some results of other experiments in which H was believed to have sensibly the same value inside as outside the metal. Values of I are derived from (B - H)/4[pi] and of µ from B/H.
+--------------+--------+--------+------+-------+ | Metal. | H | B | I | µ | +--------------+--------+--------+------+-------+ | | 1,490 | 22,650 | 1680 | 15.20 | | | 6,070 | 27,130 | 1680 | 4.47 | | Swedish Iron | 8,600 | 30,270 | 1720 | 3.52 | | | 19,450 | 40,820 | 1700 | 2.10 | | | 19,880 | 41,140 | 1700 | 2.07 | +--------------+--------+--------+------+-------+ | | 4,560 | 20,070 | 1230 | 4.40 | | Cast Iron | 13,460 | 28,710 | 1210 | 2.13 | | | 16,200 | 30,920 | 1170 | 1.91 | | | 16,900 | 31,760 | 1180 | 1.88 | +--------------+--------+--------+------+-------+ | | 6,210 | 25,480 | 1530 | 4.10 | | | 9,970 | 29,650 | 1570 | 2.97 | | Tool Steel | 12,170 | 31,620 | 1550 | 2.60 | | | 14,660 | 34,550 | 1580 | 2.36 | | | 15,530 | 35,820 | 1610 | 2.31 | +--------------+--------+--------+------+-------+ | | 2,220 | 7,100 | 390 | 3.20 | | | 4,440 | 9,210 | 380 | 2.09 | | Hard Nickel | 7,940 | 12,970 | 400 | 1.63 | | | 14,660 | 19,640 | 400 | 1.34 | | | 16,000 | 21,070 | 400 | 1.32 | +--------------+--------+--------+------+-------+ | | 1,350 | 16,000 | 1260 | 12.73 | | Cobalt | 4,040 | 18,870 | 1280 | 4.98 | | | 8,930 | 23,890 | 1290 | 2.82 | | | 14,990 | 30,210 | 1310 | 2.10 | +--------------+--------+--------+------+-------+
These results are of extreme interest, for they show that under sufficiently strong magnetizing forces the intensity of magnetization I reaches a maximum value, as required by W. E. Weber's theory of molecular magnetism. There appears to be no definite limit to the value to which the induction B may be raised, but the magnetization I attains a true saturation value under magnetizing forces which are in most cases comparatively moderate. Thus the magnetization which the sample of Swedish iron received in a field of 1490 was not increased (beyond the limits of experimental error) when the intensity of the field was multiplied more than thirteen-fold, though the induction was nearly doubled. When the saturation value of I has been reached, the relation of magnetic induction to magnetic force may be expressed by
B = H + constant.
The annexed table gives the saturation values of I for the particular metals examined by Ewing and Low:--
Saturation Value of I
Wrought iron 1,700 Cast iron 1,240 Nickel (0.75% iron) 515 " (0.56% " ) 400 Cobalt (1.66% " ) 1,300
It is shown in the paper that the greatest possible force which the isthmus method can apply at a point in the axis of the bobbin is
F = 11.137 I_s log 10 b/a,
I_s being the saturation value of the magnet poles, a the radius of the neck on which the cones converge, and b the radius of the bases of the cones.
Some experiments made by H. du Bois (_Phil. Mag._, 1890, 29, 293) with an electromagnet specially designed for the production of strong fields, confirm Ewing's results for iron, nickel and cobalt. The method employed did not admit of the production of such high magnetizing forces, but was of special interest in that both B and I were measured optically--B by means of the rotation of a polarized ray inside a glass plate, as before described, and I by the rotation of a polarized ray reflected from the polished surface of the magnetized metal (see "Kerr's constant," MAGNETO-OPTICS). H(= B - 4[pi]I) was calculated from corresponding values of I and B. Taylor Jones (_Wied. Ann._, 1896, 57, 258, and _Phil. Mag._, 1896, 41, 153), working with du Bois's electromagnet and using a modification of the isthmus method, succeeded in pushing the induction B up to 74,200 with H = 51,600, the corresponding value of I being 1798, and of µ only 1.44. The diameter of the isthmus was 0.241 mm., and the electromagnet was excited by a current of 40 amperes.
_Tractive Force of a Magnet._--Closely connected with the results just discussed is the question what is the greatest tractive force that can be exerted by a magnet. In the year 1852 J. P. Joule (_Phil. Mag._, 1852, 3, 32) expressed the opinion that no "force of current could give an attraction equal to 200 lb. per sq. in.," or 14,000 grms. per square centimetre, and a similar view prevailed among high authorities more than twenty years later. For the greatest possible "lifting power" of permanent magnets this estimate is probably not very far from the truth, but it is now clearly understood that the force which can be exerted by an electromagnet, or by a pair of electromagnets with opposite poles in contact, is only limited by the greatest value to which it is practically possible to raise the magnetizing force H. This is at once evident when the tractive force due to magnetization is expressed as 2[pi]I²+ HI. For fields of moderate intensity the first term of the expression is the more important, but when the value of H exceeds 12,000 or thereabouts, the second preponderates, and with the highest values that have been actually obtained, HI is several times greater than 2[pi]I². If H could be increased without limit, so also could the tractive force. The following table shows the greatest "lifting powers" experimentally reached at the dates mentioned:--
+-----------+-----------+---------+------+ | Observer. | Kilos per | lb. per | Date.| | | sq. cm. | sq. in. | | +-----------+-----------+---------+------+ | Joule | 12.3 | 175 | 1852 | | Bidwell | 15.9 | 226 | 1886 | | Wilde | 26.8 | 381 | 1891 | | T. Jones | 114.9 | 1634 | 1896 | +-----------+-----------+---------+------+
5. MAGNETIZATION IN VERY WEAK FIELDS
Some interesting observations have been made of the effects produced by very small magnetic forces. It was first pointed out by C. Baur (_Wied. Ann._, 1880, 11, 399) that in weak fields the relation of the magnetization I to the magnetizing force H is approximately expressed by an equation of the form
I = aH + bH²,
or
[kappa] = I/H = a + bH,
whence it appears that within the limits of Baur's experiments the magnetization curve is a parabola, and the susceptibility curve an inclined straight line, [kappa] being therefore a known function of H. If these equations could be assumed to hold when H is indefinitely small, it would follow that [kappa] has a finite initial value, from which there would be no appreciable deviation in fields so weak that bH was negligibly small in comparison with a. Such an assumption could not, however, without dangerous extrapolation, be founded upon the results of Baur's experiments, which did not go far enough to justify it. In some experiments carried out in 1887, Lord Rayleigh (_Phil. Mag._, 1887, 23, 225) approached very much more nearly than Baur to the zero of magnetic force. Using an unannealed Swedish iron wire, he found that when H was gradually diminished from 0.04 to 0.00004 C.G.S. unit, the ratio of magnetization to magnetizing force remained sensibly constant at 6.4, which may therefore with great probability be assumed to represent the initial value of [kappa] for the specimen in question. Experiments with annealed iron gave less satisfactory results, on account of the slowness with which the metal settled down into a new magnetic state, thus causing a "drift" of the magnetometer needle, which sometimes persisted for several seconds. Apart from this complication, it appeared that I was proportional to H when the value of H was less than 0.02.
The observations of Baur and Rayleigh have been confirmed and discussed by (amongst others) W. Schmidt (_Wied. Ann._, 1895, 54, 655), who found the limiting values of [kappa] to be 7.5 to 9.5 for iron, and 11.2 to 13.5 for steel, remaining constant up to H = .06; by P. Culmann (_Elekt. Zeit._, 1893, 14, 345; _Wied. Ann._, 1895, 56, 602); and by L. Holborn (_Berl. Ber._, 1897, p. 95, and _Wied. Ann._, 1897, 61, 281). The latter gives values of the constants a and b for different samples of iron and steel, some of which are shown in the following table:--
[kappa] = a + bH
Metal. a b
English tungsten steel 8.90 0.264 Tungsten steel, hardened 2.23 0.032 Silver steel 8.66 0.384 Tool steel 8.30 0.400 Refined steel 11.28 1.92 Cast iron 3.16 0.236 Soft iron 16.6 18.6 Hard drawn iron 5.88 1.76
For most samples of steel the straight-line law was found to hold approximately up to H = 3; in the case of iron and of soft steel the approximation was less close.
The behaviour of nickel in weak fields has been observed by Ewing (_Phil. Trans._, 1888, 179A, 325), who found that the initial value of [kappa] was 1.7, and that it remained sensibly constant until H had reached a value of about five units. While therefore the initial susceptibility of nickel is less than that of iron and steel, the range of magnetic force within which it is approximately constant is about one hundred times greater. Ewing has also made a careful study (_Proc. Roy. Soc._, 1889, 46, 269) of "magnetic viscosity" under small forces--the cause of the magnetometer "drift" referred to by Rayleigh. On the application of a small magnetizing force to a bar of soft annealed iron, a certain intensity of magnetization is instantly produced; this, however, does not remain constant, but slowly increases for some seconds or even minutes, and may ultimately attain a value nearly twice as great as that observed immediately after the force was applied.[30] When the magnetizing current is broken, the magnetization at once undergoes considerable diminution, then gradually falls to zero, and a similar sudden change followed by a slow one is observed when a feeble current is reversed. Ewing draws attention to a curious consequence of this time-lag. By the alternate application and withdrawal of a small magnetizing force a cyclic condition may be established in an iron rod. If now the alternations are performed so rapidly that time is not allowed for more than the first sudden change in the magnetization, there will be no hysteresis loss, the magnetization exactly following the magnetizing force. Further, if the alternations take place so slowly that the full maximum and minimum values of the magnetization are reached in the intervals between the reversals, there will again be no dissipation of energy. But at any intermediate frequency the ascending and descending curves of magnetization will enclose a space, and energy will be dissipated. It is remarkable that the phenomena of magnetic viscosity are much more evident in a thick rod than in a thin wire, or even in a large bundle of thin wires. In hardened iron and steel the effect can scarcely be detected, and in weak fields these metals exhibit no magnetic hysteresis of any kind.
6. CHANGES OF DIMENSIONS ATTENDING MAGNETIZATION
It is well known that the form of a piece of ferromagnetic metal is in general slightly changed by magnetization. The phenomenon was first noticed by J. P. Joule, who in 1842 and 1847 described some experiments which he had made upon bars of iron and steel. His observations, were for the most part confirmed by a number of subsequent workers, notably by A. M. Mayer; but with the single exception of the discovery by W. F. Barrett in 1882 that a nickel bar contracts when magnetized, nothing of importance was added by Joule's results for nearly forty years. Later researches have however thrown much new light upon a class of phenomena which cannot fail to have an important bearing upon the complete theory of molecular magnetism.[31] According to Joule's observations, the length of a bar of iron or soft steel was increased by magnetization, the elongation being proportional up to a certain point to the square of the intensity of magnetization; but when the "saturation point" was approached the elongation was less than this law would require, and a stage was finally reached at which further increase of the magnetizing force produced little or no effect upon the length. From data contained in Joule's paper it may be calculated that the strongest external field H0 produced by his coil was about 126 C.G.S. units, but since the dimensional ratio of his bars was comparatively small, the actual magnetizing force H must have been materially below that value. In 1885 it was shown by Bidwell, in the first of a series of papers on the subject, that if the magnetizing force is pushed beyond the point at which Joule discontinued his experiments, the extension of the bar does not remain unchanged, but becomes gradually less and less, until the bar, after first returning to its original length, ultimately becomes actually shorter than when in the unmagnetized condition. The elongation is generally found to reach a maximum under a magnetizing force of 50 to 120 units, and to vanish under a force of 200 to 400, retraction occurring when still higher forces are applied. In order to meet the objection that the phenomenon might be due to electromagnetic action between the coil and the rod, Bidwell made some experiments with iron rings, and found that the length of their diameters varied under magnetization in precisely the same manner as the length of a straight rod. Experiments were afterwards made with rods of iron, nickel, and cobalt, the external field being carried up to the high value of 1500 units. The results are indicated in Fig. 24. It appears that the contraction which followed the initial extension of the iron reached a limit in fields of 1000 or 1100. Nickel exhibited retraction from the very beginning (as observed by Barrett), its greatest change of length considerably exceeding that undergone by iron; in a field of 800 the original length was diminished by as much as 1/40,000 part, but stronger forces failed to produce any further effect. The curve for cobalt is a very remarkable one. Little or no change of length was observed until the strength of the field H0 reached about 50; then the rod began to contract, and after passing a minimum at H0 = 400, recovered its original length at H0 = 750; beyond this point there was extension, the amount of which was still increasing fast when the experiment was stopped at H0 = 1400. Similar results were obtained with three different samples of the metal. Roughly speaking, therefore, cobalt behaves oppositely to iron.
Joule and others experimented with hardened steel, but failed to find a key to the results they obtained, which are rather complex, and have been thought to be inconsistent. The truth appears to be that a hardened steel rod generally behaves like one of iron or soft steel in first undergoing extension under increasing magnetizing force, and recovering its original length when the force has reached a certain critical value, beyond which there is contraction. But this "critical value" of the force is found to depend in an unexpected manner upon the hardness of the steel; the critical value diminishes as the hardness becomes greater _up to a certain point_, corresponding to a yellow temper, after which it increases and with the hardest steel becomes very high. For steel which has been made red-hot, suddenly cooled, and then let down to a yellow temper, the critical value of the magnetizing force is smaller than for steel which is either softer or harder; it is indeed so small that the metal contracts like nickel even under weak magnetizing forces, without undergoing any preliminary extension that can be detected.
Joule also made experiments upon iron wires under tension, and drew the erroneous inference (which has been often quoted as if it were a demonstrated fact) that under a certain critical tension (differing for different specimens of iron but independent of the magnetizing force) magnetization would produce no effect whatever upon the dimensions of the wire. What actually happens when an iron wire is loaded with various weights is clearly shown in Fig. 25. Increased tension merely has the effect of diminishing the maximum elongation and hastening the contraction; with the two greatest loads used in the experiment there was indeed no preliminary extension at all.[32] The effects of tension upon the behaviour of a nickel wire are of a less simple character. In weak fields the magnetic contraction is always diminished by pulling stress; in strong fields the contraction increases under a small load and diminishes under a heavy one. Cobalt, curiously enough, was found to be quite unaffected by tensile stress.
Certain experiments by C. G. Knott on magnetic twist, which will be referred to later, led him to form the conclusion that in an iron wire carrying an electric current the magnetic elongation would be increased. This forecast was shown by Bidwell to be well founded. The effect produced by a current is exactly opposite to that of tension, raising the elongation curve instead of depressing it. In the case of a wire 0.75 mm. in diameter the maximum elongation was nearly doubled when a current of two amperes was passing through the iron, while the "critical value" of the field was increased from 130 to 200. Yet notwithstanding this enormous effect in iron, the action of a current upon nickel and cobalt turned out to be almost inappreciable.
Some experiments were next undertaken with the view of ascertaining how far magnetic changes of length in iron were dependent upon the hardness of the metal, and the unexpected result was arrived at that softening produces the same effect as tensile stress; it depresses the elongation curve, diminishing the maximum extension, and reducing the "critical value" of the magnetizing force. A thoroughly well annealed ring of soft iron indeed showed no extension at all, beginning to contract, like nickel, under the smallest magnetizing forces. The experiments were not sufficiently numerous to indicate whether, as is possible, there is a critical degree of hardness for which the height of the elongation curve is a maximum.
Finally, experiments were made to ascertain the effect of magnetization upon the dimensions of iron rings in directions perpendicular to the magnetization, and upon the volume of the rings.[33] It was found that the curve showing the relation of transverse changes of dimensions to magnetizing force was similar in general character to the familiar elongation curves, but the signs were reversed; the curve was inverted, indicating at first retraction, which, after passing a maximum and vanishing in a critical field, was succeeded by elongation. The curve showing the circumferential (or longitudinal) changes was also plotted, and from the two curves thus obtained it was easy, on the assumption that the metal was isotropic in directions at right angles to the magnetization, to calculate changes of volume; for if circumferential elongation be denoted by l1, and transverse elongation by l2, then the cubical dilatation (+ or -) = l1 + 2l2 approximately. If l1 were exactly equal to -2l2 for all values of the magnetizing force, it is clear that the volume of the ring would be unaffected by magnetization. In the case of the ring in question, the circumferential changes were in weak fields less than twice as great as the transverse ones, while in strong fields they were more than twice as great; under increasing magnetic force therefore the volume of the ring was first diminished, then it regained its original value (for H = 90), and ultimately increased. It was also shown that annealing, which has such a large effect upon circumferential (or longitudinal) changes, has almost none upon transverse ones. Hence the changes of volume undergone by a given sample of wrought iron under increasing magnetization must depend largely upon the state of the metal as regards hardness; there may be always contraction, or always expansion, or first one and then the other.
Most of the experiments described above have been repeated and the results confirmed by other workers, some of whom have added fresh observations. The complicated hysteresis effects which attend magnetic elongation and retraction have been studied by H. Nagaoka, who also, in conjunction with K. Honda, measured the changes of length of various metals shaped in the form of ovoids instead of cylindrical rods, and determined the magnetization curves for the same specimens; a higher degree of accuracy was thus attained, and satisfactory data were provided for testing theories. Among other things, it was found that the behaviour of cast cobalt was entirely changed by annealing; the sinuous curve shown in Fig. 24 was converted into an almost perfectly straight line passing through the origin, and lying below the horizontal axis; while the permeability of the metal was greatly diminished by the operation. They also tested several varieties of nickel-steel in the form of both ovoids and wires. With a sample containing 25% of nickel no appreciable change was detected; others containing larger percentages, and tested in fields up to 2000, all exhibited elongation, which tended to an asymptotic value as the field was increased. The influence of temperature varying between wide limits has formed the subject of a research by K. Honda and S. Shimizu. For soft iron, tungsten-steel and nickel little difference appeared to result from lowering the temperature down to -186° C. (the temperature of liquid air); at sufficiently high temperatures, 600° to 1000° or more, it was remarked that the changes of length in iron, steel and cobalt tended in every case to become proportional to the magnetic force, the curves being nearly straight lines entirely above the axis. The retraction of nickel was diminished by rising temperature, and at 400° had almost vanished. The influence of high temperature on cobalt was very remarkable, completely altering the character of the change of length: the curves for annealed cobalt show that at 450° this metal behaves just like iron at ordinary temperatures, lengthening in fields up to about 300 and contracting in stronger ones. The same physicists have made some additional experiments upon the effect of tension on magnetic change of length. Bidwell's results for iron and nickel were confirmed, and it was further shown that the elongation of nickel-steel was very greatly diminished by tension; when magnetized under very heavy loads, the wire was indeed found to undergo slight contraction. Honda subjected tubes of iron, steel and nickel to the simultaneous action of circular and longitudinal fields, and observed the changes of length when one of the fields was varied while the other remained constant at different successive values from zero upwards. The experimental results agreed in sign though not in magnitude with those calculated from the changes produced by simple longitudinal magnetization, discrepancies being partly accounted for by the fact that the metals employed were not actually isotropic. Heusler's alloy has been tested for change of length by L. Austin, who found continuous elongation with increasing fields, the curves obtained bearing some resemblance to curves of magnetization.
As regards the effect of magnetization upon volume there are some discrepancies. Nagaoka and Honda, who employed a fluid dilatometer, found that the volume of several specimens of iron, steel and nickel was always slightly increased, no diminution being indicated in low fields; cobalt, on the other hand, was diminished in volume, and the amount of the change, though still very small, was greater than that shown by the other metals. Various nickel-steels all expanded under magnetization, the increase being generally considerable and proportional to the field; in the case of an alloy containing 29% of nickel the change was nearly 40 times greater than in soft iron. C. G. Knott, who made an exhaustive series of experiments upon various metals in the form of tubes, concluded that in iron there was always a slight increase of volume, and in nickel and cobalt a slight decrease. It is uncertain how far these various results are dependent upon the physical condition of the metals.
Attempts have been made to explain magnetic deformation by various theories of magnetic stress,[34] notably that elaborated by G. R. Kirchhoff (_Wied. Ann._, 1885, 24, 52, and 1885, 25, 601), but so far with imperfect success. E. Taylor Jones showed in 1897 that only a small proportion of the contraction exhibited by a nickel wire when magnetized could be accounted for on Kirchhoff's theory from the observed effects of pulling stress upon magnetization; and in a more extended series of observations Nagaoka and Honda found wide quantitative divergences between the results of experiment and calculation, though in nearly all cases there was agreement as to quality. They consider, however, that Kirchhoff's theory, which assumes change of magnetization to be simply proportional to strain, is still in its infancy, the present stage of its evolution being perhaps comparable with that reached by the theory of magnetization at the time when the ratio I/H was supposed to be constant. In the light of future researches further development may reasonably be expected.
It has been suggested[35] that an iron rod under magnetization may be in the same condition as if under a mechanically applied longitudinal stress tending to shorten the iron. If a long magnetized rod is divided transversely and the cut ends placed nearly in contact, the magnetic force inside the narrow air gap will be B = H + 4[pi]I. The force acting on the magnetism of one of the faces, and urging this face towards the other, will be less than B by 2[pi]I, the part of the total force due to the first face itself; hence the force per unit of area with which the faces would press against each other if in contact is
P = (B - 2[pi]I)I = 2[pi]I² + HI = (B² - H²) / 8[pi].
The width of the gap may be diminished until it is no greater than the distance between two neighbouring molecules, when it will cease to be distinguishable, but, assuming the molecular theory of magnetism to be true, the above statement will still hold good for the intermolecular gap. The same pressure P will be exerted across any imaginary section of a magnetized rod, the stress being sustained by the intermolecular springs, whatever their physical nature may be, to which the elasticity of the metal is due. The whole of the rod will therefore be subject to a compressive longitudinal stress P, the associated contraction R, expressed as a fraction of the original length, being
R = P/M = (B² - H²) / 8[pi]M,
where M is Young's modulus. This was found to be insufficient to account for the whole of the retraction exhibited by iron in strong fields, but it was pointed out by L. T. More[36] that R ought to be regarded as a "correction" to be applied to the results of experiments on magnetic change of length, the magnetic stress being no less an extraneous effect than a stress applied mechanically. Those who support this view generally speak of the stress as "Maxwell's stress," and assume its value to be B^2/8[pi]. The stress in question seems, however, to be quite unconnected with the "stress in the medium" contemplated by Maxwell, and its value is not exactly B^2/8[pi] except in the particular case of a permanent ring magnet, when H = O. Further, Maxwell's stress is a tension along the lines of force, and is equal to B^2/8[pi] only when B = H, and there is no magnetization.[37] Some writers have indeed contended that the stress in magnetized iron is not compressive, but tensile, even when, as in the case of a ring-magnet, there are no free ends. The point at issue has an important bearing upon the possible correlation of magnetic phenomena, but, though it has given rise to much discussion, no accepted conclusion has yet been reached.[38]
7. EFFECTS OF MECHANICAL STRESS UPON MAGNETIZATION
The effects of traction, compression and torsion in relation to magnetism have formed the subject of much patient investigation, especially at the hands of J. A. Ewing, C. G. Knott and the indefatigable physicists of Tokyo University. The results of their experiments embrace a multiplicity of details of which it is impossible to give an adequate summary. Only a few of the most important can be mentioned here; the reader who wishes for fuller information should consult the original papers.[39]
It was first discovered by E. Villari in 1868 that the magnetic susceptibility of an iron wire was increased by stretching when the magnetization was below a certain value, but diminished when that value was exceeded; this phenomenon has been termed by Lord Kelvin, who discovered it independently, the "Villari reversal," the value of the magnetization for which stretching by a given load produces no effect being known as the "Villari critical point" for that load. The Villari critical point for a given sample of iron is reached with a smaller magnetizing force when the stretching load is great than when it is small; the reversal also occurs with smaller loads and with weaker fields when the iron is soft than when it is hard. The following table shows the values of I and H corresponding to the Villari critical point in some of Ewing's experiments:--
+------------------------------+-----------------------------+ | Soft Iron. | Hard Iron. | +-----------------+------+-----+-----------------+------+----+ |Kilos per sq. mm.| I. | H. |Kilos per sq. mm.| I. | H. | +-----------------+------+-----+-----------------+------+----+ | 2.15 | 1220 | 7.3 | 27.6 | 1180 | 34 | | 4.3 | 1040 | 4.3 | 32.2 | 1150 | 32 | | 8.6 | 840 | 3.4 | 37.3 | 1110 | 29 | | 12.9 | 690 | 3.05| 42.5 | 1020 | 25 | +-----------------+------+-----+-----------------+------+----+
The effects of pulling stress may be observed either when the wire is stretched by a constant load while the magnetizing force is varied, or when the magnetizing force is kept constant while the load is varied. In the latter case the first application of stress is always attended by an increase--often a very great one--of the magnetization, whether the field is weak or strong, but after a load has been put on and taken off several times the changes of magnetization become cyclic. From experiments of both classes it appears that for a given field there is a certain value of the load for which the magnetization is a maximum, the maximum occurring at a smaller load the stronger the field. In very strong fields the maximum may even disappear altogether, the effect of the smallest stress being to diminish the magnetization; on the other hand, with very weak fields the maximum may not have been reached with the greatest load that the wire can support without permanent deformation. When the load on a hardened wire is gradually increased, the maximum value of I is found to correspond with a greater stress than when the load is gradually diminished, this being an effect of hysteresis. Analogous changes are observed in the residual magnetization which remains after the wire has been subjected to fields of different strength. The effects of longitudinal pressure are opposite to those of traction; when the cyclic condition has been reached, pressure reduces the magnetization of iron in weak fields and increases it in strong fields (Ewing, _Magnetic Induction_, 1900, 223).
The influence of traction in diminishing the susceptibility of nickel was first noticed by Kelvin (W. Thomson), and was subsequently investigated by Ewing and Cowan. The latter found the effect to be enormous, not only upon the induced magnetization, but in a still greater degree upon the residual. Even under so "moderate" a load as 33 kilogrammes per square mm., the induced magnetization of a hard-drawn nickel wire in a field of 60 fell from 386 to 72 units, while the residual was reduced from about 280 to 10. Ewing has also examined the effects produced by longitudinal compression upon the susceptibility and retentiveness of nickel, and found, as was to be expected, that both were greatly increased by pressure. The maximum susceptibility of one of his bars rose from 5.6 to 29 under a stress of 19.8 kilos per square mm. There were reasons for believing that no Villari reversal would be found in nickel. Ewing and Cowan looked carefully for it, especially in weak fields, but failed to discover anything of the kind.[40] Some experiments by A. Heydweiller,[41] which appeared to indicate a reversal in weak fields (corresponding to I = 5, or thereabouts), have been shown by Honda and Shimizu to be vitiated by the fact that his specimen was not initially in a magnetically neutral state; they found that when the applied field had the same direction as that of the permanent magnetization, Heydweiller's fallacious results were easily obtained; but if the field were applied in the direction opposite to that of the permanent magnetization, or if, as should rightly be the case, there were no permanent magnetization at all, then there was no indication of any Villari reversal. Thus a very important question, which has given rise to some controversy, appears to be now definitely settled.
The effects of longitudinal pressure upon the magnetization of cast cobalt have been examined by C. Chree,[42] and also by J. A. Ewing.[43] Chree's experiments were undertaken at the suggestion of J. J. Thomson, who, from the results of Bidwell's observations on the magnetic deformation of cobalt, was led to expect that that metal would exhibit a reversal opposite in character to the effect observed in iron. The anticipated reversal was duly found by Chree, the critical point corresponding, under the moderate stress employed, to a field of about 120 units. Ewing's independent experiments showed that the magnetization curve for a cobalt rod under a load of 16.2 kilogrammes per square mm. crossed the curve for the same rod when not loaded at H = 53. Both observers noticed analogous effects in the residual magnetization. The effect of tension was subsequently studied by Nagaoka and Honda, who in 1902 confirmed, _mutatis mutandis_, the results obtained by Chree and Ewing for cast cobalt, while for annealed cobalt it turned out that tension always caused diminution of magnetization, the diminution increasing with increasing fields. They also investigated the magnetic behaviour of various nickel-steels under tension, and found that there was always increase of magnetization. Thus it has been proved that in annealed cobalt and in nickel-steel there is no Villari reversal.
It has been pointed out by J. J. Thomson (_Applications of Dynamics to Physics and Chemistry_, 47) that on dynamical principles there must be a reciprocal relation between the changes of dimensions produced by magnetization and the changes of magnetization attending mechanical strain. Since, for example, stretching diminishes the magnetization of nickel, it follows from theory that the length of a nickel rod should be diminished by magnetization and conversely. So, too, the Villari reversals in iron and cobalt might have been predicted--as indeed that in cobalt actually was--from a knowledge of the changes of length which those metals exhibit when magnetized.
The complete reciprocity of the effects of magnetization upon length and of stretching upon magnetization is shown by the following parallel statements:--
_Iron._
Magnetization produces increase Tension produces increase of of length in weak fields, magnetization in weak fields, decrease in strong fields. decrease in strong fields.
_Cast Cobalt._
Magnetization produces decrease Tension produces decrease of of length in weak fields, magnetization in weak fields, increase in strong fields. increase in strong fields.
_Nickel and Annealed Cobalt._
Magnetization produces decrease Tension produces decrease of of length in all fields. magnetization in all fields.
_Nickel-Steel._
Magnetization produces increase Tension produces increase of of length in all fields. magnetization in all fields.
Nagaoka and Honda (_Phil. Mag._, 1898, 46, 261) have investigated the effects of hydrostatic pressure upon magnetization, using the same pieces of iron and nickel as were employed in their experiments upon magnetic change of volume. In the iron cylinder and ovoid, which expanded when magnetized, compression caused a diminution of magnetization; in the nickel rod, which contracted when magnetized, pressure was attended by an increase of magnetization. The amount of the change was in both cases exceedingly small, that in iron being less than 0.1 C.G.S. unit with a pressure of 250 atmospheres and H = 54. It would hardly be safe to generalize from these observations; the effects may possibly be dependent upon the physical condition of the metals. In the same paper Nagaoka and Honda describe an important experiment on the effect of transverse stress. An iron tube, having its ends closed by brass caps, was placed inside a compressing vessel into which water was forced until the pressure upon the outer surface of the tube reached 250 atmospheres. The experiment was the reverse of one made by Kelvin with a gun-barrel subjected to internal hydrostatic pressure (_Phil. Trans._, 1878, 152, 64), and the results were also the reverse. Under increasing magnetizing force the magnetization first increased, reached a maximum, and then diminished until its value ultimately became less than when the iron was in the unstrained condition. Experiments on the effect of external hydrostatic pressure upon the magnetization of iron rings have also been made by F. Frisbie,[44] who found that for the magnetizing forces used by Nagaoka and Honda pressure produced a small _increase_ of magnetization, a result which appears to be in accord with theory.
The relations of torsion to magnetization were first carefully studied by G. Wiedemann, whose researches are described in his _Elektricität_, iii. 671. The most interesting of his discoveries, now generally known as the "Wiedemann effect," is the following: If we magnetize longitudinally a straight wire which is fixed at one end and free at the other, and then pass an electric current through the wire (or first pass the current and then magnetize), the free end of the wire will twist in a certain direction depending upon circumstances: if the wire is of iron, and is magnetized (with a moderate force) so that its free end has north polarity, while the current through it passes from the fixed to the free end, then the free end as seen from the fixed end will twist in the direction of the hands of a watch; if either the magnetization or the current is reversed, the direction of the twist will be reversed. To this mechanical phenomenon there is a magnetic reciprocal. If we twist the free end of a ferromagnetic wire while a current is passing through it, the wire becomes longitudinally magnetized, the direction of the magnetization depending upon circumstances: if the wire is of iron and is twisted so that its free end as seen from the fixed end turns in the direction of the hands of a watch, while the current passes from the fixed to the free end, then the direction of the resulting magnetization will be such as to make the free end a north pole. The twist effect exhibited by iron under moderate longitudinal magnetization has been called by Knott a _positive_ Wiedemann effect; if the twist were reversed, the other conditions remaining the same, the sign of the Wiedemann effect would be _negative_. An explanation of the twist has been given by Maxwell (_Electricity and Magnetism_, § 448). The wire is subject to two superposed magnetizations, the one longitudinal, the other circular, due to the current traversing the wire; the resultant magnetization is consequently in the direction of a screw or spiral round the wire, which will be right-handed or left-handed according as the relation between the two magnetizations is right-handed or left-handed; the magnetic expansion or contraction of the metal along the spiral lines of magnetization produces the Wiedemann twist. Iron (moderately magnetized) expands along the lines of magnetization, and therefore for a right-handed spiral exhibits a right-handed twist. This explanation was not accepted by Wiedemann,[45] who thought that the effect was accounted for by molecular friction. Now nickel contracts instead of lengthening when it is magnetized, and an experiment by Knott showed, as he expected, that _caeteris paribus_ a nickel wire twists in a sense opposite to that in which iron twists. The Wiedemann effect being positive for iron is negative for nickel. Further, although iron lengthens in fields of moderate strength, it contracts in strong ones; and if the wire is stretched, contraction occurs with smaller magnetizing forces than if it is unstretched. Bidwell[46] accordingly found upon trial that the Wiedemann twist of an iron wire vanished when the magnetizing force reached a certain high value, and was reversed when that value was exceeded; he also found that the vanishing point was reached with lower values of the magnetizing force when the wire was stretched by a weight. These observations have been verified and extended by Knott, whose researches have brought to light a large number of additional facts, all of which are in perfect harmony with Maxwell's explanation of the twist.
Maxwell has also given an explanation of the converse effect, namely, the production of longitudinal magnetization by twisting a wire when circularly magnetized by a current passing through it. When the wire is free from twist, the magnetization at any point P is in the tangential direction PB (see fig. 26). Suppose the wire to be fixed at the top and twisted at the bottom in the direction of the arrow-head T; then the element of the wire at P will be stretched in the direction Pe and compressed in the direction Pr. But tension and compression produce opposite changes in the magnetic susceptibility; if the metal is iron and its magnetization is below the Villari critical point, its susceptibility will be greater along Pe than along Pr; the direction of the magnetization therefore tends to approach Pe and to recede from Pr, changing, in consequence of the twist, from PB to some such direction as PB´, which has a vertical component downwards; hence the lower and upper ends will respectively acquire north and south polarity, which will disappear when the wire is untwisted. This effect has never been actually reversed in iron, probably, as suggested by Ewing, because the strongest practicable circular fields fail to raise the components of the magnetization along Pe and Pr up to the Villari critical value. Nagaoka and Honda have approached very closely to a reversal, and consider that it would occur if a sufficiently strong current could be applied without undue heating.
One other effect of torsion remains to be noticed. If a longitudinally magnetized wire is twisted, circular magnetization is developed; this is evidenced by the transient electromotive force induced in the iron, generating a current which will deflect a galvanometer connected with the two ends of the wire. The explanation given of the last described phenomenon will with the necessary modification apply also to this; it is a consequence of the aeolotropy produced by the twist. There are then three remarkable effects of torsion:
A. A wire magnetized longitudinally and circularly becomes twisted.
B. Twisting a circularly magnetized wire produces longitudinal magnetization.
C. Twisting a longitudinally magnetized wire produces circular magnetization.
And it has been shown earlier that--
D. Magnetization produces change of length.
E. Longitudinal stress produces change of magnetization.
Each of these five effects may occur in two opposite senses. Thus in A the twist may be right-handed or left-handed; in B the polarity of a given end may become north or south; in C the circular magnetization may be clockwise or counter-clockwise; in D the length may be increased or diminished; in E the magnetization may become stronger or weaker. And, other conditions remaining unchanged, the "sense" of any effect depends upon the nature of the metal under test, and (sometimes) upon the intensity of its magnetization. Let each of the effects A, B, C, D and E be called positive when it is such as is exhibited by moderately magnetized iron, and negative when its sense is opposite. Then the results of a large number of investigations may be briefly summarized as follows:
(W) = weakly magnetized. (S) = strongly magnetized.
_Metal._ _Effects._ _Sign._
Iron (W) A, B, C, D, E + Unannealed Cobalt (S) A, D, E + Nickel-Steel (W) A, D, E + Nickel A, B, C, D, E - Annealed Cobalt D, E - Iron (S) A, C, D, E - Unannealed Cobalt A, D, E -
Several gaps remain to be filled, but the results so far recorded can leave no doubt that the five effects, varied as they may at first sight appear, are intimately connected with one another. For each of the metals tabulated in the first column all the effects hitherto observed have the same sign; there is no single instance in which some are positive and others negative. Until the mysteries of molecular constitution have been more fully explored, perhaps D may be most properly regarded as the fundamental phenomenon from which the others follow. Nagaoka and Honda have succeeded in showing that the observed relations between twist and magnetization are in qualitative agreement with an extension of Kirchhoff's theory of magnetostriction.
The effects of magnetization upon the torsion of a previously twisted wire, which were first noticed by Wiedemann, have been further studied by F. J. Smith[47] and by G. Moreau.[48] Nagaoka[49] has described the remarkable influence of combined torsion and tension upon the magnetic susceptibility of nickel, and has made the extraordinary observation that, under certain conditions of stress, the magnetization of a nickel wire may have a direction opposite to that of the magnetizing force.
8. EFFECTS OF TEMPERATURE UPON MAGNETISM
_High Temperature._--It has long been known that iron, when raised to a certain "critical temperature" corresponding to dull red heat, loses its susceptibility and becomes magnetically indifferent, or, more accurately, is transformed from a ferromagnetic into a paramagnetic body. Recent researches have shown that other important changes in its properties occur at the same critical temperature. Abrupt alterations take place in its density, specific heat, thermo-electric quality, electrical conductivity, temperature-coefficient of electrical resistance, and in some at least of its mechanical properties. Ordinary magnetizable iron is in many respects an essentially different substance from the non-magnetizable metal into which it is transformed when its temperature is raised above a certain point (see _Brit. Assoc. Report_, 1890, 145). The first exact experiments demonstrating the changes which occur in the permeability of iron, steel and nickel when heated up to high temperatures were those of J. Hopkinson (_Phil. Trans._, 1889, 180, 443; _Proc. Roy. Soc._, 1888, 44, 317). The metal to be tested was prepared in the form of a ring, upon which were wound primary and secondary coils of copper wire insulated with asbestos. The primary coil carried the magnetizing current; the secondary, which was wound inside the other, could be connected either with a ballistic galvanometer for determining the induction, or with a Wheatstone's bridge for measuring the resistance, whence the temperature was calculated. The ring thus prepared was placed in a cast-iron box and heated in a gas furnace. The following are the chief results of Hopkinson's experiments: For small magnetizing forces the magnetization of iron steadily increases with rise of temperature till the critical temperature is approached, when the rate of increase becomes very high, the permeability in some cases attaining a value of about 11,000; the magnetization then with remarkable suddenness almost entirely disappears, the permeability falling to about 1.14. For strong magnetizing forces (which in these experiments did not exceed H = 48.9) the permeability remains almost constant at its initial value (about 400), until the temperature is within nearly 100° of the critical point; then the permeability diminishes more and more rapidly until the critical point is reached and the magnetization vanishes. Steel behaves in a similar manner, but the maximum permeability is not so high as in iron, and the fall, when the critical point is approached, is less abrupt. The critical temperature for various samples of iron and steel ranges from 690° C. to 870° C.; it is the temperature at which Barrett's "recalescence" occurs. The critical temperature for the specimen of nickel examined (which contained nearly 5% of impurities) was 310° C. F. Lydall and A. W. Pocklington found that the critical temperature of nearly pure iron was 874° C. (_Proc. Roy. Soc._, 1893, 52, 228).
An exhaustive research into the effects of heating on the magnetic properties of iron has been carried out by D. K. Morris (_Proc. Phys. Soc._, 1897, 15, 134; and _Phil. Mag._, 1897, 44, 213), the results being embodied in a paper containing twelve pages of tables and upwards of 120 curves. As in Hopkinson's experiments, ring magnets were employed; these were wound with primary and secondary coils of insulated platinum wire, which would bear a much higher temperature than copper without oxidation or fusion. A third platinum coil, wound non-inductively between the primary and the secondary, served to carry the current by which the ring was heated; a current of 4.6 amperes, with 16 volts across the terminals, was found sufficient to maintain the ring at a temperature of 1150° C. In the ring itself was embedded a platinum-thermometer wire, from the resistance of which the temperature was determined. The whole was wrapped in several coverings of asbestos and placed in a glass vessel from which the air was partially exhausted, additional precautions being taken to guard against oxidation of the iron.
Some preliminary experiments showed the striking difference in the effects of annealing at a red heat (840° C.) and at a low white heat (1150° C). After one of the rings had been annealed at 840°, its maximum permeability at ordinary temperatures was 4000 for H = 1.84; when it had been subsequently annealed at 1150°, the maximum permeability rose to 4680 for H = 1.48, while the hysteresis loss for B= ±4000 was under 500 ergs per c.cm. As regards the effects of temperature, Morris's results are in general agreement with those of Hopkinson, though no doubt they indicate details with greater clearness and accuracy. Specimens of curves showing the relation of induction to magnetic field at various temperatures, and of permeability to temperature with fields of different intensities, are given in figs. 27 and 28. The most striking feature presented by these is the enormous value, 12,660, which, with H = 0.153, is attained by the permeability at 765° C., followed by a drop so precipitous that when the temperature is only 15° higher, the value of the permeability has become quite insignificant. The critical temperatures for three different specimens of iron were 795°, 780°, and 770° respectively. Above these temperatures the little permeability that remained was found to be independent of the magnetizing force, but it appeared to vary a little with the temperature, one specimen showing a permeability of 100 at 820°, 2.3 at 950°, and 17 at 1050°. These last observations are, however, regarded as uncertain. The effects of temperature upon hysteresis were also carefully studied, and many hysteresis loops were plotted. The results of a typical experiment are given in the annexed table, which shows how greatly the hysteresis loss is diminished as the critical temperature is approached. The coercive force at 764°.5 is stated to have been little more than 0.1 C.G.S. unit; above the critical temperature no evidence of hysteresis could be obtained.
Hysteresis Loss in Ergs per c.cm. Max. H. = ±6.83.
Temp. C.° Ergs. Temp. C.° Ergs.
764.5 120 | 457 2025 748 328 | 352 2565 730 426 | 249 3130 695 797 | 137.5 3500 634 1010 | 24 3660 554 1345 |
A paper by H. Nagaoka and S. Kusakabe[50] generally confirms Morris's results for iron, and gives some additional observations for steel, nickel and cobalt. The magnetometric method was employed, and the metals, in the form of ovoids, were heated by a specially designed burner, fed with gas and air under pressure, which directed 90 fine jets of flame upon the asbestos covering the ovoid. The temperature was determined by a platinum-rhodium and platinum thermo-junction in contact with the metal. Experiments were made at several constant temperatures with varying magnetic fields, and also at constant fields with rising and falling temperatures. For ordinary steel the critical temperature, at which magnetization practically disappeared, was found to be about 830°, and the curious fact was revealed that, on cooling, magnetization did not begin to reappear until the temperature had fallen 40° below the critical value. This retardation was still more pronounced in the case of tungsten-steel, which lost its magnetism at 910° and remained non-magnetic till it was cooled to 570°, a difference of 240°. For nearly pure nickel the corresponding temperature-difference was about 100°. This phenomenon is of the same nature as that first discovered by J. Hopkinson for nickel-steel. The paper contains tables and curves showing details of the magnetic changes, sometimes very complex, at different temperatures and with different fields. The behaviour of cobalt is particularly noticeable; its permeability increased with rising temperature up to a maximum at 500°, when it was about twice as great as at ordinary temperatures, while at 1600°, corresponding to white heat, there was still some magnetization remaining.
Further contributions to the subject have been made by K. Honda and S. Shimizu,[51] who experimented at temperatures ranging from -186° to 1200°. As regards the higher temperatures, the chief point of interest is the observation that the curve of magnetization for annealed cobalt shows a small depression at about 450°, the temperature at which they had found the sign of the length-change to be reversed for all fields. In the case of all the metals tested a small but measurable trace of magnetization remained after the so-called critical temperature had been exceeded; this decreased very slightly up to the highest temperature reached (1200°) without undergoing any such variation as had been suspected by Morris. When the curve after its steep descent has almost reached the axis, it bends aside sharply and becomes a nearly horizontal straight line; the authors suggest that the critical temperature should be defined as that corresponding to the point of maximum curvature. As thus defined the critical temperatures for iron, nickel and cobalt were found to be 780°, 360° and 1090° respectively, but these values are not quite independent of the magnetizing force.
Experiments on the effect of high temperatures have also been made by M. P. Ledeboer,[52] H. Tomlinson,[53] P. Curie,[54] and W. Kunz,[55] R. L. Wills,[56] J. R. Ashworth[57] and E. P. Harrison.[58]
_Low Temperature._--J. A. Fleming and J. Dewar (_Proc. Roy. Soc._, 1896, 60, 81) were the first to experiment on the permeability and hysteresis of iron at low temperatures down to that of liquid air (-186° C.). Induction curves of an annealed soft-iron ring were taken first at a temperature of 15° C., and afterwards when the ring was immersed in liquid air, the magnetizing force ranging from about 0.8 to 22. After this operation had been repeated a few times the iron was found to have acquired a stable condition, and the curves corresponding to the two temperatures became perfectly definite. They showed that the permeability of this sample of iron was considerably diminished at the lower temperature. The maximum permeability (for H = 2) was 3400 at 15° and only 2700 at -186°, a reduction of more than 20%; but the percentage reduction became less as the magnetizing force departed from the value corresponding to maximum permeability. Observations were also made of the changes of permeability which took place as the temperature of the sample slowly rose from -186° to 15°, the magnetizing force being kept constant throughout an experiment. The values of the permeability corresponding to the highest and lowest temperatures are given in the following table. Most of the permeability-temperature curves were more or less convex
+------------------+--------+------------+-------------+ | Sample of Iron. | H. | µ at 15°. | µ at -186°. | +------------------+--------+------------+-------------+ | Annealed Swedish | 1.77 | 2835 | 2332 | | Unannealed " | 1.78 | 917 | 1272 | | " " | 9.79 | 1210 | 1293 | | Hardened " | 2.66 | 56 | 132 | | " " | 4.92 | 106.5 | 502 | | " " | 11.16 | 447.5 | 823 | | " " | 127.7 | 109 | 124 | | Steel wire | 7.50 | 86 | 64.5 | | " | 20.39 | 361 | 144 | +------------------+--------+------------+-------------+
towards the axis of temperature, and in all the experiments, except those with annealed iron and steel wire, the permeability was greatest at the lowest temperature.[59] The hysteresis of the soft annealed iron turned out to be sensibly the same for equal values of the induction at -186° as at 15°, the loss in ergs per c.cm. per cycle being approximately represented by 0.002 B(1.56) when the maximum limits of B were ±9000. Experiments with the sample of unannealed iron failed to give satisfactory results, owing to the fact that no constant magnetic condition could be obtained.
Honda and Shimizu have made similar experiments at the temperature of liquid air, employing a much wider range of magnetizing forces (up to about 700 C.G.S.) and testing a greater variety of metals. They found that the permeability of Swedish iron, tungsten-steel and nickel, when the metals were cooled to -186°, was diminished in weak fields but increased in strong ones, the field in which the effect of cooling changed its sign being 115 for iron and steel and 580 for nickel. The permeability of cobalt, both annealed and unannealed, was always diminished at the low temperature. The hysteresis-loss in Swedish iron was decreased for inductions below about 9000 and increased for higher inductions; in tungsten-steel, nickel and cobalt the hysteresis-loss was always increased by cooling. The range of ±B within which Steinmetz's formula is applicable becomes notably increased at low temperature. It may be remarked that, whereas Fleming and Dewar employed the ballistic method, their specimens having the form of rings, Honda and Shimizu worked magnetometrically with metals shaped as ovoids.
_Permanent Magnets._--Fleming and Dewar (loc. cit. p. 57) also investigated the changes which occurred in permanently magnetized metals when cooled to the temperature of liquid air. The metals, which were prepared in the form of small rods, were magnetized between the poles of an electromagnet and tested with a magnetometer at temperatures of -186° and 15°. The first immersion into liquid air generally produced a permanent decrease of magnetic moment, and there was sometimes a further decrease when the metal was warmed up again; but after a few alternations of temperature the changes of moment became definite and cyclic. When the permanent magnetic condition had been thus established, it was found that in the case of all the metals, except the two alloys containing large percentages of nickel, the magnetic moment was temporarily increased by cooling to -186°. The following table shows the principal results. It is suggested that a permanent magnet might conveniently be "aged" (or brought into a constant condition) by dipping it several times into liquid air.
+---------------------------------+--------------------------------+ | | Percentage Gain or Loss | | Metal. | of Moment at -186° C. | | +----------------+---------------+ | | First Effect. | Cyclic Effect.| +---------------------------------+----------------+---------------+ | Carbon steel, hard | -6 | +12 | | " " medium | Decrease | +22 | | " " annealed | -33 | +33 | | Chromium steels (four samples) | Increase | +12 | | Aluminium steels (three samples)| -2 | +10 | | Nickel steels, up to 7.65% | Small | +10 | | " " " 19.64% | -50 | -25 | | " " " 29% | -20 | -10 | | Pure nickel | Decrease | +3 | | Silicon steel, 2.67% | " | +4 | | Iron, soft | None | +2.5 | | " hard | Decrease | +10 | | Tungsten steel, 15% | " | +6 | | " " 7.5% | " | +10 | | " " 1% | " | +12 | +---------------------------------+----------------+---------------+
Other experiments relating to the effect of temperature upon permanent magnets have been carried out by J. R. Ashworth,[60] who showed that the temperature coefficient of permanent magnets might be reduced to zero (for moderate ranges of temperature) by suitable adjustment of temper and dimension ratio; also by R. Pictet,[61] A. Durward[62] and J. Trowbridge.[63]
_Alloys of Nickel and Iron._--A most remarkable effect of temperature was discovered by Hopkinson (_Proc. Roy. Soc._, 1890, 47, 23; 1891, 48, 1) in 1889. An alloy containing about 3 parts of iron and 1 of nickel--both strongly magnetic metals--is under ordinary conditions practically non-magnetizable (µ = 1.4 for any value of H). If, however, this non-magnetic substance is cooled to a temperature a few degrees below freezing-point, it becomes as strongly magnetic as average cast-iron (µ = 62 for H = 40), and retains its magnetic properties indefinitely at ordinary temperatures. But if the alloy is heated up to 580° C. it loses its susceptibility--rather suddenly when H is weak, more gradually when H is strong--and remains non-magnetizable till it is once more cooled down below the freezing-point. This material can therefore exist in either of two perfectly stable conditions, in one of which it is magnetizable, while in the other it is not. When magnetizable it is a hard steel, having a specific electrical resistance of 0.000052; when non-magnetizable it is an extremely soft, mild steel, and its specific resistance is 0.000072. Alloys containing different proportions of nickel were found to exhibit the phenomenon, but the two critical temperatures were less widely separated. The following approximate figures for small magnetizing forces are deduced from Hopkinson's curves:--
Percentage of Susceptibility lost Susceptibility gained Nickel. at temp. C. at temp. C.
0.97 890 -- 4.7 820 660 4.7 780 600 24.5 680 -10 30.0 140 125 33.0 207 193 73.0 202 202
Honda and Shimizu (_loc. cit._) have determined the two critical temperatures for eleven nickel-steel ovoids, containing from 24.04 to 70.32% of nickel, under a magnetizing force of 400, and illustrated by an interesting series of curves, the gradual transformation of the magnetic properties as the percentage of nickel was decreased. They found that the hysteresis-loss, which at ordinary temperatures is very small, was increased in liquid air, the increase for the alloys containing less than 30% of nickel being enormous. Steinmetz's formula applies only for very weak inductions when the alloys are at the ordinary temperature, but at the temperature of liquid air it becomes applicable through a wide range of inductions. According to C. E. Guillaume[64] the temperature at which the magnetic susceptibility of nickel-steel is recovered is lowered by the presence of chromium; a certain alloy containing chromium was not rendered magnetic even by immersion in liquid air. Experiments on the subject have also been made by E. Dumont[65] and F. Osmond.[66]
9. ALLOYS AND COMPOUNDS OR IRON
In 1885 Hopkinson (_Phil. Trans._, 1885, 176, 455) employed his yoke method to test the magnetic properties of thirty-five samples of iron and steel, among which were steels containing substantial proportions of manganese, silicon, chromium and tungsten. The results, together with the chemical analysis of each sample, are given in a table contained in this paper, some of them being also represented graphically. The most striking phenomenon which they bring into prominence is the effect of any considerable quantity of manganese in annihilating the magnetic property of iron. A sample of Hadfield's manufacture, containing 12.36% of manganese, differed hardly at all from a non-magnetic substance, its permeability being only 1.27. According to Hopkinson's calculation, this sample behaved as if 91% of the iron contained in it had completely lost its magnetic property.[67] Another point to which attention is directed is the exceptionally great effect which hardening has upon the magnetic properties of chrome steel; one specimen had a coercive force of 9 when annealed, and of no less than 38 when oil-hardened. The effect of the addition of tungsten in increasing the coercive force is very clearly shown; in two specimens containing respectively 3.44 and 2.35% of tungsten the coercive force was 64.5 and 70.7. These high values render hardened tungsten-steel particularly suitable for the manufacture of permanent magnets. Hopkinson (_Proc. Roy. Soc._, 1890, 48, 1) also noticed some peculiarities of an unexpected nature in the magnetic properties of the nickel-steel alloys already referred to. The permeability of the alloys containing from 1 to 4.7% of nickel, though less than that of good soft iron for magnetizing forces up to about 20 or 30, was greater for higher forces, the induction reached in a field of 240 being nearly 21,700. The induction for considerable forces was found to be greater in a steel containing 73% of nickel than in one with only 33%, though the permeability of pure nickel is much less than that of iron.
The magnetic qualities of various alloys of iron have been submitted to a very complete examination by W. F. Barrett, W. Brown and R. A. Hadfield (_Trans. Roy. Dub. Soc._, 1900, 7, 67; _Journ. Inst. Elec. Eng._, 1902, 31, 674).[68] More than fifty different specimens were tested, most of which contained a known proportion of manganese, nickel, tungsten, aluminium, chromium, copper or silicon: in some samples two of the substances named were present. Of the very numerous results published, a few of the most characteristic are collected in the following table. The first column contains the symbols of the various elements which were added to the iron, and the second the percentage proportion in which each element was present; the sample containing 0.03% of carbon was a specimen of the best commercial iron, the values obtained for it being given for comparison. All the metals were annealed.
A few among several interesting points should be specially noticed. The addition of 15.2% of manganese produced an enormous effect upon the magnetism of iron, while the presence of only 2.25% was comparatively unimportant. When nickel was added to the iron in increasing quantities the coercive force increased until the proportion of nickel reached 20%; then it diminished, and when the proportion of nickel was 32% the coercive force had fallen to the exceedingly low value of 0.5. In the case of iron containing 7.5% of tungsten (W), the residual induction had a remarkably high value; the coercive force, however, was not very great. The addition of silicon in small quantities considerably diminished permeability and increased coercive force; but when the proportion amounted to 2.5% the maximum permeability (µ = 5100 for H = 2) was greater than that of the nearly pure iron used for comparison, while the coercive force was only 0.9.[69] A small percentage of aluminium produced still higher permeability (µ = 6000 for H = 2), the induction in fields up to 60 being greater than in any other known substance, and the hysteresis-loss for moderate limits of B far less than in the purest commercial iron. Certain non-magnetizable alloys of nickel, chromium-nickel and chromium-manganese were rendered magnetizable by annealing.
+--------+---------+-----------+---------+----------+--------+ |Element.|Per cent.| B | B | µ |Coercive| | | |for H = 45.|residual.|for H = 8.| Force. | +--------+---------+-----------+---------+----------+--------+ | C | 0.03 | 16800 | 9770 | 1625 | 1.66 | | Cu | 2.5 | 14300 | 10410 | .. | 5.4 | | Mn | 2.25 | 14720 | 10460 | 1080 | 6.0 | | Mn | 15.2 | 0 | .. | .. | .. | | Ni | 3.82 | 16190 | 9320 | 1375 | 2.76 | | Ni | 19.64 | 7770 | 4770 | 90 | 20.0 | | Ni | 31.4 | 4460 | 1720 | 357 | 0.5 | | W | 7.5 | 15230 | 13280 | 500 | 9.02 | | Al | 2.25 | 16900 | 10500 | 1700 | 1.0 | | Cr | 3.25 | .. | .. | .. | 12.25 | | Si | 2.5 | 16420 | 4080 | 1680 | 0.9 | | Si | 5.5 | 15980 | 3430 | 1630 | 0.85 | +--------+---------+-----------+---------+----------+--------+
Later papers[70] give the results of a more minute examination of those specimens which were remarkable for very low and very high permeabilities, and were therefore likely to be of commercial importance. The following table gives the exact composition of some alloys which were found to be non-magnetizable, or nearly so, in a field of 320.
+---------------------------------------------------------------+ | An. = Annealed. Un. = Unannealed. | +------+----------------------------------------+---------------+ |State.| Percentage Composition. |I, for H = 320.| +------+----------------------------------------+---------------+ | Un. | Fe, 85.77; C, 1.23; Mn, 13. | 0 | | An. | Fe, 84.64; C, 0.15; Mn, 15.2 | 0 | | An. | Fe, 80.16; C, 0.8; Mn, 5.04; Ni, 14.55.| 3 | | Un. | Ditto | 0 | | Un. | Fe, 75.36; C, 0.6; Mn, 5.04; Ni, 19. | 3 | | An. | Fe, 86.61; C, 1.08; Mn, 10.2; W, 2.11. | 5 | +------+----------------------------------------+---------------+
A very small difference in the constitution often produces a remarkable effect upon the magnetic quality, and it unfortunately happens that those alloys which are hardest magnetically are generally also hardest mechanically and extremely difficult to work; they might however be used rolled or as castings. The specimens distinguished by unusually high permeability were constituted as follows:--
Silicon-iron.--Fe, 97.3; C, 0.2; Si, 2.5.
Aluminium-iron.--Fe, 97.33; C, 0.18; Al, 2.25.
The silicon-iron had, in fields up to about 10, a greater permeability than a sample of the best Swedish charcoal-iron, and its hysteresis-loss for max. B = 9000, at a frequency of 100 per second, was only 0.254 watt per pound, as compared with 0.382 for the Swedish iron. The aluminium-iron attained its greatest permeability in a field of 0.5, about that of the earth's force, when its value was 9000, this being more than twice the maximum permeability of the Swedish iron. Its hysteresis-loss for B = 9000 was 0.236 per pound. It was, however, found that the behaviour of this alloy was in part due to a layer of pure iron ("ferrite") averaging 0.1 mm. in thickness, which occurred on the outside of the specimen, and the exceptional magnetic quality which has been claimed for aluminium-iron cannot yet be regarded as established.
A number of iron alloys have been examined by Mme. Curie (_Bull. Soc. d'Encouragement_, 1898, pp. 36-76), chiefly with the object of determining their suitability for the construction of permanent magnets. Her tests appear to show that molybdenum is even more effective than tungsten in augmenting the coercive force, the highest values observed being 70 to 74 for tungsten-steel, and 80 to 85 for steel containing 3.5 to 4% of molybdenum. For additional information regarding the composition and qualities of permanent magnet steels reference may be made to the publications cited below.[71] Useful instructions have been furnished by Carl Barus (_Terrestrial Magnetism_, 1897, 2, 11) for the preparation of magnets calculated to withstand the effects of time, percussion and ordinary temperature variations. The metal, having first been uniformly tempered glass-hard, should be annealed in steam at 100° C. for twenty or thirty hours; it should then be magnetized to saturation, and finally "aged" by a second immersion in steam for about five hours.
_Magnetic Alloys of Non-Magnetic Metals._--The interesting discovery was made by F. Heusler[72] in 1903 that certain alloys of the non-magnetic metal manganese with other non-magnetic substances were strongly magnetizable, their susceptibility being in some cases equal to that of cast iron. The metals used in different combinations included tin, aluminium, arsenic, antimony, bismuth and boron; each of these, when united in certain proportions with manganese, together with a larger quantity of copper (which appears to serve merely as a menstruum), constituted a magnetizable alloy. So far, the best results have been attained with aluminium, and the permeability was greatest when the percentages of manganese and aluminium were approximately proportional to the atomic weights of the two metals. Thus in an alloy containing 26.5% of manganese and 14.6% of aluminium, the rest being copper, the induction for H = 20 was 4500, and for H = 150, 5550. When the proportion of aluminium to manganese was made a little greater or smaller, the permeability was diminished. Next to aluminium, tin was found to be the most effective of the metals enumerated above. In all such magnetizable alloys the presence of manganese appears to be essential, and there can be little doubt that the magnetic quality of the mixtures is derived solely from this component. Manganese, though belonging (with chromium) to the iron group of metals, is commonly classed as a paramagnetic, its susceptibility being very small in comparison with that of the recognized ferromagnetics; but it is remarkable that its atomic susceptibility in solutions of its salts is even greater than that of iron. Now iron, nickel and cobalt all lose their magnetic quality when heated above certain critical temperatures which vary greatly for the three metals, and it was suspected by Faraday[73] as early as 1845 that manganese might really be a ferromagnetic metal having a critical temperature much below the ordinary temperature of the air. He therefore cooled a piece of the metal to -105° C., the lowest temperature then attainable, but failed to produce any change in its magnetic quality. The critical temperature (if there is one) was not reached in Faraday's experiment; possibly even the temperature of -250° C., which by the use of liquid hydrogen has now become accessible, might still be too high.[74] But it has been shown that the critical temperatures of iron and nickel may be changed by the addition of certain other substances. Generally they are lowered, sometimes, however, they are raised[75]; and C. E. Guillaume[76] explains the ferromagnetism of Heusler's alloy by supposing that the naturally low critical temperature of the manganese contained in it is greatly raised by the admixture of another appropriate metal, such as aluminium or tin; thus the alloy as a whole becomes magnetizable at the ordinary temperature. If this view is correct, it may also be possible to prepare magnetic alloys of chromium, the only other paramagnetic metals of the iron group.
J. A. Fleming and R. A. Hadfield[77] have made very careful experiments on an alloy containing 22.42% of manganese, 11.65% of aluminium and 60.49% of copper. The magnetization curve was found to be of the same general form as that of a paramagnetic metal, and gave indications that with a sufficient force magnetic saturation would probably be attained. There was considerable hysteresis, the energy-loss per cycle being fairly represented by W = 0.0005495B^(2.238). The hysteretic exponent is therefore much higher than in the case of iron, nickel and cobalt, for which its value is approximately 1.6.
10. MISCELLANEOUS EFFECTS OF MAGNETIZATION
_Electrical Conductivity._--The specific resistance of many electric conductors is known to be temporarily changed by the action of a magnetic field, but except in the case of bismuth the effect is very small.
A. Gray and E. Taylor Jones (_Proc. Roy. Soc._, 1900, 67, 208) found that the resistance of a soft iron wire was increased by about 1/700 in a field of 320 C.G.S. units. The effect appeared to be closely connected with the intensity of magnetization, being approximately proportional to I. G. Barlow (_Proc. Roy. Soc._, 1903, 71, 30), experimenting with wires of iron, steel and nickel, showed that in weak fields the change of resistance was proportional to a function aI^2 + bI^4 + cI^6, where a, b and c are constants for each specimen. W. E. Williams (_Phil. Mag._, 1902, 4, 430) found that for nickel the curves showing changes of resistance in relation to magnetizing force were strikingly similar in form to those showing changes of length. H. Tomlinson (_Phil. Trans._, 1883, Part I., 153) discovered in 1881 that the resistance of a bismuth rod was slightly increased when the rod was subjected to longitudinal magnetic force, and a year or two later A. Righi (_Atti R. A. Lincei_, 1883-1884, 19, 545) showed that a more considerable alteration was produced when the magnetic force was applied transversely to the bismuth conductor; he also noticed that the effect was largely dependent upon temperature (see also P. Lenard, _Wied. Ann._, 1890, 39, 619). Among the most important experiments on the influence of magnetic force at different temperatures are those of J. B. Henderson and of Dewar and Fleming. Henderson (_Phil. Mag._, 1894, 38, 488) used a little spiral of the pure electrolytic bismuth wire prepared by Hartmann and Braun; this was placed between the pole-pieces of an electromagnet and subjected to fields of various strengths up to nearly 39,000 units. At constant temperature the resistance increased with the field; the changes in the resistance of the spiral when the temperature was 18° C. are indicated in the annexed table, from which it will be seen that in the strongest
H. R. | H. R. 0 1.000 | 27450 2.540 6310 1.253 | 32730 2.846 12500 1.630 | 38900 3.334 20450 2.160 |
transverse field reached the resistance was increased more than threefold. Other experiments showed the relation of resistance to temperature (from 0° to about 90°) in different constant fields. It appears that as the temperature rises the resistance decreases to a minimum and then increases, the minimum point occurring at a higher temperature the stronger the field. For H = 11,500 the temperature of minimum resistance was about 50°; for much lower or higher values of H the actual minimum did not occur within the range of temperature dealt with. Dewar and Fleming (_Proc. Roy. Soc._, 1897, 60, 425) worked with a similar specimen of bismuth, and their results for a constant temperature of 19° agree well with those of Henderson. They also experimented with constant temperatures of -79°, -185° and -203°, and found that at these low temperatures the effect of magnetization was enormously increased. The following table gives some of their results, the specific resistance of the bismuth being expressed in C.G.S. units.
+-----------+-----------------------+------------------------+ | | Temp. 19°C. | Temp. -185°C. | | Field +-----------+-----------+-----------+------------+ | Strength. | Spec. Res.| Comp. Res.| Spec. Res.| Comp. Res. | +-----------+-----------+-----------+-----------+------------+ | 0 | 116200 | 1.000 | 41000 | 1.00 | | 1375 | 118200 | 1.017 | 103300 | 2.52 | | 2750 | 123000 | 1.059 | 191500 | 4.67 | | 8800 | 149200 | 1.284 | 738000 | 18.0 | | 14150 | 186200 | 1.602 | 1730000 | 42.2 | | 21800 | 257000 | 2.212 | 6190000 | 151 | +-----------+-----------+-----------+-----------+------------+
At the temperature of liquid air (-185°) the application of a field of 21,800 multiplied the resistance of the bismuth no less than 150 times. Fig. 29 shows the variations of resistance in relation to temperature for fields of different constant values. It will be seen that for H = 2450 and H = 5500 the minimum resistance occurs at temperatures of about -80° and -7° respectively.
_Hall Effect._--If an electric current is passed along a strip of thin metal, and the two points at opposite ends of an equipotential line are connected with a galvanometer, its needle will of course not be deflected. But the application of a magnetic field at right angles to the plane of the metal causes the equipotential lines to rotate through a small angle, and the points at which the galvanometer is connected being no longer at the same potential, a current is indicated by the galvanometer.[78] The tranverse electromotive force is equal to KCH/D, where C is the current, H the strength of the field, D the thickness of the metal, and K a constant which has been termed the _rotatory power_ or _rotational coefficient_. (See Hopkinson, _Phil. Mag._, 1880, 10, 430). The following values of K for different metals are given by E. H. Hall, the positive sign indicating that the electromotive force is in the same direction as the mechanical force acting upon the conductor. A. von Ettinghausen and W. Nernst (_Wien. Ber._, 1886, 94, 560) have found that the rotational coefficient of tellurium is more than fifty times greater than that of bismuth, its sign being positive. Several experimenters have endeavoured to find a Hall effect in liquids, but such results as have been hitherto obtained are by no means free from doubt. E. A. Marx (_Ann. d. Phys._, 1900, 2, 798) observed a well-defined Hall effect in incandescent gases. A large effect, proportional to the field, has been found by H. A. Wilson (_Cam. Phil. Soc. Proc._, 1902, 11, pp. 249, 391) in oxygen, hydrogen and air at low pressures, and by C. D. Child (_Phys. Rev._, 1904, 18, 370) in the electric arc.
Metal. K × 10^15 | Metal. K × 10^15 | Antimony +114000 | Copper -520 Steel +12060 | Gold -660 Iron +7850 | Nickel -14740 Cobalt +2460 | Bismuth[79] -8580000 Zinc +820 |
_Electro-Thermal Relations._--The Hall electromotive force is only one of several so-called "galvano-magnetic effects" which are observed when a magnetic field acts normally upon a thin plate of metal traversed by an electric current. It is remarkable that if a flow of heat be substituted for a current of electricity a closely allied group of "thermo-magnetic effects" is presented. The two classes of phenomena have been collated by M. G. Lloyd (_Am. Journ. Sci._, 1901, 12, 57), as follows:--
_Galvano-Magnetic Effects._ _Thermo-Magnetic Effects._
1. A transverse difference of i. A transverse difference of electric potential (Hall effect). electric potential (Nernst effect).
2. A transverse difference of ii. A transverse difference of temperature(Ettinghausen effect). temperature (Leduc effect).
3. Longitudinal change of iii. Longitudinal change of electric conductivity. thermal conductivity.
4. Longitudinal difference of iv. Longitudinal difference of temperature. electric potential.[80]
+---------------------+ | C | | | | A B | | D | +---------------------+
If in the annexed diagram ABCD represents the metallic plate through which the current of electricity or heat flows in the direction AB, then effects (1), (2), (i.) and (ii.) are exhibited at C and D, effects (4) and (iv.) at A and B, and effects (3) and (iii.) along AB. The transverse effects are reversed in direction when either the magnetic field or the primary current (electric or thermal) is reversed, but the longitudinal effects are independent of the direction of the field. It has been shown by G. Moreau (_C. R._, 1900, 130, pp. 122, 412, 562) that if K is the coefficient of the Hall effect (1) and K´ the analogous coefficient of the Nernst effect (i.) (which is constant for small values of H), then K´ = K[sigma]/[rho], [sigma] being the coefficient of the Thomson effect for the metal and [rho] its specific resistance. He considers that Hall's is the fundamental phenomenon, and that the Nernst effect is essentially identical with it, the primary electromotive force in the case of the latter being that of the Thomson effect in the unequally heated metal, while in the Hall experiment it is derived from an external source.
Attempts have been made to explain these various effects by the electron theory.[81]
_Thermo-electric Quality._--The earliest observations of the effect of magnetization upon thermo-electric power were those of W. Thomson (Lord Kelvin), who in 1856 announced that magnetization rendered iron and steel positive to the unmagnetized metals.[82] It has been found by Chassagny,[83] L. Houllevigue[84] and others that when the magnetizing force is increased, this effect passes a maximum, while J. A. Ewing[85] has shown that it is diminished and may even be reversed by tensile stress. Nickel was believed by Thomson to behave oppositely to iron, becoming negative when magnetized; but though his conclusion was accepted for nearly fifty years, it has recently been shown to be an erroneous one, based, no doubt, upon the result of an experiment with an impure specimen. Nickel when magnetized is always positive to the unmagnetized metal. So also is cobalt, as was found by H. Tomlinson.[86] The curves given by Houllevigue for the relation of thermo-electric force to magnetic field are of the same general form as those showing the relation of change of length to field. E. Rhoads[87] obtained a cyclic curve for iron which indicated thermo-electric hysteresis of the kind exhibited by Nagaoka's curves for magnetic strain. He also experimented with nickel and again found a resemblance to the strain curve. The subject was further investigated by S. Bidwell,[88] who, adopting special precautions against sources of error by which former work was probably affected, measured the changes of thermo-electric force for iron, steel, nickel and cobalt produced by magnetic fields up to 1500 units. In the case of iron and nickel it was found that, when correction was made for mechanical stress due to magnetization, magnetic change of thermo-electric force was, within the limits of experimental error, proportional to magnetic change of length. Further, it was shown that the thermo-electric curves were modified both by tensile stress and by annealing in the same manner as were the change-of-length curves, the modification being sometimes of a complex nature. Thus a close connexion between the two sets of phenomena seems to be established. In the case of cobalt no such relation could be traced; it appeared that the thermo-electric power of the unmagnetized with respect to the magnetized cobalt was proportional to the square of the magnetic induction or of the magnetization. Of nickel six different specimens were tested, all of which became, like iron, thermo-electrically positive to the unmagnetized metals.
As to what effect, if any, is produced upon the thermo-electric quality of bismuth by a magnetic field there is still some doubt. E. van Aubel[89] believes that in pure bismuth the thermo-electric force is increased by the field; impurities may neutralize this effect, and in sufficient quantities reverse it.
_Elasticity._--The results of experiments as to the effect of magnetization were for long discordant and inconclusive, sufficient care not having been taken to avoid sources of error, while the effects of hysteresis were altogether disregarded. The subject, which is of importance in connexion with theories of magnetostriction, has been investigated by K. Honda and T. Terada in a research remarkable for its completeness and the ingenuity of the experimental methods employed.[90] The results are too numerous to discuss in detail; some of those to which special attention is directed are the following: In Swedish iron and tungsten-steel the change of elastic constants (Young's modulus and rigidity) is generally positive, but its amount is less than 0.5%; changes of Young's modulus and of rigidity are almost identical. In nickel the maximum change of the elastic constants is remarkably large, amounting to about 15% for Young's modulus and 7% for rigidity; with increasing fields the elastic constants first decrease and then increase. In nickel-steels containing about 50 and 70% of nickel the maximum increase of the constants is as much as 7 or 8%. In a 29% nickel-steel, magnetization increases the constants by a small amount. Changes of elasticity are in all cases dependent, not only upon the field, but also upon the tension applied; and, owing to hysteresis, the results are not in general the same when the magnetization follows as when it precedes the application of stress; the latter is held to be the right order.
_Chemical and Voltaic Effects._--If two iron plates, one of which is magnetized, are immersed in an electrolyte, a current will generally be indicated by a galvanometer connected with the plates.
As to whether the magnetized plate becomes positive or negative to the other, different experimenters are not in agreement. It has, however, been shown by Dragomir Hurmuzescu (_Rap. du Congrès Int. de Phys._, Paris, 1900, p. 561) that the true effect of magnetization is liable to be disguised by secondary or parasitic phenomena, arising chiefly from polarization of the electrodes and from local variations in the concentration and magnetic condition of the electrolyte; these may be avoided by working with weak solutions, exposing only a small surface in a non-polar region of the metal, and substituting a capillary electrometer for the galvanometer generally used. When such precautions are adopted it is found that the "electromotive force of magnetization" is, for a given specimen, perfectly definite both in direction and in magnitude; it is independent of the nature of the corrosive solution, and is a function of the field-strength alone, the curves showing the relation of electromotive force to field-intensity bearing a rough resemblance to the familiar I-H curves. The value of the E.M.F. when H = 2000 is of the order of 1/100 volt for iron, 1/1000 volt for nickel and 1/10,000 for bismuth. When the two electrodes are ferromagnetic, the direction of the current through the liquid is from the unmagnetized to the magnetized electrode, the latter being least attacked; with diamagnetic electrodes the reverse is the case. Hurmuzescu shows that these results are in accord with theory. Applying the principle of the conservation of internal energy, he demonstrates that for iron in a field of 1000 units and upwards the E.M.F. of magnetization is
l I² E = ------- × -------- approximately, [delta] 2[kappa]
l being the electrochemical equivalent and [delta] the density of the metal. Owing to the difficulty of determining the magnetization I and the susceptibility [kappa] with accuracy, it has not yet been possible to submit this formula to a quantitative test, but it is said to afford an indication of the results given by actual experiment. It has been discovered by E. L. Nichols and W. S. Franklin (_Am. Journ. Sci._, 1887, 34, 419; 1888, 35, 290) that the transition from the "passive" to the active state of iron immersed in strong nitric acid is facilitated by magnetization, the temperature of transition being lowered. This is attributed to the action of local currents set up between unequally magnetized portions of the iron. Similar results have been obtained by T. Andrews (_Proc. Roy. Soc._, 1890, 48, 116).
11. FEEBLY SUSCEPTIBLE SUBSTANCES
_Water._--The following are recent determinations of the magnetic susceptibility of water:--
Observer. [kappa] × 10^6. Publication.
G. Quincke -0.797 at 18° C. _Wied. Ann._, 1885, 24, 387. H. du Bois -0.837 (1 - 0.0025t - 15°) _Wied. Ann._, 1888, 35, 137. P. Curie -0.790 at 4° C. _C. R._, 1893, 116, 136. J. Townsend -0.77 _Phil. Trans._, 1896, 187, 544. J. A. Fleming -0.74 _Proc. Roy. Soc._, 1898, 63, and J. Dewar 311. G. Jäger and -0.689(1 - 0.0016t) _Wied. Ann._, 1899, 67, S. Meyer 707. J. Koenigsberger -0.781 at 22° C. _Ann. d. Phys._, 1901, 6, 506. H. D. Stearns -0.733 at 22° C. _Phys. Rev._, 1903, 16, 1. A. P. Wills -0.720 at 18° C. _Phys. Rev._, 1905, 20, 188.
Wills found that the susceptibility was constant in fields ranging from 4200 to 15,000.
_Oxygen and Air._--The best modern determinations of the value of [kappa] for gaseous oxygen agree very fairly well with that given by Faraday in 1853 (_Exp. Res._ III, 502). Assuming that for water [kappa] = -0.8 × 10^(-6), his value of [kappa] for oxygen at 15° C. reduces to 0.15 × 10^(-6). Important experiments on the susceptibility of oxygen at different pressures and temperatures were carried out by P. Curie (_C.R._ 1892, 115, 805; 1893, 116, 136). _Journ. de Phys._, 1895, 4, 204. He found that the susceptibility for unit of mass, K, was independent of both pressure and magnetizing force, but varied inversely as the absolute temperature, [theta], so that 10^6K = 33700/[theta]. Since the mass of 1 cub. cm. of oxygen at 0° C. and 760 mm. pressure is 0.00141 grm., the mass at any absolute temperature [theta] is by Charles's law 0.00141 × 273[theta] = 0.3849/[theta] grm.; hence the susceptibility per unit of volume at 760 mm. will be
[kappa] = 10^(-6) × 0.3849 × 33700/[theta]² = 10^(-6) × 12970/[theta]².
At 15° C. [theta] = 273 + 15 = 288, and therefore [kappa] = 0.156 × 10^(-6), nearly the same as the value found by Faraday. At 0° C., [kappa] = 0.174 × 10^(-6). For air Curie calculated that the susceptibility per unit mass was 10^6K = 7830/[theta]; or, taking the mass of 1 c.c. of air at 0° C. and 760 mm. as 0.001291 grm., [kappa] = 10^(-6) × 2760/[theta]² for air at standard atmospheric pressure. It is pointed out that this formula may be used as a temperature correction in magnetic determinations carried out in air.
Fleming and Dewar determined the susceptibility of liquid oxygen (_Proc. Roy. Soc._, 1896, 60, 283; 1898, 63, 311) by two different methods. In the first experiments it was calculated from observations of the mutual induction of two conducting circuits in air and in the liquid; the results for oxygen at -182° C. were
µ = 1.00287, [kappa] = 228 × 10^(-6).
In the second series, to which greater importance is attached, measurements were made of the force exerted in a divergent field upon small balls of copper, silver and other substances, first when the balls were in air and afterwards when they were immersed in liquid oxygen. If V is the volume of a ball, H the strength of the field at its centre, and [kappa]´ its apparent susceptibility, the force in the direction x is f = [kappa]´VH × dH/dx; and if [kappa]´_a and [kappa]´^0 are the apparent susceptibilities of the same ball in air and in liquid oxygen, [kappa]´_a - [kappa]´0 is equal to the difference between the susceptibilities of the two media. The susceptibility of air being known--practically it was negligible in these experiments--that of liquid oxygen can at once be found. The mean of 36 experiments with 7 balls gave
µ = 1.00407, [kappa] = 324 × 10^(-6).
A small but decided tendency to a decrease of susceptibility in very strong fields was observed. It appears, therefore, that liquid oxygen is by far the most strongly paramagnetic liquid known, its susceptibility being more than four times greater than that of a saturated solution of ferric chloride. On the other hand, its susceptibility is about fifty times less than that of Hadfield's 12% manganese steel, which is commonly spoken of as non-magnetizable.
_Bismuth._--Bismuth is of special interest, as being the most strongly diamagnetic substance known, the mean value of the best determinations of its susceptibility being about -14 × 10^(-6) (see G. Meslin, _C. R._, 1905, 140, 449). The magnetic properties of the metal at different temperatures and in fields up to 1350 units have been studied by P. Curie (_loc. cit._), who found that its "specific susceptibility" (K) was independent of the strength of the field, but decreased with rise of temperature up to the melting-point, 273°C. His results appear to show the relation
-[Kappa] × 10^6 = 1.381 - 0.00155t°.
Assuming the density of Bi to be 9.8, and neglecting corrections for heat dilatation, his value for the susceptibility at 20°C. is equivalent to [kappa] = -13.23 × 10^(-6). As the temperature was raised up to 273°, [kappa] gradually fell to -9.38 × 10^[-6], rising suddenly when fusion occurred to -0.37 × 10^(-6), at which value it remained constant when the fluid metal was further heated. Fleming and Dewar give for the susceptibility the values -13.7 × 10^(-6) at 15°C. and -15.9 × 10^(-6) at -182°, the latter being approximately equivalent to [Kappa] × 10^6 = -1.62. Putting t° = -182 in the equation given above for Curie's results, we get [Kappa] × 10^6 = -1.66, a value sufficiently near that obtained by Fleming and Dewar to suggest the probability that the diamagnetic susceptibility varies inversely as the temperature between -182° and the melting-point.
_Other Diamagnetics._--The following table gives Curie's determinations (_Journ. de Phys._, 1895, 4, 204) of the specific susceptibility [Kappa] of other diamagnetic substances at different temperatures. It should be noted that [Kappa] = [kappa]/density.
Substance Temp. °C. -[Kappa] × 10^6.
Water 15-189 0.790 Rock salt 16-455 0.580 Potassium chloride 18-465 0.550 " sulphate 17-460 0.430 " nitrate (fusion 350°) 18-420 0.330 Quartz 18-430 0.441 Sulphur, solid or fused 18-225 0.510 Selenium, solid or fused 20-200 0.320 " fused 240-415 0.307 Tellurium 20-305 0.311 Bromine 20 0.410 Iodine, solid or fused 18-164 0.385 Phosphorus, solid or fused 19-71 0.920 " amorphous 20-275 0.730 Antimony, electrolytic 20 0.680 " 540 0.470 Bismuth, solid 20 1.350 " " 273 0.957 " fused 273-405 0.038
For all diamagnetic substances, except antimony and bismuth, the value of [Kappa] was found to be independent of the temperature.
_Paramagnetic Substances._--Experiments by J. S. Townsend (_Phil. Trans._, 1896, 187, 533) show that the susceptibility of solutions of salts of iron is independent of the magnetizing force, and depends only on the quantity of iron contained in unit volume of the liquid. If W is the weight of iron present per c.c. at about 10°C., then for ferric salts
10^6[kappa] = 266W - 0.77
and for ferrous salts
10^6[kappa] = 206W - 0.77,
the quantity -0.77 arising from the diamagnetism of the water of solution. Annexed are values of 10^6[kappa] for the different salts examined, w being the weight of the salt per c.c. of the solution.
Salt. 10^6[kappa] + 0.77 | Salt. 10^6[kappa] + 0.77 | Fe2Cl6 91.6w | FeCl2 90.8w Fe2(SO4)3 74.5w | FeSO4 74.9w Fe2(NO3)6 61.5w
Susceptibility was found to diminish greatly with rise of temperature. According to G. Jäger and S. Meyer (_Wien. Akad. Sitz._, 1897, 106, II. a, p. 623, and 1898, 107, II. a, p. 5) the atomic susceptibilities k of the metals nickel, chromium, iron, cobalt and manganese in solutions of their salts are as follows:--
Metal. k × 10^6 | Metal. k × 10^6. | Ni 4.95 = 2.5 × 2 | Co 10.0 = 2.5 × 4 Cr 6.25 = 2.5 × 2.5 | Fe(2) 12.5 = 2.5 × 5 Fe(1) 7.5 = 2.5 × 3 | Mn 15.0 = 2.5 × 6
Fe(1) is iron contained in FeCl2 and Fe(2) iron contained in Fe2(NO3)6.
Curie has shown, for many paramagnetic bodies, that the specific susceptibility K is inversely proportional to the absolute temperature [theta]. Du Bois believes this to be an important general law, applicable to the case of every paramagnetic substance, and suggests that the product K[theta] should be known as "Curie's constant" for the substance.
_Elementary Bodies and Atomic Susceptibility._--Among a large number of substances the susceptibilities of which have been determined by J. Koenigsberger (_Wied. Ann._, 1898, 66, 698) are the following elements:--
Element. [kappa] × 10^6. | Element. [kappa] × 10^6. | Copper -0.82 | Tellurium - 2.10 Silver -1.51 | Graphite + 2 Gold -3.07 | Aluminium + 1.80 Zinc -0.96 | Platinum +22 Tin +0.46 | Palladium +50 to 60 Lead -1.10 | Tungsten +14 Thallium -4.61 | Magnesium + 4 Sulphur -0.86 | Sodium + 2.2 Selenium (red) -0.50 | Potassium + 3.6
In a table accompanying Koenigsberger's paper the elements are arranged upon the periodic system and the atomic susceptibility (product of specific susceptibility into atomic weight) is given for each. It appears that the elements at about the middle of each row are the most strongly paramagnetic; towards the ends of a row the susceptibility decreases, and ultimately becomes negative. Thus a relation between susceptibility and atomic weight is clearly indicated. Tables similarly arranged, but much more complete, have been published by S. Meyer (_Wied. Ann._, 1899, 68, 325 and 1899, 69, 236), whose researches have filled up many previously existing gaps. The values assigned to the atomic susceptibilities of most of the known elements are appended. According to the notation adopted by Meyer the atomic susceptibility k = [kappa] × atomic-weight/(density × 1000).
Meyer thinks that the susceptibilities of the metals praseodymium, neodymium, ytterbium, samarium, gadolinium, and erbium, when obtained in a pure form, will be found to equal or even exceed those of the well-known ferromagnetic metals. Many of their compounds are very strongly magnetic; erbium, for example, in Er2O3 being four times as strong as iron in the familiar magnetite or lodestone, Fe2O3. The susceptibilities of some hundreds of inorganic compounds have also been determined by the same investigator (loc. cit.). Among other researches relating to atomic and molecular magnetism are those of O. Liebknecht and A. P. Wills (_Ann. d. Phys._, 1900, 1, 178), H. du Bois and O. Liebknecht (ibid. p. 189), and Meyer (ibid. p. 668). An excellent summary regarding the magnetic properties of matter, with many tables and references, has been compiled by du Bois (_Report to the Congrès Int. de Phys._, Paris, 1900, ii. 460).
+--------------------+--------------------+-------------------+ | _Element_ 10^6k | _Element_ 10^6k | _Element_ 10^6k | +--------------------+--------------------+-------------------+ | Be +0.72 | Cu -0.006 | Cs -0.03* | | B +0.05 | Zn -0.010 | Ba -0.02* | | C -0.05 | Ga - | La +13.0 | | N ? | Ge - | Ce +34.0 | | O + | As ? | Pr +\ | | F -0.01* | Se -0.025 | Nd +| Strong| |....................| Br -0.033 | Sa +| | | Na -0.005* |....................| Gd +/ | | Mg +0.014 | Rb -0.02* |...................| | Al + | Sr -0.02* | Er +41.8(?) | | Si +0.002 | Y +3.2(?) |...................| | P -0.007 | Zr -0.014 | Yb + (?) | | S -0.011 | Nb +0.49(?) | Ta +1.02(?) | | Cl -0.02* | Mo +0.024 | W +0.1 | |....................| Ru + | Os +0.074 | | K -0.001* | Rh + | Ir + | | Ca -0.003* | Pd +0.55 | Pt +0.227 | | Sc ? | Ag -0.016 | Au -0.031 | | Ti +0.09 | Cd -0.015 | Hg -0.030 | | V +0.17 | In +0.01* | Tl -0.93 | | Cr +\ | Sn +0.004* | Pb -0.025 | | Mn +| | Sb -0.069 | Bi -0.023 | | Fe +|Strong | Te -0.039 |...................| | Co +| | I -0.040 | Th +16.0(?) | | Ni +/ |....................| U +0.21 | +--------------------+--------------------+-------------------+ * Calculated.
12. MOLECULAR THEORY OF MAGNETISM
According to W. E. Weber's theory, the molecules of a ferromagnetic metal are small permanent magnets, the axes of which under ordinary conditions are turned indifferently in every direction, so that no magnetic polarity is exhibited by the metal as a whole; a magnetic force acting upon the metal tends to turn the axes of the little magnets in one direction, and thus the entire piece acquires the properties of a magnet. If, however, the molecules could turn with perfect freedom, it is clear that the smallest magnetizing force would be sufficient to develop the highest possible degree of magnetization, which is of course not the case. Weber therefore supposed each molecule to be acted on by a force tending to preserve it in its original direction, the position actually assumed by the axis being in the direction of the resultant of this hypothetical force and the applied magnetizing force. Maxwell (_Electricity and Magnetism_, § 444), recognizing that the theory in this form gave no account of residual magnetization, made the further assumption that if the deflection of the axis of the molecule exceeded a certain angle, the axis would not return to its original position when the deflecting force was removed, but would retain a permanent set. Although the amended theory as worked out by Maxwell is in rough agreement with certain leading phenomena of magnetization, it fails to account for many others, and is in some cases at variance with observed facts.
J. A. Ewing (_Proc. Roy. Soc._, 1890, 48, 342) has demonstrated that it is quite unnecessary to assume either the directive force of Weber, the permanent set of Maxwell, or any kind of frictional resistance, the forces by which the molecular magnets are constrained being simply those due to their own mutual attractions and repulsions. The effect of these is beautifully illustrated by a model consisting of a number of little compass needles pivoted on sharp points and grouped near to one another upon a board, which is placed inside a large magnetizing coil. When no current is passing through the coil and the magnetic field is of zero strength, the needles arrange themselves in positions of stable equilibrium under their mutual forces, pointing in many different directions, so that there is no resultant magnetic moment. This represents the condition of the molecules in unmagnetized iron. If now a gradually increasing magnetizing force is applied, the needles at first undergo a stable deflection, giving to the group a small resultant moment which increases uniformly with the force; and if the current is interrupted while the force is still weak, the needles merely return to their initial positions. This illustrates the first stage in the process of magnetization, when the moment is proportional to the field and there is no hysteresis or residual magnetism (see _ante_). A somewhat stronger field will deflect many of the needles beyond the limits of stability, causing them to turn round and form new stable combinations, in which the direction assumed by most of them approximates to that of the field. The rearrangement is completed within a comparatively small range of magnetizing force, a rapid increase of the resultant moment being thus brought about. When the field is removed, many of the newly formed combinations are but slightly disturbed, and the group may consequently retain a considerable resultant moment. This corresponds to the second stage of magnetization, in which the susceptibility is large and permanent magnetization is set up. A still stronger magnetizing force has little effect except in causing the direction of the needles to approach still more nearly to that of the field; if the force were infinite, every member of the group would have exactly the same direction and the greatest possible resultant moment would be reached; this illustrates "magnetic saturation"--the condition approached in the third stage of magnetization. When the strong magnetizing field is gradually diminished to zero and then reversed, the needles pass from one stable position of rest to another through a condition of instability; and if the field is once more reversed, so that the cycle is completed, the needles again pass through a condition of instability before a position of stable equilibrium is regained. Now the unstable movements of the needles are of a mechanically irreversible character; the energy expended in dissociating the members of a combination and placing them in unstable positions assumes the kinetic form when the needles turn over, and is ultimately frittered down into heat. Hence in performing a cycle there is a waste of energy corresponding to what has been termed hysteresis-loss.
Supposing Ewing's hypothesis to be correct, it is clear that if the magnetization of a piece of iron were reversed by a strong rotating field instead of by a field alternating through zero, the loss of energy by hysteresis should be little or nothing, for the molecules would rotate with the field and no unstable movements would be possible.[91] Some experiments by F. G. Baily (_Phil. Trans._, 1896, 187, 715) show that this is actually the case. With small magnetizing forces the hysteresis was indeed somewhat larger than that obtained in an alternating field, probably on account of the molecular changes being forced to take place in one direction only; but at an induction of about 16,000 units in soft iron and 15,000 in hard steel the hysteresis reached a maximum and afterwards rapidly diminished. In one case the hysteresis loss per cubic centimetre per cycle was 16,100 ergs for B = 15,900, and only 1200 ergs for B = 20,200, the highest induction obtained in the experiment; possibly it would have vanished before B had reached 21,000.[92] These experiments prove that actual friction must be almost entirely absent, and, as Baily remarks, the agreement of the results with the previously suggested deduction affords a strong verification of Ewing's form of the molecular theory. Ewing has himself also shown how satisfactorily this theory accords with many other obscure and complicated phenomena, such as those presented by coercive force, differences of magnetic quality, and the effects of vibration, temperature and stress; while as regards simplicity and freedom from arbitrary assumptions it leaves little to be desired.
The fact being established that magnetism is essentially a molecular phenomenon, the next step is to inquire what is the constitution of a magnetic molecule, and why it is that some molecules are ferromagnetic, others paramagnetic, and others again diamagnetic. The best known of the explanations that have been proposed depend upon the magnetic action of an electric current. It can be shown that if a current i circulates in a small plane circuit of area S, the magnetic action of the circuit for distant points is equivalent to that of a short magnet whose axis is perpendicular to the plane of the circuit and whose moment is iS, the direction of the magnetization being related to that of the circulating current as the thrust of a right-handed screw to its rotation. Ferromagnetism was explained by Ampère on the hypothesis that the magnetization of the molecule is due to an electric current constantly circulating within it. The theory now most in favour is merely a development of Ampère's hypothesis, and applies not only to ferromagnetics, but to paramagnetics as well. To account for diamagnetism, Weber supposed that there exist within the molecules of diamagnetic substances certain channels around which an electric current can circulate without any resistance. The creation of an external magnetic field H will, in accordance with Lenz's law, induce in the molecule an electric current so directed that the magnetization of the equivalent magnet is opposed to the direction of the field. The strength of the induced current is -HScos[theta]/L, where [theta] is the inclination of the axis of the circuit to the direction of the field, and L the coefficient of self-induction; the resolved part of the magnetic moment in the direction of the field is equal to -HS²cos²[theta]/L, and if there are n molecules in a unit of volume, their axes being distributed indifferently in all directions, the magnetization of the substance will be -(1/3)nHS²/L, and its susceptibility -(1/3)S²/L (Maxwell, _Electricity and Magnetism_, § 838). The susceptibility is therefore constant and independent of the field, while its negative sign indicates that the substance is diamagnetic. There being no resistance, the induced current will continue to circulate round the molecule until the field is withdrawn, when it will be stopped by the action of an electromotive force tending to induce an exactly equal current in the opposite direction. The principle of Weber's theory, with the modification necessitated by lately acquired knowledge, is the basis of the best modern explanation of diamagnetic phenomena.
There are strong reasons for believing that magnetism is a phenomenon involving rotation, and as early as 1876 Rowland, carrying out an experiment which had been proposed by Maxwell, showed that a revolving electric charge produced the same magnetic effects as a current. Since that date it has more than once been suggested that the molecular currents producing magnetism might be due to the revolution of one or more of the charged atoms or "ions" constituting the molecule. None of the detailed hypotheses which were based on this idea stood the test of criticism, but towards the end of the 19th century the researches of J. J. Thomson and others once more brought the conception of moving electric charges into prominence. Thomson has demonstrated the existence under many different conditions of particles more minute than anything previously known to science. The mass of each is about 1/1700th part of that of a hydrogen atom, and with each is indissolubly associated a charge of negative electricity equal to about 3.1 × 10^(-10) C.G.S. electrostatic unit. These particles, which were termed by their discoverer _corpuscles_, are more commonly spoken of as _electrons_,[93] the particle thus being identified with the charge which it carries. An electrically neutral atom is believed to be constituted in part, or perhaps entirely, of a definite number of electrons in rapid motion within a "sphere of uniform positive electrification" not yet explained. One or more of the electrons may be detached from the system by a finite force, the number so detachable depending on the valency of the atom; if the atom loses an electron, it becomes positively electrified; if it receives additional electrons, it is negatively electrified. The process of electric conduction in metals consists in the movement of detached electrons, and many other phenomena, both electrical and thermal, can be more or less completely explained by their agency. It has been supposed that certain electrons revolve like satellites in orbits around the atoms with which they are associated, a view which receives strong support from the phenomena of the Zeeman effect, and on this assumption a theory has been worked out by P. Langevin,[94] which accounts for many of the observed facts of magnetism. As a consequence of the structure of the molecule, which is an aggregation of atoms, the planes of the orbits around the latter may be oriented in various positions, and the direction of revolution may be right-handed or left-handed with respect to the direction of any applied magnetic field. For those orbits whose projection upon a plane perpendicular to the field is right-handed, the period of revolution will be accelerated by the field (since the electron current is negative), and the magnetic moment consequently increased; for those which are left-handed, the period will be retarded and the moment diminished. The effect of the field upon the speed of the revolving electrons, and therefore upon the moments of the equivalent magnets, is necessarily a very small one. If S is the area of the orbit described in time [tau] by an electron of charge e, the moment of the equivalent magnet is M = eS[tau]; and the change in the value of M due to an external field H is shown to be [Delta]M = -He^2 S/4[pi]m, m being the mass of the electron. Whence
[Delta]M H[tau]e -------- = -------. M 4[pi]m
According to the best determinations the value of e/m does not exceed 1.8 × 10^7, and [tau] is of the order of 10^(-15) second, the period of luminous vibrations; hence [Delta]M/M must always be less than 10^(-9)H, and therefore the strongest fields yet reached experimentally, which fall considerably short of 10^5, could not change the magnetic moment M by as much as a ten-thousandth part. If the structure of the molecule is so perfectly symmetrical that, in the absence of any external field, the resultant magnetic moment of the circulating electrons is zero, then the application of a field, by accelerating the right-handed (negative) revolutions, and retarding those which are left-handed, will induce in the substance a resultant magnetization opposite in direction to the field itself; a body composed of such symmetrical molecules is therefore diamagnetic. If however the structure of the molecule is such that the electrons revolving around its atoms do not exactly cancel one another's effects, the molecule constitutes a little magnet, which under the influence of an external field will tend to set itself with its axis parallel to the field. Ordinarily a substance composed of asymmetrical molecules is paramagnetic, but if the elementary magnets are so conditioned by their strength and concentration that mutual action between them is possible, then the substance is ferromagnetic. In all cases however it is the diamagnetic condition that is initially set up--even iron is diamagnetic--though the diamagnetism may be completely masked by the superposed paramagnetic or ferromagnetic condition. Diamagnetism, in short, is an atomic phenomenon; paramagnetism and ferromagnetism are molecular phenomena. Hence may be deduced an explanation of the fact that, while the susceptibility of all known diamagnetics (except bismuth and antimony) is independent of the temperature, that of paramagnetics varies inversely as the absolute temperature, in accordance with the law of Curie.
13. HISTORICAL AND CHRONOLOGICAL NOTES
The most conspicuous property of the lodestone, its attraction for iron, appears to have been familiar to the Greeks at least as early as 800 B.C., and is mentioned by Homer, Plato, Aristotle, Theophrastus and others. A passage in _De rerum natura_ (vi. 910-915) by the Roman poet, Lucretius (96-55 B.C.), in which it is stated that the stone can support a chain of little rings, each adhering to the one above it, indicates that in his time the phenomenon of magnetization by induction had also been observed. The property of orientation, in virtue of which a freely suspended magnet points approximately to the geographical north and south, is not referred to by any European writer before the 12th century, though it is said to have been known to the Chinese at a much earlier period. The application of this property to the construction of the mariner's compass is obvious, and it is in connexion with navigation that the first references to it occur (see COMPASS). The needles of the primitive compasses, being made of iron, would require frequent re-magnetization, and a "stone" for the purpose of "touching the needle" was therefore generally included in the navigator's outfit. With the constant practice of this operation it is hardly possible that the repulsion acting between like poles should have entirely escaped recognition; but though it appears to have been noticed that the lodestone sometimes repelled iron instead of attracting it, no clear statement of the fundamental law that unlike poles attract while like poles repel was recorded before the publication in 1581 of the _New Attractive_ by Robert Norman, a pioneer in accurate magnetic work. The same book contains an account of Norman's discovery and correct measurement of the dip (1576). The downward tendency of the north pole of a magnet pivoted in the usual way had been observed by G. Hartmann of Nüremberg in 1544, but his observation was not published till much later.
The foundations of the modern science of magnetism were laid by William Gilbert (q.v.). His _De magnete magneticisque corporibus et de magno magnete tellure physiologia nova_ (1600), contains many references to the expositions of earlier writers from Plato down to those of the author's own age. These show that the very few facts known with certainty were freely supplemented by a number of ill-founded conjectures, and sometimes even by "figments and falsehoods, which in the earliest times, no less than nowadays, used to be put forth by raw smatterers and copyists to be swallowed of men."[95] Thus it was taught that "if a lodestone be anointed with garlic, or if a diamond be near, it does not attract iron," and that "if pickled in the salt of a sucking fish, there is power to pick up gold which has fallen into the deepest wells." There were said to be "various kinds of magnets, some of which attract gold, others silver, brass, lead; even some which attract flesh, water, fishes;" and stories were told about "mountains in the north of such great powers of attraction that ships are built with wooden pegs, lest the iron nails should be drawn from the timber." Certain occult powers were also attributed to the stone. It was "of use to thieves by its fume and sheen, being a stone born, as it were, to aid theft," and even opening bars and locks; it was effective as a love potion, and possessed "the power to reconcile husbands to their wives, and to recall brides to their husbands." And much more of the same kind, which, as Gilbert says, had come down "even to [his] own day through the writings of a host of men, who, to fill out their volumes to a proper bulk, write and copy out pages upon pages on this, that and the other subject, of which they know almost nothing for certain of their own experience." Gilbert himself absolutely disregarded authority, and accepted nothing at second-hand. His title to be honoured as the "Father of Magnetic Philosophy" is based even more largely upon the scientific method which he was the first to inculcate and practise than upon the importance of his actual discoveries. Careful experiment and observation, not the inner consciousness, are, he insists, the only foundations of true science. Nothing has been set down in his book "which hath not been explored and many times performed and repeated" by himself. "It is very easy for men of acute intellect, apart from experiment and practice, to slip and err." The greatest of Gilbert's discoveries was that the globe of the earth was magnetic and a magnet; the evidence by which he supported this view was derived chiefly from ingenious experiments made with a spherical lodestone or _terrella_, as he termed it, and from his original observation that an iron bar could be magnetized by the earth's force. He also carried out some new experiments on the effects of heat, and of screening by magnetic substances, and investigated the influence of shape upon the magnetization of iron. But the bulk of his work consisted in imparting scientific definiteness to what was already vaguely known, and in demolishing the errors of his predecessors.
No material advance upon the knowledge recorded in Gilbert's book was made until the establishment by Coulomb in 1785 of the law of magnetic action. The difficulties attending the experimental investigation of the forces acting between magnetic poles have already been referred to, and indeed a rigorously exact determination of the mutual action could only be made under conditions which are in practice unattainable. Coulomb,[96] however, by using long and thin steel rods, symmetrically magnetized, and so arranged that disturbing influences became negligibly small, was enabled to deduce from his experiments with reasonable certainty the law that the force of attraction or repulsion between two poles varies inversely as the square of the distance between them. Several previous attempts had been made to discover the law of force, with various results, some of which correctly indicated the inverse square; in particular the German astronomer, J. Tobias Mayer (_Gött. Anzeiger_, 1760), and the Alsatian mathematician, J. Heinrich Lambert (_Hist. de l'Acad. Roy. Berlin_, 1766, p. 22), may fairly be credited with having anticipated the law which was afterwards more satisfactorily established by Coulomb. The accuracy of this law was in 1832 confirmed by Gauss,[97] who employed an indirect but more perfect method than that of Coulomb, and also, as Maxwell remarks, by all observers in magnetic observatories, who are every day making measurements of magnetic quantities, and who obtain results which would be inconsistent with each other if the law of force had been erroneously assumed.
Coulomb's researches provided data for the development of a mathematical theory of magnetism, which was indeed initiated by himself, but was first treated in a complete form by Poisson in a series of memoirs published in 1821 and later.[98] Poisson assumed the existence of two dissimilar magnetic fluids, any element of which acted upon any other distant element in accordance with Coulomb's law of the inverse square, like repelling and unlike attracting one another. A magnetizable substance was supposed to consist of an indefinite number of spherical particles, each containing equivalent quantities of the two fluids, which could move freely within a particle, but could never pass from one particle to another. When the fluids inside a particle were mixed together, the particle was neutral; when they were more or less completely separated, the particle became magnetized to an intensity depending upon the magnetic force applied; the whole body therefore consisted of a number of little spheres having north and south poles, each of which exerted an elementary action at a distance. On this hypothesis Poisson investigated the forces due to bodies magnetized in any manner, and also originated the mathematical theory of magnetic induction. The general confirmation by experiment of Poisson's theoretical results created a tendency to regard his hypothetical magnetic fluids as having a real existence; but it was pointed out by W. Thomson (afterwards Lord Kelvin) in 1849 that while no physical evidence could be adduced in support of the hypothesis, certain discoveries, especially in electromagnetism, rendered it extremely improbable (_Reprint_, p. 344). Regarding it as important that all reasoning with reference to magnetism should be conducted without any uncertain assumptions, he worked out a mathematical theory upon the sole foundation of a few well-known facts and principles. The results were substantially the same as those given by Poisson's theory, so far as the latter went, the principal additions including a fuller investigation of magnetic distribution, and the theory of magnetic induction in aeolotropic or crystalline substances. The mathematical theory which was constructed by Poisson, and extended and freed from doubtful hypotheses by Kelvin, has been elaborated by other investigators, notably F. E. Neumann, G. R. Kirchhoff, and Maxwell. The valuable work of Gauss on magnetic theory and measurements, especially in relation to terrestrial magnetism, was published in his _Intensitas vis magneticae terrestris_, 1833, and in memoirs communicated to the _Resultate aus den Beobachtungen des magnetischen Vereins_, 1838 and 1839, which, with others, are contained in vol. 5 of the collected _Werke_. Weber's molecular theory, which has already been referred to, appeared in 1852.[99]
An event of the first importance was the discovery made in 1819 by H. C. Oersted [100] that a magnet placed near a wire carrying an electric current tended to set itself at right angles to the wire, a phenomenon which indicated that the current was surrounded by a magnetic field. This discovery constituted the foundation of electromagnetism, and its publication in 1820 was immediately followed by A. M. Ampère's experimental and theoretical investigation of the mutual action of electric currents,[101] and of the equivalence of a closed circuit to a polar magnet, the latter suggesting his celebrated hypothesis that molecular currents were the cause of magnetism. In the same year D. F. Arago[102] succeeded in magnetizing a piece of iron by the electric current, and in 1825 W. Sturgeon[103] publicly exhibited an apparatus "acting on the principle of powerful magnetism and feeble galvanism" which is believed to have constituted the first actual electromagnet. Michael Faraday's researches were begun in 1831 and continued for more than twenty years. Among the most splendid of his achievements was the discovery of the phenomena and laws of magneto-electric induction, the subject of two papers communicated to the Royal Society in 1831 and 1832. Another was the magnetic rotation of the plane of polarization of light, which was effected in 1845, and for the first time established a relation between light and magnetism. This was followed at the close of the same year by the discovery of the magnetic condition of all matter, a discovery which initiated a prolonged and fruitful study of paramagnetic and diamagnetic phenomena, including magnecrystallic action and "magnetic conducting power," now known as permeability. Throughout his researches Faraday paid special regard to the medium as the true seat of magnetic action, being to a large extent guided by his pregnant conception of "lines of force," or of induction, which he considered to be "closed curves passing in one part of the course through the magnet to which they belong, and in the other part through space," always tending to shorten themselves, and repelling one another when they were side by side (_Exp. Res._ §§ 3266-8, 3271). In 1873 James Clerk Maxwell published his classical _Treatise on Electricity and Magnetism_, in which Faraday's ideas were translated into a mathematical form. Maxwell explained electric and magnetic forces, not by the action at a distance assumed by the earlier mathematicians, but by stresses in a medium filling all space, and possessing qualities like those attributed to the old luminiferous ether. In particular, he found that the calculated velocity with which it transmitted electromagnetic disturbances was equal to the observed velocity of light; hence he was led to believe, not only that his medium and the ether were one and the same, but, further, that light itself was an electromagnetic phenomenon. Since the experimental confirmation of Maxwell's views by H. R. Hertz in 1888 (_Weid. Ann._, 1888, 34, 155, 551, 609; and later vols.) they have commanded universal assent, and his methods are adopted in all modern work on electricity and magnetism.
The practice of measuring magnetic induction and permeability with scientific accuracy was introduced in 1873 by H. A. Rowland,[104] whose careful experiments led to general recognition of the fact previously ignored by nearly all investigators, that magnetic susceptibility and permeability are by no means constants (at least in the case of the ferromagnetic metals) but functions of the magnetizing force. New light was thrown upon many important details of magnetic science by J. A. Ewing's _Experimental Researches_ of 1885; throughout the whole of his work special attention was directed to that curious lagging action to which the author applied the now familiar term "hysteresis."[105] His well-known modification[106] of Weber's molecular theory, published in 1890, presented for the first time a simple and sufficient explanation of hysteresis and many other complexities of magnetic quality. The amazing discoveries made by J. J. Thomson in 1897 and 1898[107] resulted in the establishment of the electron theory, which has already effected developments of an almost revolutionary character in more than one branch of science. The application of the theory by P. Langevin to the case of molecular magnetism has been noticed above, and there can be little doubt that in the near future it will contribute to the solution of other problems which are still obscure.
See W. Gilbert, _De magnete_ (London, 1600; trans. by P. F. Mottelay, New York, 1893, and for the Gilbert Club, London, 1900); M. Faraday, _Experimental Researches in Electricity_, 3 vols. (London, 1839, 1844 and 1855); W. Thomson (Lord Kelvin), _Reprint of Papers on Electrostatics and Magnetism_ (London, 1884, containing papers on magnetic theory originally published between 1844 and 1855, with additions); J. C. Maxwell, _Treatise on Electricity and Magnetism_ (3rd ed., Oxford, 1892); E. Mascart and J. Joubert, _Leçons sur l'électricité et le magnétisme_ (2nd ed., Paris, 1896-1897; trans., not free from errors, by E. Atkinson, London, 1883); J. A. Ewing, _Magnetic Induction in Iron and other Metals_ (3rd ed., London, 1900); J. J. Thomson, _Recent Researches in Electricity and Magnetism_ (Oxford, 1893); _Elements of Mathematical Theory of Electricity and Magnetism_ (3rd ed., Cambridge, 1904); H. du Bois, _The Magnetic Circuit_ (trans. by E. Atkinson, London, 1896); A. Gray, _Treatise on Magnetism and Electricity_, vol. i. (London, 1898); J. A. Fleming, _Magnets and Electric Currents_ (London, 1898); C. Maurain, _Le magnétisme du fer_ (Paris, 1899; a lucid summary of the principal facts and laws, with special regard to their practical application); _Rapports présentés au Congrès international de physique_, vol. ii. (Paris, 1900); G. C. Foster and A. W. Porter, _Treatise on Electricity and Magnetism_ (London, 1903); A. Winkelmann, _Handbuch der Physik_, vol. v. part i. (2nd ed., Leipzig, 1905; the most exhaustive compendium of magnetic science yet published, containing references to all important works and papers on every branch of the subject). (S. Bi.)
FOOTNOTES:
[1] In London in 1910 the needle pointed about 16° W. of the geographical north. (See TERRESTRIAL MAGNETISM.)
[2] For the relations between magnetism and light see MAGNETO-OPTICS.
[3] Clerk Maxwell employed German capitals to denote vector quantities. J. A. Fleming first recommended the use of blockletters as being more convenient both to printers and readers.
[4] The C.G.S. unit of current = 10 amperes.
[5] The principal theoretical investigations are summarized in Mascart and Joubert's _Electricity and Magnetism_, i. 391-398 and ii. 646-657. The case of a long iron bar has been experimentally studied with great care by C. G. Lamb, _Proc. Phys. Soc._, 1899, 16, 509.
[6] _Wied. Ann._, 1884, 22, 411.
[7] See C. G. Lamb, _loc. cit._ p. 518.
[8] Hopkinson specified the retentiveness by the numerical value of the "residual induction" (= 4[pi]I).
[9] For all except ferromagnetic substances the coefficient is sensibly equal to [kappa].
[10] See W. Thomson's _Reprint_, §§ 615, 634-651.
[11] Ibid. §§ 646, 684.
[12] Faraday, _Exp. Res._ xxi.
[13] J. J. Thomson, _Electricity and Magnetism_, § 205.
[14] Maxwell, _Electricity and Magnetism_, § 431.
[15] H. du Bois, _Electrician_, 1898, 40, 317.
[16] M. Faraday, _Exp. Res._ xxii., xxiii.; W. Thomson, _Reprint_, § 604; J. C. Maxwell, _Treatise_, § 435; E. Mascart and J. Joubert, _Electricity and Magnetism_, §§ 384, 396, 1226; A. Winkelmann, _Physik_, v. 287.
[17] See A. Winkelmann, _Physik_, v. 69-94; Mascart and Joubert. _Electricity and Magnetism_, ii. 617.
[18] _Sci. Abs._ A, 1906, 9, 225.
[19] See C. G. Lamb, _Proc. Phys. Soc._, 1899, 16, 517.
[20] _Soc. Franc. Phys. Séances_, 1904, 1, 27.
[21] E. G. Warburg, _Wied. Ann._ 1881, 13, 141; Ewing, _Phil. Trans._, 1885, 176, 549; Hopkinson, _Phil. Trans._ 1885, 176, 466. For a simple proof, see Ewing, _Magnetic Induction_ (1900), p. 99. Hopkinson pointed out that the greatest dissipation of energy which can be caused by a to-and-fro reversal is approximately represented by _Coercive force_ × _maximum induction_ /[pi].
[22] _Magnetic Induction_, 1900, 378.
[23] _Phil. Trans._, 1902, 198, 33.
[24] _Phil. Mag._, 1903, 5, 117.
[25] Some experiments by F. G. Baily showed that hysteresis ceased to increase when B was carried beyond 23,000. This value of B corresponds to I = 1640, the saturation point for soft iron.--_Brit. Assoc. Rep._, 1895, p. 636.
[26] _Tokyo Phys.-Math. Soc._, 1904, 2, No. 14.
[27] _Phil. Mag._, 1873, 46, 140.
[28] S. Bidwell, _Proc. Roy. Soc._, 1886, 40, 495.
[29] Since in most practicable experiments H³ is negligible in comparison with B², the force may be taken as B²/8[pi] without sensible error.
[30] The same phenomenon is exhibited in a less marked degree when soft iron is magnetized in stronger fields (Ewing, _Phil. Trans._, 1885, 176, 569).
[31] Principal publications: J. P. Joule, _Scientific Papers_, pp. 46, 235; A. M. Meyer, _Phil. Mag._, 1873, 46, 177; W. F. Barrett, _Nature_, 1882, 26, 585; S. Bidwell, _Phil. Trans._, 1888, 179A, 205; _Proc. Roy. Soc._, 1886, 40, 109 and 257; 1888, 43, 406; 1890, 47, 469; 1892, 51, 495; 1894, 55, 228; 1894, 56, 94; 1904, 74, 60; _Nature_, 1899, 60, 222; M. Cantone, _Mem. d. Acc d. Lincei_, 1889, 6, 487; _Rend. d. Acc. d. Lincei_, 1890, 6, 252; A. Berget, _C.R._, 1892, 115, 722; S. J. Lochner, _Phil. Mag._, 1893, 36, 498; H. Nagaoka, _Phil. Mag._, 1894, 37, 131; _Wied. Ann._, 1894, 53, 487; C. G. Knott, _Proc. Roy. Soc. Ed._, 1891, 18, 315; _Phil. Mag._, 1894, 37, 141; _Trans. Roy. Soc. Ed._, 1896, 38, 527; 1898, 39, 457; C. G. Knott and A. Shand, _Proc. Roy. Soc. Ed._, 1892, 19, 85 and 249; 1894, 20, 295; L. T. More, _Phil. Mag._, 1895, 40, 345; G. Klingenberg, _Rostock Univ. Thesis_, Berlin, 1897; E. T. Jones, _Phil. Trans._, 1897, 189A, 189; B. B. Brackett, _Phys. Rev._, 1897, 5, 257; H. Nagaoka and K. Honda, _Phil. Mag._, 1898, 46, 261; 1900, 49, 329; _Journ. Coll. Sci. Tokyo_, 1900, 13, 57; 1903, 19, art. 11; J. S. Stevens, _Phys. Rev._, 1898, 7, 19; E. Rhoads, _Phys. Rev._, 1898, 7, 5; _Phil. Mag._, 1901, 2, 463; G. A. Shakespear, _Phil. Mag._, 1899, 17, 539; K. Honda, _Journ. Coll. Sci. Tokyo_, 1900, 13, 77; L. W. Austin, _Phys. Rev._, 1900, 10, 180; _Deutsch. Phys. Gesell. Verh._, 1904, 6, 4, 211; K. Honda and S. Shimizu, _Phil. Mag._, 1902, 4, 338; 1905, 10, 548.
[32] The loads were successively applied in decreasing order of magnitude. They are indicated in fig. 25 as kilos per sq. cm.
[33] Joule believed that the volume was unchanged.
[34] For a discussion of theories of magnetic stress, with copious references, see Nagaoka, _Rap. du Congrès International de Physique_ (Paris, 1900), ii. 545. Also Nagaoka and Jones, _Phil. Mag._, 1896, 41, 454.
[35] S. Bidwell, _Phil. Trans._, 1888, 179a, 321.
[36] _Phil. Mag._, 1895, 40, 345.
[37] J. C. Maxwell, _Treatise_, § 643.
[38] See correspondence in _Nature_, 1896, 53, pp. 269, 316, 365, 462, 533; 1906, 74, pp. 317, 539; B. B. Brackett, _loc. cit._, quotes the opinion of H. A. Rowland in support of compressive stress.
[39] J. A. Ewing, _Phil. Trans._, 1885, 176, 580; 1888, 179, 333; _Magnetic Induction_, 1900, ch. ix.; J. A. Ewing and G. C. Cowan, _Phil. Trans._, 1888, 179a, 325; C. G. Knott, _Trans. Roy. Soc. Ed._, 1882-1883, 32, 193; 1889, 35, 377; 1891, 36, 485; _Proc. Roy. Soc. Ed._, 1899, 586; H. Nagaoka, _Phil. Mag._, 1889, 27, 117; 1890, 29, 123; H. Nagaoka and K. Honda, _Journ. Coll. Sci. Tokyo_, 1900, 13, 263; 1902, 16, art. 8; _Phil. Mag._, 1898, 46, 261; 1902, 4, 45; K. Honda and S. Shimizu, _Ann. d. Phys._, 1904, 14, 791; _Tokyo Physico-Math. Soc. Rep._, 1904, 2, No. 13; K. Honda and T. Terada, _Journ. Coll. Sci. Tokyo_, 1906, 21, art. 4.
[40] H. Tomlinson found a critical point in the "temporary magnetization" of nickel (_Proc. Phys. Soc._, 1890, 10, 367, 445), but this does not correspond to a Villari reversal. Its nature is made clear by Ewing and Cowan's curves (_Phil. Trans._, 1888, 179, plates 15, 16).
[41] _Wied. Ann._, 1894, 52, 462; _Electrician_, 1894, 34, 143.
[42] _Phil. Trans._, 1890, 131, 329.
[43] _Magnetic Induction_, 1900, 222.
[44] _Phys. Rev._, 1904, 18, 432.
[45] _Phil. Mag._, 1886, 22, 50.
[46] _Ibid._ 251.
[47] _Phil. Mag._, 1891, 32, 383.
[48] _C.R._, 1896, 122, 1192; 1898, 126, 463.
[49] _Phil. Mag._, 1889, 27, 117.
[50] _Journ. Coll. Sci. Tokyo_, 1904, 19, art. 9.
[51] _Phil. Mag._, 1905, 10, 548; _Tokyo Phys.-Math. Soc. Rep._, 1904, 2, No. 14; _Journ. Coll. Sci. Tokyo_, 1905, 20, art. 6.
[52] _C.R._, 1888, 106, 129.
[53] _Proc. Phys. Soc._, 1888, 9, 181.
[54] _C.R._, 1892, 115, 805; 1894, 118, 796 and 859.
[55] _Elekt. Zeits._, 1894, 15, 194.
[56] _Phil. Mag._, 1900, 50, 1.
[57] _Phil. Trans._, 1903, 201, 1.
[58] _Phil. Mag._, 1904, 8, 179.
[59] A. M. Thiessen (_Phys._, 1899, 8, 65) and G. Claude (C. R., 1899, 129, 409) found that for considerable inductions (B = 15,000) the permeability and hysteresis-loss remained nearly constant down to -186°; for weak inductions both notably diminished with temperature.
[60] _Proc. Roy. Soc._, 1898, 62, 210.
[61] _C.R._, 1895, 120, 263.
[62] _Amer. Journ. Sci._, 1898, 5, 245.
[63] _Phys. Rev._, 1901, 14, 181.
[64] _C.R._, 1897, 124, 176 and 1515; 1897, 125, 235; 1898, 126, 738.
[65] Ibid., 1898, 126, 741.
[66] Ibid., 1899, 128, 304 and 1395.
[67] See also J. Hopkinson, _Journ. Inst. Elect. Eng._, 1890, 19, 20, and J. A. Ewing, _Phil. Trans._, 1889, 180, 239.
[68] Many of the figures which, through an error, were inaccurately stated in the first paper are corrected in the second.
[69] The marked effect of silicon in increasing the permeability of cast iron has also been noticed by F. C. Caldwell, _Elect. World_, 1898, 32, 619.
[70] _Trans. Roy. Dub. Soc._, 1902-4, 8, 1 and 123.
[71] J. Trowbridge and S. Sheldon, _Phil. Mag._, 1890, 29, 136; W. H. Preece, _Journ. Inst. Elec. Eng._, 1890, 19, 62; _Electrician_, 1890, 25, 546; I. Klemençiç, _Wien. Ber._, 1896, 105, IIa, 635; B. O. Peirce, _Am. Journ. Sci._, 1896, 2, 347; A. Abt, _Wied. Ann._, 1898, 66, 116; F. Osmond, _C. R._, 1899, 128, 1513.
[72] _Deutsch. phys. Gesell. Verh._, 1903, 5, 220 and 224.
[73] _Exp. Res._, iii. 440.
[74] No record can be found of experiments with manganese at the temperature of liquid air or hydrogen; probably, however, negative results would not be published.
[75] The critical temperature of iron, for instance, is raised more than 100° by the addition of a little carbon and tungsten.
[76] _Bull. Soc. Int. des Électriciens_, 1906, 6, 301.
[77] _Proc. Roy. Soc._, 1905, 76A, 271.
[78] E. H. Hall, _Phil. Mag._, 1880, 9, 225; 1880, 10, 301; 1881, 12, 157; 1883, 15, 341; 1885, 19, 419.
[79] The large Hall effect in bismuth was discovered by Righi, _Journ. de Phys._, 1884, 3, 127.
[80] REFERENCES.--(2) A. von Ettinghausen, _Wied. Ann._, 1887, 31, 737.--(4) H. W. Nernst, ibid., 784.--(i.) and (iv.); A. von Ettinghausen and H. W. Nernst, _Wied. Ann._, 1886, 29, 343.--(ii.) and (iii.); A. Righi, _Rend. Acc. Linc._, 1887, 3 II, 6 and I, 481; and A. Leduc, _Journ. de Phys._, 1887, 6, 78. Additional authorities are quoted by Lloyd, _loc. cit._
[81] P. Drude, _Ann. d. Phys._, 1900, 1, 566; 1900, 3, 369; 1902, 7, 687. See also E. van Everdingen, _Arch. Néerlandaises_, 1901, 4, 371; G. Barlow, _Ann. d. Phys._, 1903, 12, 897; H. Zahn, ibid. 1904, 14, 886; 1905, 16, 148.
[82] _Phil. Trans._, 1856, p. 722. According to the nomenclature adopted by the best modern authorities, a metal A is said to be thermo-electrically positive to another metal B when the thermo-current passes from A to B through the cold junction, and from B to A through the hot (see THERMO-ELECTRICITY).
[83] _C.R._, 1893, 116, 997.
[84] _Journ. de Phys._, 1896, 5, 53.
[85] _Phil. Trans._, 1887, 177, 373.
[86] _Proc. Roy. Soc._, 1885, 39, 513.
[87] _Phys. Rev._, 1902, 15, 321. The sign of the thermo-electric effect for nickel, as given by Rhoads, is incorrect.
[88] _Proc. Roy. Soc._, 1904, 73, 413.
[89] _C.R._, 1903, 136, 1131.
[90] _Journ. Coll. Sci. Tokyo_, 1906, 21, art. 4. The paper contains 40 tables and 85 figures.
[91] This deduction from Ewing's theory appears to have been first suggested by J. Swinburne. See _Industries_, 1890, 289.
[92] R. Beattie (_Phil. Mag._, 1901, 1, 642) has found similar effects in nickel and cobalt.
[93] The charge associated with a corpuscle is the same as that carried by a hydrogen atom. G. J. Stoney in 1881 (_Phil. Mag._, 1881, 11, 387) pointed out that this latter constituted the indivisible "atom of electricity" or natural unit charge. Later he proposed (_Trans. Roy. Dub. Soc._, 1891, 4, 583) that such unit charge should be called an "electron." The application of this term to Thomson's corpuscle implies, rightly or wrongly, that notwithstanding its apparent mass, the corpuscle is in fact nothing more than an atom of electricity. The question whether a corpuscle actually has a material gravitating nucleus is undecided, but there are strong reasons for believing that its mass is entirely due to the electric charge.
[94] _Jour. de Phys._, 1905, 4, 678; translated in _Electrician_, 1905, 56, 108 and 141.
[95] The quotations are from the translation published by the Gilbert Club, London, 1900.
[96] C. A. Coulomb, _Mem. Acad. Roy. Paris_, 1785, p. 578.
[97] _Intensitas vis magneticae_, § 21, C. F. Gauss's _Werke_, 5, 79. See also J. J. Thomson, _Electricity and Magnetism_, § 132.
[98] S. D. Poisson, _Mém. de l'Institut_, 1821 and 1822, 5, 247, 488; 1823, 6, 441; 1838, 16, 479.
[99] For outlines of the mathematical theory of magnetism and references see H. du Bois, _Magnetic Circuit_, chs. iii. and iv.
[100] Gilbert's _Ann. d. phys._, 1820, 6, 295.
[101] _Ann. de chim. et de phys._, 1820, 15, 59, 170; _Recueil d'observations électrodynamiques_, 1822; _Théories des phénomènes électrodynamiques_, 1826.
[102] _Ann. de chim. et de phys._, 1820, 15, 93.
[103] _Trans. Soc. Arts_, 1825, 43, 38.
[104] _Phil. Mag._, 1873, 46, 140; 1874, 48, 321.
[105] _Phil. Trans._, 1885, 176, 523; _Magnetic Induction_, 1900.
[106] _Proc. Roy. Soc._, 1890, 48, 342.
[107] _Phil. Mag._, 1897, 44, 293; 1898, 46, 528.
MAGNETISM, TERRESTRIAL, the science which has for its province the study of the magnetic phenomena of the earth.
Historical.
§ 1. Terrestrial magnetism has a long history. Its early growth was slow, and considerable uncertainty prevails as to its earliest developments. The properties of the magnet (see MAGNETISM) were to some small extent known to the Greeks and Romans before the Christian era, and compasses (see COMPASS) of an elementary character seem to have been employed in Europe at least as early as the 12th century. In China and Japan compasses of a kind seem to have existed at a much earlier date, and it is even claimed that the Chinese were aware of the declination of the compass needle from the true north before the end of the 11th century. Early scientific knowledge was usually, however, a mixture of facts, very imperfectly ascertained, with philosophical imaginings. When an early writer makes a statement which to a modern reader suggests a knowledge of the declination of the compass, he may have had no such definite idea in his mind. So far as Western civilization is concerned, Columbus is usually credited with the discovery--in 1492 during his first voyage to America--that the pointing of the compass needle to the true north represents an exceptional state of matters, and that a _declination_ in general exists, varying from place to place. The credit of these discoveries is not, however, universally conceded to Columbus. G. Hellmann[6][A] considers it almost certain that the departure of the needle from the true north was known in Europe before the time of Columbus. There is indirect evidence that the declination of the compass was not known in Europe in the early part of the 15th century, through the peculiarities shown by early maps believed to have been drawn solely by regard to the compass. Whether Columbus was the first to observe the declination or not, his date is at least approximately that of its discovery.
The next fundamental discovery is usually ascribed to Robert Norman, an English instrument maker. In _The Newe Attractive_ (1581) Norman describes his discovery made some years before of the _inclination_ or _dip_. The discovery was made more or less by accident, through Norman's noticing that compass needles which were truly balanced so as to be horizontal when unmagnetized, ceased to be so after being stroked with a magnet. Norman devised a form of dip-circle, and found a value for the inclination in London which was at least not very wide of the mark.
Another fundamental discovery, that of the secular change of the declination, was made in England by Henry Gellibrand, professor of mathematics at Gresham College, who described it in his _Discourse Mathematical on the Variation of the Magneticall Needle together with its Admirable Diminution lately discovered_ (1635). The history of this discovery affords a curious example of knowledge long delayed. William Borough, in his _Discourse on the Variation of the Compas or Magneticall Needle_ (1581), gave for the declination at Limehouse in October 1580 the value 11°¼ E. approximately. Observations were repeated at Limehouse, Gellibrand tells us, in 1622 by his colleague Edmund Gunter, professor of astronomy at Gresham College, who found the much smaller value 6° 13´. The difference seems to have been ascribed at first to error on Borough's part, and no suspicion of the truth seems to have been felt until 1633, when some rough observations gave a value still lower than that found by Gunter. It was not until midsummer 1634 that Gellibrand felt sure of his facts, and yet the change of declination since 1580 exceeded 7°. The delay probably arose from the strength of the preconceived idea, apparently universally held, that the declination was absolutely fixed. This idea, it would appear, derived some of its strength from the positive assertion made on the point by Gilbert of Colchester in his _De magnete_ (1600).
A third fundamental discovery, that of the diurnal change in the declination, is usually credited to George Graham (1675-1751), a London instrument maker. Previous observers, e.g. Gellibrand, had obtained slightly different values for the declination at different hours of the day, but it was natural to assign them to instrumental uncertainties. In those days the usual declination instrument was the compass with pivoted needles, and Graham himself at first assigned the differences he observed to friction. The observations on which he based his conclusions were made in 1722; an account of them was communicated to the Royal Society and published in the _Philosophical Transactions_ for 1724.
The movements of the compass needle throughout the average day represent partly a regular diurnal variation, and partly irregular changes in the declination. The distinction, however, was not at first very clearly realized. Between 1756 and 1759 J. Canton observed the declination-changes on some 600 days, and was thus able to deduce their general character. He found that the most prominent part of the regular diurnal change in England consisted of a westerly movement of the north-pointing pole from 8 or 9 a.m. to 1 or 2 p.m., followed by a more leisurely return movement to the east. He also found that the amplitude of the movement was considerably larger in summer than in winter. Canton further observed that in a few days the movements were conspicuously irregular, and that aurora was then visible. This association of magnetic disturbance and aurora had, however, been observed somewhat before this time, a description of one conspicuous instance being contributed to the Royal Society in 1750 by Pehr Vilhelm Wargentin (1717-1783), a Swede.
Another landmark in the history of terrestrial magnetism was the discovery towards the end of the 18th century that the intensity of the resultant magnetic force varies at different parts of the earth. The first observations clearly showing this seem to be those of a Frenchman, Paul de Lamanon, who observed in 1785-1787 at Teneriffe and Macao, but his results were not published at the time. The first published observations seem to be those made by the great traveller Humboldt in tropical America between 1798 and 1803. The delay in this discovery may again be attributed to instrumental imperfections. The method first devised for comparing the force at different places consisted in taking the time of oscillation of the dipping needle, and even with modern circles this is hardly a method of high precision. Another discovery worth chronicling was made by Arago in 1827. From observations made at Paris he found that the inclination of the dipping needle and the intensity of the horizontal component of the magnetic force both possessed a diurnal variation.
§ 2. Whilst Italy, England and France claim most of the early observational discoveries, Germany deserves a large share of credit for the great improvement in instruments and methods during the first half of the 19th century. Measurements of the intensity of the magnetic force were somewhat crude until Gauss showed how absolute results could be obtained, and not merely relative data based on observations with some particular needle. Gauss also devised the bifilar magnetometer, which is still largely represented in instruments measuring changes of the horizontal force; but much of the practical success attending the application of his ideas to instruments seems due to Johann von Lamont (1805-1879), a Jesuit of Scottish origin resident in Germany.
The institution of special observatories for magnetic work is largely due to Humboldt and Gauss. The latter's observatory at Göttingen, where regular observations began in 1834, was the centre of the Magnetic Union founded by Gauss and Weber for the carrying out of simultaneous magnetic observations and it was long customary to employ Göttingen time in schemes of international co-operation.
In the next decade, mainly through the influence of Sir Edward Sabine (1788-1883), afterwards president of the Royal Society, several magnetic observatories were established in the British colonies, at St Helena, Cape of Good Hope, Hobarton (now Hobart) and Toronto. These, with the exception of Toronto, continued in full action for only a few years; but their records--from their widely distributed positions--threw much fresh light on the differences between magnetic phenomena in different regions of the globe. The introduction of regular magnetic observatories led ere long to the discovery that there are notable differences between the amplitudes of the regular daily changes and the frequency of magnetic disturbances in different years. The discovery that magnetic phenomena have a period closely similar to, if not absolutely identical with, the "eleven year" period in sun-spots, was made independently and nearly simultaneously about the middle of the 19th century by Lamont, Sabine and R. Wolf.
The last half of the 19th century showed a large increase in the number of observatories taking magnetic observations. After 1890 there was an increased interest in magnetic work. One of the contributory causes was the magnetic survey of the British Isles made by Sir A. Rücker and Sir T. E. Thorpe, which served as a stimulus to similar work elsewhere; another was the institution by L. A. Bauer of a magazine. _Terrestrial Magnetism_, specially devoted to the subject. This increased activity added largely to the stock of information, sometimes in forms of marked practical utility; it was also manifested in the publication of a number of papers of a speculative character. For historical details the writer is largely indebted to the works of E. Walker[1] and L. A. Bauer.[3]
Observational Methods and Records.
§ 3. All the more important magnetic observatories are provided with instruments of two kinds. Those of the first kind give the absolute value of the magnetic elements at the time of observation. The unifilar magnetometer (q.v.), for instance, gives the absolute values of the declination and horizontal force, whilst the inclinometer (q.v.) or dip circle gives the inclination of the dipping needle. Instruments of the second kind, termed magnetographs (q.v.), are differential and self-recording, and show the changes constantly taking place in the magnetic elements. The ordinary form of magnetograph records photographically. Light reflected from a fixed mirror gives a base line answering to a constant value of the element in question; the light is cut off every hour or second hour so that the base line also serves to make the time. Light reflected from a mirror carried by a magnet gives a curved line answering to the changes in position of the magnet. The length of the ordinate or perpendicular drawn from any point of the curved line on to the base line is proportional to the extent of departure of the magnet from a standard position. If then we know the absolute value of the element which corresponds to the base line, and the equivalent of 1 cm. of ordinate, we can deduce the absolute value of the element answering to any given instant of time. In the case of the declination the value of 1 cm. of ordinate is usually dependent almost entirely on the distance of the mirror carried by the magnet from the photographic paper, and so remains invariable or very nearly so. In the case of the horizontal force and vertical force magnetographs--these being the two force components usually recorded--the value of 1 cm. of ordinate alters with the strength of the magnet. It has thus to be determined from time to time by observing the deflection shown on the photographic paper when an auxiliary magnet of known moment, at a measured distance, deflects the magnetograph magnet. Means are provided for altering the sensitiveness, for instance, by changing the effective distance in the bifilar suspension of the horizontal force magnet, and by altering the height of a small weight carried by the vertical force magnet. It is customary to aim at keeping the sensitiveness as constant as possible. A very common standard is to have 1 cm. of ordinate corresponding to 10´ of arc in the declination and to 50[gamma] (1[gamma] = 0.00001 C.G.S.) in the horizontal and vertical force magnetographs.
As an example of how the curves are standardized, suppose that absolute observations of declination are taken four times a month, and that in a given month the mean of the observed values is 16° 34´.6 W. The curves are measured at the places which correspond to the times of the four observations, and the mean length of the four ordinates is, let us say, 2.52 cms. If 1 cm. answers to 10´, then 2.52 cms. represents 25´.2, and thus the value of the base line--i.e. the value which the declination would have if the curve came down to the base line--is for the month in question 16° 34´.6 less 25´.2 or 16° 9´.4. If now we wish to know the declination at any instant in this particular month all we have to do is to measure the corresponding ordinate and add its value, at the rate of 10´ per cm., to the base value 16° 9´.4 just found. Matters are a little more complicated in the case of the horizontal and vertical force magnetographs. Both instruments usually possess a sensible temperature coefficient, i.e. the position of the magnet is dependent to some extent on the temperature it happens to possess, and allowance has thus to be made for the difference from a standard temperature. In the case of the vertical force an "observed" value is derived by combining the observed value of the inclination with the simultaneous value of the horizontal force derived from the horizontal force magnetograph after the base value of the latter has been determined. In themselves the results of the absolute observations are of minor interest. Their main importance is that they provide the means of fixing the value of the base line in the curves. Unless they are made carefully and sufficiently often the information derivable from the curves suffers in accuracy, especially that relating to the secular change. It is from the curves that information is derived as to the regular diurnal variation and irregular changes. In some observatories it is customary to publish a complete record of the values of the magnetic elements at every hour for each day of the year. A useful and not unusual addition to this is a statement of the absolutely largest and smallest values of each element recorded during each day, with the precise times of their occurrence. On days of large disturbance even hourly readings give but a very imperfect idea of the phenomena, and it is customary at some observatories, e.g. Greenwich, to reproduce the more disturbed curves in the annual volume. In calculating the regular diurnal variation it is usual to consider each month separately. So far as is known at present, it is entirely or almost entirely a matter of accident at what precise hours specially high or low values of an element may present themselves during an individual highly disturbed day; whilst the range of the element on such a day may be 5, 10 or even 20 times as large as on the average undisturbed day of the month. It is thus customary when calculating diurnal inequalities to omit the days of largest disturbance, as their inclusion would introduce too large an element of uncertainty. Highly disturbed days are more than usually common in some years, and in some months of the year, thus their omission may produce effects other than that intended. Even on days of lesser disturbance difficulties present themselves. There may be to and fro movements of considerable amplitude occupying under an hour, and the hour may come exactly at the crest or at the very lowest part of the trough. Thus, if the reading represents in every case the ordinate at the precise hour a considerable element of chance may be introduced. If one is dealing with a mean from several hundred days such "accidents" can be trusted to practically neutralize one another, but this is much less fully the case when the period is as short as a month. To meet this difficulty it is customary at some observatories to derive hourly values from a freehand curve of continuous curvature, drawn so as to smooth out the apparently irregular movements. Instead of drawing a freehand curve it has been proposed to use a planimeter, and to accept as the hourly value of the ordinate the mean derived from a consideration of the area included between the curve, the base line and ordinates at the thirty minutes before and after each hour.
§ 4. Partly on account of the uncertainties due to disturbances, and partly with a view to economy of labour, it has been the practice at some observatories to derive diurnal inequalities from a comparatively small number of undisturbed or quiet days. Beginning with 1890, five days a month were selected at Greenwich by the astronomer royal as conspicuously quiet. In the selection regard was paid to the desirability that the arithmetic mean of the five dates should answer to near the middle of the month. In some of the other English observatories the routine measurement of the curves was limited to these selected quiet days. At Greenwich itself diurnal inequalities were derived regularly from the quiet days alone and also from all the days of the month, excluding those of large disturbance. If a quiet day differed from an ordinary day only in that the diurnal variation in the latter was partly obscured by irregular disturbances, then supposing enough days taken to smooth out irregularities, one would get the same diurnal inequality from ordinary and from quiet days. It was found, however, that this was hardly ever the case (see §§ 29 and 30). The quiet day scheme thus failed to secure exactly what was originally aimed at; on the other hand, it led to the discovery of a number of interesting results calculated to throw valuable sidelights on the phenomena of terrestrial magnetism.
The idea of selecting quiet days seems due originally to H. Wild. His selected quiet days for St Petersburg and Pavlovsk were very few in number, in some months not even a single day reaching his standard of freedom from disturbance. In later years the International Magnetic Committee requested the authorities of each observatory to arrange the days of each month in three groups representing the quiet, the moderately disturbed and the highly disturbed. The statistics are collected and published on behalf of the committee, the first to undertake the duty being M. Snellen. The days are in all cases counted from Greenwich midnight, so that the results are strictly synchronous. The results promise to be of much interest.
§ 5. The intensity and direction of the resultant magnetic force at a spot--i.e. the force experienced by a unit magnetic pole--are known if we know the three components of force parallel to any set of orthogonal axes. It is usual to take for these axes the vertical at the spot and two perpendicular axes in the horizontal plane; the latter are usually taken in and perpendicular to the geographical meridian. The usual notation in mathematical work is X to the north, Y to the west or east, and Z vertically downwards. The international magnetic committee have recommended that Y be taken positive to the east, but the fact that the declination is westerly over most of Europe has often led to the opposite procedure, and writers are not always as careful as they should be in stating their choice. Apart from mathematical calculations, the more usual course is to define the force by its horizontal and vertical components--usually termed H and V--and by the declination or angle which the horizontal component makes with the astronomical meridian. The declination is sometimes counted from 0° to 360°, 0° answering to the case when the so-called north pole (or north seeking pole) is directed towards geographical north, 90° to the case when it is directed to the east, and so on. It is more usual, however, to reckon declination only from 0° to 180°, characterizing it as easterly or westerly according as the north pole points to the east or to the west of the geographical meridian. The force is also completely defined by H or V, together with D the declination, and I the inclination to the horizon of the dipping needle. Instead of H and D some writers make use of N the northerly component, and W the westerly (or E the easterly). The resultant force itself is denoted sometimes by R, sometimes by T (total force). The following relationships exist between the symbols
X [equiv] N, Y [equiv] W or E, Z [equiv] V, R [equiv] T,
H [equiv] [root](X² + Y²), R [equiv] [root](X² + Y² + Z²),
tan D = Y/X, tan I = V/H.
The term _magnetic element_ is applied to R or any of the components, and even to the angles D and I.
Charts.
§ 6. Declination is the element concerning which our knowledge is most complete and most reliable. With a good unifilar magnetometer, at a fixed observatory distant from the magnetic poles, having a fixed mark of known azimuth, the observational uncertainty in a single observation should not exceed 0´.5 or at most 1´.0. It cannot be taken for granted that different unifilars, even by the best makers, will give absolutely identical values for the declination, but as a matter of fact the differences observed are usually very trifling. The chief source of uncertainty in the observation lies in the torsion of the suspension fibre, usually of silk or more rarely of phosphor bronze or other metal. A very stout suspension must be avoided at all cost, but the fibre must not be so thin as to have a considerable risk of breaking even in skilled hands. Near a magnetic pole the directive force on the declination magnet is reduced, and the effects of torsion are correspondingly increased. On the other hand, the regular and irregular changes of declination are much enhanced. If an observation consisting of four readings of declination occupies twelve minutes, the chances are that in this time the range at an English station will not exceed 1´, whereas at an arctic or antarctic station it will frequently exceed 10´. Much greater uncertainty thus attaches to declination results in the Arctic and Antarctic than to those in temperate latitudes. In the case of secular change data one important consideration is that the observations should be taken at an absolutely fixed spot, free from any artificial source of disturbance. In the case of many of the older observations of which records exist, the precise spot cannot be very exactly fixed, and not infrequently the site has become unsuitable through the erection of buildings not free from iron. Apart from buildings, much depends on whether the neighbourhood is free from basaltic and other magnetic rocks. If there are no local disturbances of this sort, a few yards difference is usually without appreciable influence, and even a few miles difference is of minor importance when one is calculating the mean secular change for a long period of years. When, however, local disturbances exist, even a few feet difference in the site may be important, and in the absence of positive knowledge to the contrary it is only prudent to act as if the site were disturbed. Near a magnetic pole the declination naturally changes very rapidly when one travels in the direction perpendicular to the lines of equal declination, so that the exact position of the site of observation is there of special importance.
The usual method of conveying information as to the value of the declination at different parts of the earth's surface is to draw curves on a map--the so-called _isogonals_--such that at all points on any one curve the declination at a given specified epoch has the same value. The information being of special use to sailors, the preparation of magnetic charts has been largely the work of naval authorities--more especially of the hydrographic department of the British admiralty. The object of the admiralty world charts--four of which are reproduced here, on a reduced scale, by the kind permission of the Hydrographer--is rather to show the general features boldly than to indicate minute details. Apart from the immediate necessities of the case, this is a counsel of prudence. The observations used have mostly been taken at dates considerably anterior to that to which the chart is intended to apply. What the sailor wants is the declination now or for the next few years, not what it was five, ten or twenty years ago. Reliable secular change data, for reasons already indicated, are mainly obtainable from fixed observatories, and there are enormous areas outside of Europe where no such observatories exist. Again, as we shall see presently, the rate of the secular change sometimes alters greatly in the course of a comparatively few years. Thus, even when the observations themselves are thoroughly reliable, the prognostication made for a future date by even the most experienced of chart makers may be occasionally somewhat wide of the mark. Fig. 1 is a reduced copy of the British admiralty declination chart for the epoch 1907. It shows the isogonals between 70° N. and 65° S. latitude. Beyond the limits of this chart, the number of exact measurements of declination is somewhat limited, but the general nature of the phenomena is easily inferred. The geographical and the magnetic poles--where the dipping needle is vertical--are fundamental points. The north magnetic pole is situated in North America near the edge of the chart. We have no reason to suppose that the magnetic pole is really a fixed point, but for our present purpose we may regard it as such. Let us draw an imaginary circle round it, and let us travel round the circle in the direction, west, north, east, south, starting from a point where the north pole of a magnet (i.e. the pole which in Europe or the United States points to the north) is directed exactly towards the astronomical north. The point we start from is to the geographical south of the magnetic pole. As we go round the circle the needle keeps directed to the magnetic pole, and so points first slightly to the east of geographical north, then more and more to the east, then directly east, then to south of east, then to due south, to west of south, to west, to north-west, and finally when we get round to our original position due north once more. Thus, during our course round the circle the needle will have pointed in all possible directions. In other words, isogonals answering to all possible values of the declination have their origin in the north magnetic pole. The same remark applies of course to the south magnetic pole.
Now, suppose ourselves at the north geographical pole of the earth. Neglecting as before diurnal variation and similar temporary changes, and assuming no abnormal local disturbance, the compass needle at and very close to this pole will occupy a fixed direction relative to the ground underneath. Let us draw on the ground through the pole a straight line parallel to the direction taken there by the compass needle, and let us carry a compass needle round a _small_ circle whose centre is the pole. At all points on the circle the positions of the needle will be parallel; but whereas the north pole of the magnet will point exactly towards the centre of the circle at one of the points where the straight line drawn on the ground cuts the circumference, it will at the opposite end of the diameter point exactly away from the centre. The former part is clearly on the isogonal where the declination is 0°, the latter on the isogonal where it is 180°. Isogonals will thus radiate out from the north geographical pole (and similarly of course from the south geographical pole) in all directions. If we travel along an isogonal, starting from the north magnetic pole, our course will generally take us, often very circuitously, to the north geographical pole. If, for example, we select the isogonal of 10° E., we at first travel nearly south, but then more and more westerly, then north-westerly across the north-east of Asia; the direction then gets less northerly, and makes a dip to the south before finally making for the north geographical pole. It is possible, however, according to the chart, to travel direct from the north magnetic to the south geographical pole, provided we select an isogonal answering to a small westerly or easterly declination (from about 19° W. to 7° E.).
Special interest attaches to the isogonals answering to declination 0°. These are termed _agonic lines_, but sailors often call them _lines of no variation_, the term _variation_ having at one time been in common use in the sense of declination. If we start from the north magnetic pole the agonic line takes us across Canada, the United States and South America in a fairly straight course to the south geographical pole. A curve continuous with this can be drawn from the south geographical to the south magnetic pole at every point of which the needle points in the geographical meridian; but here the north pole of the needle is pointing south, not north, so that this portion of curve is really an isogonal of 180°. In continuation of this there emanates from the south magnetic pole a second isogonal of 0°, or agonic line, which traverses Australia, Arabia and Russia, and takes us to the north geographical pole. Finally, we have an isogonal of 180°, continuous with this second isogonal of 0° which takes us to the north magnetic pole, from which we started. Throughout the whole area included within these isogonals of 0° and 180°--excluding locally disturbed areas--the declination is westerly; outside this area the declination is in general easterly. There is, however, as shown in the chart, an isogonal of 0° enclosing an area in eastern Asia inside which the declination is westerly though small.
§ 7. Fig. 2 is a reduced copy of the admiralty chart of inclination or dip for the epoch 1907. The places where the dip has the same value lie on curves called _isoclinals_. The dip is northerly (north pole dips) or southerly (south pole dips) according as the place is north or south of the isoclinal of 0°. At places actually on this isoclinal the dipping needle is horizontal. The isoclinal of 0° is nowhere very far from the geographical equator, but lies to the north of it in Asia and Africa, and to the south of it in South America. As we travel north from the isoclinal of 0° along the meridian containing the magnetic pole the dipping needle's north pole dips more and more, until when we reach the magnetic pole the needle is vertical. Going still farther north, we have the dip diminishing. The northerly inclination is considerably less in Europe than in the same latitudes of North America; and correspondingly the southerly inclination is less in South America than in the same latitudes of Africa.
Fig. 3 is a reduced copy of the admiralty horizontal force chart for 1907. The curves, called _isomagnetics_, connect the places where the horizontal force has the same value; the force is expressed in C.G.S. units. The horizontal force vanishes of course at the magnetic poles. The chart shows a maximum value of between 0.39 and 0.40 in an oval including the south of Siam and the China Sea. The horizontal force is smaller in North America than in corresponding latitudes in Europe.
Charts are sometimes drawn for other magnetic elements, especially vertical force (fig. 4) and total force. The isomagnetic of zero vertical force coincides necessarily with that of zero dip, and there is in general considerable resemblance between the forms of lines of equal vertical force and those of equal dip. The highest values of the vertical force occur in areas surrounding the magnetic poles, and are fully 50% larger than the largest values of the horizontal force. The total force is least in equatorial regions, where values slightly under 0.4 C.G.S. are encountered. In the northern hemisphere there are two distinct maxima of total force. One of these so-called _foci_ is in Canada, the other in the north-east of Siberia, the former having the higher value of the force. There are, however, higher values of the total force than at either of these _foci_ throughout a considerable area to the south of Australia. In the northern hemisphere the lines of equal total force--called _isodynamic_ lines--form two sets more or less distinct, consisting of closed ovals, one set surrounding the Canadian the other the Siberian focus.
Magnetic Elements and their Secular Change.
§ 8. As already explained, magnetic charts for the world or for large areas give only a general idea of the values of the elements. If the region is undisturbed, very fairly approximate values are derivable from the charts, but when the highest accuracy is necessary the only thing to do is to observe at the precise spot. In disturbed areas local values often depart somewhat widely from what one would infer from the chart, and occasionally there are large differences between places only a few miles apart. Magnetic observatories usually publish the mean value for the year of their magnetic elements. It has been customary for many years to collect and publish these results in the annual report of the Kew Observatory (Observatory Department of the National Physical Laboratory). The data in Tables I. and II. are mainly derived from this source. The observatories are arranged in order of latitude, and their geographical co-ordinates are given in Table II., longitude being reckoned from Greenwich. Table I. gives the mean values of the declination, inclination and horizontal force for January 1, 1901; they are in the main arithmetic means of the mean annual values for the two years 1900 and 1901. The mean annual secular changes given in this table are derived from a short period of years--usually 1898 to 1903--the centre of which fell at the beginning of 1901. Table II. is similar to Table I., but includes vertical force results; it is more extensive and contains more recent data. In it the number of years is specified from which the mean secular change is derived; in all cases the last year of the period employed was that to which the absolute values assigned to the element belong. The great majority of the stations have declination west and inclination north; it has thus been convenient to attach the + sign to increasing westerly (or decreasing easterly) declination and to increasing northerly (or decreasing southerly) inclination. In other words, in the case of the declination + means that the north end of the needle is moving to the west, while in the case of the inclination + means that the north end (whether the dipping end or not) is moving towards the nadir. In the case, however, of the vertical force + means simply _numerical_ increase, irrespective of whether the north or the south pole dips. The unit employed in the horizontal and vertical force secular changes is 1[gamma], i.e. 0.00001 C.G.S. Even in the declination, at the very best observatories, it is hardly safe to assume that the apparent change from one year to the next is absolutely truthful to nature. This is especially the case if there has been any change of instrument or observer, or if any alteration has been made to buildings in the immediate vicinity. A change of instrument is a much greater source of uncertainty in the case of horizontal force or dip than in the case of declination, and dip circles and needles are more liable to deterioration than magnetometers. Thus, secular change data for inclination and vertical force are the least reliable. The uncertainties, of course, are much less, from a purely mathematical standpoint, for secular changes representing a mean from five or ten years than for those derived from successive years' values of the elements. The longer, however, the period of years, the greater is the chance that one of the elements may in the course of it have passed through a maximum or minimum value. This possibility should always be borne in mind in cases where a mean secular change appears exceptionally small.
As Tables I. and II. show, the declination needle is moving to the east all over Europe, and the rate at which it is moving seems not to vary much throughout the continent. The needle is also moving to the east throughout the western parts of Asia, the north and east of Africa, and the east of North America. It is moving to the west in the west of North America, in South America, and in the south and east of Asia, including Japan, south-east Siberia, eastern China and most of India.
§ 9. The information in figs. 1, 2, 3 and 4 and in Tables I. and II. applies only to recent years. Owing to secular change, recent charts differ widely from the earliest ones constructed. The first charts believed to have been constructed were those of Edmund Halley the astronomer. According to L. A. Bauer,[7] who has made a special study of the subject, Halley issued two declination charts for the epoch 1700; one, published in 1701, was practically confined to the Atlantic Ocean, whilst the second, published in 1702, contained also data for the Indian Ocean and part of the Pacific. These charts showed the isogonic lines, but only over the ocean areas. Though the charts for 1700 were the first published, there are others which apply to earlier epochs. W. van Bemmelen[8] has published charts for the epochs 1500, 1550, 1600, 1650 and 1700, whilst H. Fritsche[9] has more recently published charts of declination, inclination and horizontal force for 1600, 1700, 1780, 1842 and 1915. A number of early declination charts were given in Hansteen's Atlas and in G. Hellmann's reprints. _Die Altesten Karten der Isogonen, Isoklinen, Isodynamen_ (Berlin, 1895). The data for the earlier epochs, especially those prior to 1700, are meagre, and in many cases probably of indifferent accuracy, so that the reliability of the charts for these epochs is somewhat open to doubt.
If we take either Hansteen's or Fritsche's declination chart for 1600 we notice a profound difference from fig. 1. In 1600 the agonic line starting from the north magnetic pole, after finding its way south to the Gulf of Mexico, doubled back to the north-east, and passed across or near Iceland. After getting well to the north of Iceland it doubled again to the south, passing to the east of the Baltic. The second agonic line which now lies to the west of St Petersburg appears in 1600 to have continued, after traversing Australia, in a nearly northerly direction through the extreme east of China. The nature of the changes in declination in western Europe will be understood from Table III., the data from which, though derived from a variety of places in the south-east of England,[10] may be regarded as approximately true of London. The earliest result is that obtained by Borough at Limehouse. Those made in the 16th century are due to Gunter, Gellibrand, Henry Bond and Halley. The observations from 1787 to 1805 were due to George Gilpin, who published particulars of his own and the earlier observations in the _Phil. Trans._ for 1806. The data for 1817 and 1820 were obtained by Col. Mark Beaufoy, at Bushey, Herts. They seem to come precisely at the time when the needle, which had been continuously moving to the west since the earliest observations, began to retrace its steps. The data from 1860 onwards apply to Kew.
TABLE I.--Magnetic Elements and their Rate of Secular Change for January 1, 1901.
+----------------+------------------------------+----------------------+ | | Absolute values. | Secular change. | | Place. +----------+----------+--------+-------+------+-------+ | | D. | I. | H. | D. | I. | H. | +----------------+----------+----------+--------+-------+------+-------+ | | ° ´ | ° ´ | | ´ | ´ |[gamma]| | Pavlovsk | 0 39.8E | 70 36.8N | .16553 | - 4.1 | -0.8 | + 7 | | Ekatarinburg | 10 6.3E | 70 40.5N | .17783 | - 4.6 | +0.5 | -13 | | Copenhagen | 10 10.4W | 68 38.5N | .17525 | | | | | Stonyhurst | 18 10.3W | 68 48.0N | .17330 | - 4.0 | | +22 | | Wilhelmshaven | 12 26.0W | 67 39.7N | .18108 | - 4.1 | -2.1 | +20 | | Potsdam | 9 54.2W | 66 24.5N | .18852 | - 4.2 | -1.6 | +16 | | Irkutsk | 2 1.0E | 70 15.8N | .20122 | + 0.5 | +1.6 | -14 | | de Bilt | 13 48.3W | 66 55.5N | .18516 | - 4.4 | -2.2 | +14 | | Kew | 16 50.8W | 67 10.6N | .18440 | - 4.2 | -2.2 | +25 | | Greenwich | 16 27.5W | 67 7.3N | .18465 | - 4.0 | -2.2 | +23 | | Uccle | 14 11.0W | 66 8.8N | .18954 | - 4.2 | -2.1 | +23 | | Falmouth | 18 27.3W | 66 44.0N | .18705 | - 3.8 | -2.7 | +26 | | Prague | 9 4.4W | | .19956 | - 4.4 | | +20 | | St Helier | 16 58.1W | 65 44.1N | | - 3.5 | -2.7 | | | Parc St Maur | 14 43.4W | 64 52.3N | .19755\| - 4.0 | -2.2 | +23 | | Val Joyeux | 15 13.7W | 65 0.0N | .19670/| | | | | Munich | 10 25.8W | 63 18.1N | .20629 | - 4.8 | -2.7 | +21 | | O'Gyalla | 7 26.1W | | .21164 | - 4.8 | | +13 | | Pola | 9 22.7W | 60 14.5N | .22216 | - 4.0 | | +23 | | Toulouse | 14 16.4W | 60 55.9N | .21945 | - 3.9 | -2.5 | +25 | | Perpignan | 13 34.7W | 59 57.6N | .22453 | | | | | Capo di Monte | 9 8.0W | 56 22.3N | | - 5.2 | -2.3 | | | Madrid | 15 39.0W | | | | | | | Coimbra | 17 18.1W | 59 22.0N | .22786 | - 3.7 | -4.3 | +34 | | Lisbon | 17 15.7W | 57 53.0N | .23548 | | | | | Athens | 5 38.2W | 52 7.5N | .26076 | | | | | San Fernando | 15 57.5W | 55 8.8N | .24648 | | | | | Tokyo | 4 34.9W | 49 0.3N | .29932 | | | | | Zi-ka-wei | 2 23.5W | 45 43.5N | .32875 | + 1.5 | -1.5 | +37 | | Helwan | 3 39.7W | 40 30.8N | .30136 | - 7.0 | -0.4 | - 7 | | Hong-Kong | 0 17.5E | 31 22.8N | .36753 | + 1.8 | -4.3 | +45 | | Kolaba | 0 23.2E | 21 26.5N | .37436 | + 2.2 | +7.0 | - 9 | | Manila | 0 52.2E | 16 13.5N | .38064 | + 0.1 | -5.3 | +47 | | Batavia | 1 7.3E | 30 35.5S | .36724 | + 3.0 | -7.3 | -11 | | Mauritius | 9 25.2W | 54 9.4S | .23820 | - 4.7 | +4.6 | -39 | | Rio de Janeiro | 8 2.9W | 13 20.1S | .2501 | +10.4 | -2.3 | | | Melbourne | 8 25.6E | 67 24.6S | .23295 | | | | +----------------+----------+----------+--------+-------+------+-------+
The rate of movement of the needle to the east at London--and throughout Europe generally--fell off markedly subsequent to 1880. The change of declination in fact between 1880 and 1895 was only about 75% of that between 1865 and 1880, and the mean annual change from 1895 to 1900 was less than 75% of the mean annual change of the preceding fifteen years. Thus in 1902 it was at least open to doubt whether a change in the sign of the secular change were not in immediate prospect. Subsequent, however, to that date there was little further decline in the rate of secular change, and since 1905 there has been very distinct acceleration. Thus, if we derive a mean value from the eighteen European stations for which declination secular changes are given in Tables I. and II. we find
mean value from table I. -4.18 " " " " II. -5.21
The epoch to which the data in Table II. refer is somewhat variable, but is in all cases more recent than the epoch, January 1, 1901, for Table I., the mean difference being about 5 years.
§ 10. At Paris there seems to have been a maximum of easterly declination (about 9°) about 1580; the needle pointed to true north about 1662, and reached its extreme westerly position between 1812 and 1814. The phenomena at Rome resembled those at Paris and London, but the extreme westerly position is believed to have been attained earlier. The rate of change near the turning point seems to have been very slow, and as no fixed observatories existed in those days, the precise time of its occurrence is open to some doubt.
Perhaps the most complete observations extant as to the declination phenomena near a turning point relate to Kolaba observatory at Bombay; they were given originally by N. A. F. Moos,[11] the director of the observatory. Some of the more interesting details are given in Table IV.; here W denotes movement to be west, and so answers to a numerical diminution in the declination, which is easterly.
Prior to 1880 the secular change at Kolaba was unmistakably to the east, and subsequent to 1883 it was clearly to the west; but between these dates opinions will probably differ as to what actually happened. The fluctuations then apparent in the sign of the annual change may be real, but it is at least conceivable that they are of instrumental origin. From 1870 to 1875 the mean annual change was -1´.2; from 1885 to 1890 it was +1´.5, from 1890 to 1895 it was +2´.0, while from 1895 to 1905 it was +2´.35, the + sign denoting movement to the west. Thus, in this case the rate of secular change has increased fairly steadily since the turning point was reached.
Table V. contains some data for St Helena and the Cape of Good Hope,[12] both places having a long magnetic history. The remarkable feature at St Helena is the uniformity in the rate of secular change. The figures for the Cape show a reversal in the direction of the secular change about 1840, but after a few years the arrested movement to the west again became visible. According, however, to J. C. Beattie's _Magnetic Survey of South Africa_ the movement to the west ceased shortly after 1870. A persistent movement to the east then set in, the mean annual change increasing from 1´.8 between 1873 and 1890 to 3´.8 between 1890 and 1900.
§ 11. Secular changes of declination have been particularly interesting in the United States, an area about which information is unusually complete, thanks to the labours and publications of the United States Coast and Geodetic Survey.[13] At present the agonic line passes in a south-easterly direction from Lake Superior to South Carolina. To the east of the agonic line the declination is westerly, and to the west it is easterly. In 1905 the declination varied from about 21° W. in the extreme north-east to about 24° E. in the extreme north-west. At present the motion of the agonic line seems to be towards the west, but it is very slow. To the east of the agonic line westerly declination is increasing, and to the west of the line, with the exception of a narrow strip immediately adjacent to it, easterly declination is increasing. The phenomena in short suggest a motion southwards in the north magnetic pole. Since 1750 declination has always been westerly in the extreme east of the States, and always easterly in the extreme west, but the position of the agonic line has altered a good deal. It was to the west of Richmond, Virginia, from 1750 to about 1772, then to the east of it until about 1838 when it once more passed to the west; since that time it has travelled farther to the west. Table VI. is intended to show the nature of the secular change throughout the whole country. As before, + denotes that the north pole of the magnet is moving to the west,--that it is moving to the east.
The data in Table VI. represent the mean change of declination per annum, derived from the period (ten years, except for 1900-1905) which ended in the year put at the top of the column. The stations are arranged in four groups, the first group representing the extreme eastern, the last group the extreme western states, the other two groups being intermediate. In each group the stations are arranged, at least approximately, in order of latitude. The data are derived from the values of the declination given in the Geodetic Survey's _Report_ for 1906, appendix 4, and _Magnetic Tables and Magnetic Charts_ by L. A. Bauer, 1908. The values seem, in most cases, based to some extent on calculation, and very probably the secular change was not in reality quite so regular as the figures suggest. For the Western States the earliest data are comparatively recent, but for some of the eastern states data earlier than any in the table appear in the _Report of the Coast and Geodetic Survey_ for 1902. These data indicate that the easterly movement of the magnet, visible in all the earlier figures for the Eastern States in Table VI., existed in all of them at least as far back as 1700. There is not very much evidence as to the secular change between 1700 and 1650, the earliest date to which the Coast and Geodetic Survey's figures refer. The figures show a maximum of westerly declination about 1670 in New Jersey and about 1675 in Maryland. They suggest that this maximum was experienced all along the Atlantic border some time in the 17th century, but earlier in the extreme north-east than in New York or Maryland.
Examination of Table VI. shows that the needle continued to move to the east for some time after 1750 even in the Eastern States. But the rate of movement was clearly diminishing, and about 1765 the extreme easterly position was reached in Eastport, Maine, the needle then beginning to retrace its steps to the west. The phenomena visible at Maine are seen repeating themselves at places more and more to the west, in Boston about 1785, in Albany about 1800, in Washington, D.C., about 1805, in Columbus (Ohio) about 1815, in Montgomery (Alabama) about 1825, in Bloomington (Ill.) about 1830, in Des Moines (Iowa) about 1840, in Santa Rosa (New Mexico) about 1860 and in Salt Lake about 1870. In 1885 the needle was moving to the west over the whole United States with the exception of a comparatively narrow strip along the Pacific coast. Even an acute observer would have been tempted to prophesy in 1885 that at no distant date the secular change would be pronouncedly westerly right up to the Pacific. But in a few years a complete change took place. The movement to the east, which had become exceedingly small, if existent, in the Pacific states, began to accelerate; the movement to the west continued in the central, as in the eastern states, but perceptibly slackened. In 1905 the area throughout which the movement to the west still continued had greatly contracted and lay to the east of a line drawn from the west end of Lake Superior to the west of Georgia. If we take a station like Little Rock (Arkansas), we have the secular change to the west lasting for about sixty years. Further west the period shortens. At Pueblo (Colorado) it is about forty years, at Salt Lake under thirty years, at Prescott (Arizona) about twenty years. Considering how fast the area throughout which the secular change is easterly has extended to the east since 1885, one would be tempted to infer that at no distant date it will include the whole of the United States. In the extreme north-east, however, the movement of the needle to the west, which had slackened perceptibly after 1860 or 1870, is once more accelerating. Thus the auspices do not all point one way, and the future is as uncertain as it is interesting.
TABLE II.--Recent Values of the Magnetic Elements and their Rate of Secular Change.
+----------------+-----------------------+----------------------------------------------+----------------------------------- | | Geographical position.| Absolute Values of Elements. | Secular change (mean per annum). | | Place. +-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+ | | | | | | | | | Interval | | | | | | | Latitude. | Longitude.| Year. | D. | I. | H. | V. | in years.| D. | I. | H. | V. | +----------------+-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+ | | ° ´ | ° ´ | | ° ´ | ° ´ | | | | ´ | ´ | | | | Pavlovsk | 59 41N | 30 29E | 1906 | 1 4.2E | 70 36.6N | .16528 | .46963 | 5 | -4.5 | +0.1 | - 6 | -14 | | Sitka (Alaska) | 57 3N | 135 20W | 1906 |30 3.3E | 74 41.7N | .15502 | .56646 | 4 | -3.0 | -1.6 | +18 | -38 | | Ekatarinburg | 56 49N | 60 38E | 1906 |10 31.0E | 70 49.5N | .17664 | .50796 | 5 | -4.5 | +1.7 | -23 | +18 | | Rude Skov | | | | | | | | | | | | | | (Copenhagen) | 55 51N | 12 27E | 1908 | 9 43.3W | 68 45N | .17406 | .44759 | | | | | | | Stonyhurst | 53 51N | 2 28W | 1909 |17 28.6W | 68 42.8N | .17424 | .44722 | 5 | -5.9 | -1.1 | + 6 | -25 | | Hamburg | 53 33N | 9 59E | 1903 |11 10.2W | 67 23.5N | .18126 | .43527 | | | | | | | Wilhelmshaven | 53 32N | 8 9E | 1909 |11 46.8W | | .18129 | | 5 | -5.2 | | - 7 | | | Potsdam | 52 23N | 13 4E | 1909 | 9 10.6W | 66 20.0N | .18834 | .42971 | 5 | -5.8 | +0.1 | - 9 | -19 | | Irkutsk | 52 16N | 104 16E | 1905 | 1 58.1E | 70 25.0N | .20011 | .56250 | 5 | +0.6 | +2.0 | -24 | +39 | | de Bilt | 52 5N | 5 11E | 1907 |13 19.0W | 66 49.9N | .18559 | .43368 | 5 | -4.7 | -0.6 | + 2 | -16 | | Valencia | 51 56N | 10 15W | 1909 |20 50.3W | 68 15.1N | .17877 | .44812 | 5 | -5.0 | -1.2 | + 7 | -25 | | Kew | 51 28N | 0 19W | 1909 |16 10.8W | 66 59.7N | .18506 | .43588 | 5 | -5.4 | -1.1 | + 2 | -35 | | Greenwich | 51 28N | 0 0 | 1909 |15 47.6W | 66 53.9N | .18526 | .43432 | 5 | -5.5 | -0.7 | + 1 | -20 | | Uccle | 50 48N | 4 21E | 1908 |13 36.7W | 66 1.6N | .19061 | .42867 | 4 | -5.3 | -0.8 | - 3 | -35 | | Falmouth | 50 9N | 5 5W | 1909 |17 48.4W | 66 30.6N | .18802 | .43266 | 5 | -4.7 | -1.4 | + 9 | -30 | | Prague | 50 5N | 14 25E | 1908 | 8 20.9W | | | | 5 | -6.5 | | | | | Cracow | 50 4N | 19 58E | 1909 | 5 35.1W | 64 18N | | | 3 | -7.3 | | | | | St Helier | 49 12N | 2 5W | 1907 |16 27.4W | 65 34.5N | | | 5 | -5.3 | -1.2 | | | | Val Joyeux | 48 49N | 2 1E | 1909 |14 32.9W | 64 43.9N | .19727 | .41792 | 5 | -5.4 | -1.7 | + 1 | -51 | | Vienna | 48 15N | 16 21E | 1898 | 8 24.1W | | | | | | | | | | Munich | 48 9N | 11 37E | 1906 | 9 59.5W | 63 10.0N | .20657 | .40835 | 5 | -4.8 | -1.3 | + 4 | -31 | | O'Gyalla | 47 53N | 18 12E | 1909 | 6 43.9W | | .21094 | | 5 | -5.0 | | -10 | | | Odessa | 46 26N | 30 46E | 1899 | 4 36.7W | 62 18.2N | .21869 | .41660 | | | | | | | Pola | 44 52N | 15 51E | 1908 | 8 43.2W | 60 6.8N | .22207 | .38640 | 5 | -5.5 | -0.6 | - 4 | -23 | | Agincourt | | | | | | | | | | | | | | (Toronto) | 43 47N | 79 16W | 1906 | 5 45.3W | 74 35.6N | .16397 | .59502 | 4 | +3.4 | +0.9 | -23 | -24 | | Nice | 43 43N | 7 16E | 1899 |12 4.0W | 60 11.7N | .22390 | .39087 | | | | | | | Toulouse | 43 37N | 1 28E | 1905 |13 56.3W | 60 49.1N | .22025 | .39439 | 5 | -4.5 | -1.5 | + 2 | - 2 | | Perpignan | 42 42N | 2 53E | 1907 |13 4.4W | | | | 7 | -4.7 | | | | | Tiflis | 41 43N | 44 48E | 1905 | 2 41.6E | 56 2.8N | .25451 | .37799 | 7 | -5.2 | +1.7 | -26 | + 2 | | Capo di Monte | 40 52N | 14 15E | 1906 | 8 40.3W | 56 13.5N | | | 5 | -5.1 | -1.5 | | | | Madrid | 40 25N | 3 40W | 1901 |15 35.6W | | | | | | | | | | Coimbra | 40 12N | 8 25W | 1908 |16 46.2W | 58 57.3N | .22946 | .38120 | 5 | -4.6 | -2.9 | +17 | -45 | | Baldwin | | | | | | | | | | | | | | (Kansas) | 38 47N | 95 10W | 1906 | 8 30.1E | 68 45.1N | .21807 | .56081 | 4 | -1.7 | +1.8 | -36 | - 8 | | Cheltenham | | | | | | | | | | | | | | (Maryland) | 38 44N | 76 50W | 1906 | 5 22.0W | 70 27.3N | .20035 | .56436 | 4 | +3.8 | +1.2 | -38 | -45 | | Lisbon | 38 43N | 9 9W | 1900 |17 18.0W | 57 54.8N | .23516 | .37484 | | | | | | | Athens | 37 58N | 21 23E | 1908 | 4 52.9W | 52 11.7N | .26197 | .33613 | 5 | -5.5 | | | | | San Fernando | 36 28N | 6 12W | 1908 |15 25.6W | 54 48.4N | .24829 | .35206 | 5 | -4.6 | -2.8 | +26 | -24 | | Tokyo | 35 41N | 139 45E | 1901 | 4 36.1W | 49 0.0N | .29954 | .34459 | | | | | | | Zi-ka-wei | 31 12N | 121 26E | 1906 | 2 32.0W | 45 35.3N | .33040 | .33726 | 5 | +1.5 | -1.3 | +30 | + 6 | | Dehra Dun | 30 19N | 78 3E | 1907 | 2 38.3E | 43 36.1N | .33324 | .31736 | 4 | +0.8 | +5.5 | -26 | +77 | | Helwan | 29 52N | 31 21E | 1909 | 2 49.2W | 40 40.4N | .30031 | .25804 | 5 | -5.7 | +1.2 | - 6 | +13 | | Havana | 23 8N | 82 25W | 1905 | 2 25.0E | 52 57.4N | .30531 | .40452 | | | | | | | Barrackpore | 22 46N | 88 22E | 1907 | 1 9.9E | 30 30.2N | .37288 | .21967 | 3 | +4.2 | +3.4 | +21 | +62 | | Hong-Kong | 22 18N | 114 10E | 1908 | 0 3.9E | 31 2.5N | .37047 | .22292 | 5 | +1.9 | -1.8 | +43 | - 1 | | Honolulu | 21 19N | 158 4W | 1906 | 9 21.7E | 40 1.8N | .29220 | .24545 | 4 | -0.9 | -3.2 | -19 | -62 | | Kolaba | 18 54N | 72 49E | 1905 | 0 14.0E | 21 58.5N | .37382 | .15084 | 5 | +2.1 | +7.2 | -11 | +86 | | Alibagh | 18 39N | 72 52E | 1909 | 1 0.3E | 23 29.0N | .36845 | .16008 | 3 | +1.7 | +6.8 | -10 | +82 | | Vieques | | | | | | | | | | | | | | (Porto Rico) | 18 9N | 65 26W | 1906 | 1 33.2W | 49 47.7N | .28927 | .34224 | 2 | +7.2 | +6.8 | -49 | +66 | | Manila | 14 35N | 120 59E | 1904 | 0 51.4E | 16 0.2N | .38215 | .10960 | 5 | +0.1 | -3.9 | +47 | -34 | | Kodaikanal | 10 14N | 77 28E | 1907 | 0 40.7W | 3 27.2N | .37431 | .02259 | 4 | +4.3 | +5.5 | +16 | +61 | | Batavia | 6 11S | 106 49E | 1906 | 0 54.1E | 30 48.5S | .36708 | .21889 | 4 | +2.1 | -7.7 | - 2 | +110| | Dar es Salaam | 6 49S | 39 18E | 1903 | 7 35.2W | | | | | | | | | | Mauritius | 20 6S | 57 33E | 1908 | 9 14.3W | 53 44.9S | .23415 | .31932 | 5 | -0.3 | +2.9 | -53 | -131| | Rio de Janeiro | 22 55S | 43 11W | 1906 | 8 55.5W | 13 57.1S | .24772 | .06164 | 5 | +9.1 | -6.8 | -42 | +44 | | Santiago | | | | | | | | | | | | | | (Chile) | 33 27S | 70 42W | 1906 |14 18.7E | 30 11.8S | | | 3 | +6.1 | +9.9 | | | | Melbourne | 37 50S | 144 58E | 1901 | 8 26.7E | 67 25.0S | .23305 | .56024 | | | | | | | Christchurch, | | | | | | | | | | | | | | N.Z. | 43 32S | 172 37E | 1903 |16 18.4E | 67 42.3S | .22657 | .55259 | | | | | | +----------------+-----------+-----------+-------+---------+----------+--------+--------+----------+------+------+-----+-----+
TABLE III.--Declination at London.
+-------+--------------+-------+--------------+-------+--------------+ | Date. | Declination. | Date. | Declination. | Date. | Declination. | +-------+--------------+-------+--------------+-------+--------------+ | | ° ´ | | ° ´ | | ° ´ | | 1580 | 11 15E | 1773 | 21 9W | 1860 | 21 38.9W | | 1622 | 6 0 | 1787 | 23 19 | 1865 | 20 58.7 | | 1634 | 4 6 | 1795 | 23 57 | 1870 | 20 18.3 | | 1657 | 0 0 | 1802 | 24 6 | 1875 | 19 35.6 | | 1665 | 1 22W | 1805 | 24 8 | 1880 | 18 52.1 | | 1672 | 2 30 | 1817 | 24 36 | 1885 | 18 19.2 | | 1692 | 6 0 | 1818 | 24 38 | 1890 | 17 50.6 | | 1723 | 14 17 | 1819 | 24 36 | 1895 | 17 16.8 | | 1748 | 17 40 | 1820 | 24 34 | 1900 | 16 52.7 | | | | | | 1905 | 16 32.9 | +-------+--------------+-------+--------------+-------+--------------+
§ 12. Table VII. gives particulars of the secular change of horizontal force and northerly inclination at London. Prior to the middle of the 19th century information as to the value of H is of uncertain value. The earlier inclination data[14] are due to Norman, Gilbert, Bond, Graham, Heberden and Gilpin. The data from 1857 onwards, both for H and I, refer to Kew. "London" is rather a vague term, but the differences between the values of H and I at Kew and Greenwich--in the extreme west and east--are almost nil. For some time after its discovery by Robert Norman inclination at London increased. The earlier observations are not sufficient to admit of the date of the maximum inclination or its absolute value being determined with precision. Probably the date was near 1723. This view is supported by the fact that at Paris the inclination fell from 72° 15´ in 1754 to 71° 48´ in 1780. The earlier observations in London were probably of no very high accuracy, and the rates of secular change deducible from them are correspondingly uncertain. It is not improbable that the average annual change 0´.8 derived from the thirteen years 1773-1786 is too small, and the value 6´.2 derived from the fifteen years 1786-1801 too large. There is, however, other evidence of unusually rapid secular change of inclination towards the end of the 18th century in western Europe; for observations in Paris show a fall of 56´ between 1780 and 1791, and of 90´ between 1791 and 1806. Between 1801 and 1901 inclination in London diminished by 3° 26´.5, or on the average by 2´.1 per annum, while between 1857 and 1900 H increased on the average by 22[gamma] a year. These values differ but little from the secular changes given in Table I. as applying at Kew for the epoch Jan. 1, 1901. Since the beginning, however, of the 20th century a notable change has set in, which seems shared by the whole of western Europe. This is shown in a striking fashion by contrasting the data from European stations in Tables I. and II. There are fifteen of these stations which give secular change data for H in both tables, while thirteen give secular data for I. The mean values of the secular changes derived from these stations are as follows:--
I H
From Table I. -2´.35 +21.0[gamma] From Table II. -1.12 +1.6[gamma]
The difference in epoch between the two sets of results is only about 5 years, and yet in that short time the mean rate of annual increase in H fell to a thirteenth of its original value. During 1908-1909 H diminished throughout all Europe except in the extreme west. Whether we have to do with merely a temporary phase, or whether a general and persistent diminution in the value of H is about to set in over Europe it is yet hardly possible to say.
TABLE IV.--Declination at Kolaba (Bombay).
+-------+----------------+----------------+ | Year. | Declination | Change since | | | East. | previous year. | +-------+----------------+----------------+ | | ° ´ ´´ | ´ ´´ | | 1876 | 0 55 58 | 0 37 E | | 1877 | 56 39 | 0 41 E | | 1878 | 57 6 | 0 27 E | | 1879 | 57 30 | 0 24 E | | 1880 | 57 9 | 0 21 W | | 1881 | 0 57 12 | 0 3 E | | 1882 | 0 56 50 | 0 22 W | | 1883 | 57 2 | 0 12 E | | 1884 | 55 39 | 1 23 W | | 1885 | 55 3 | 0 36 W | +-------+----------------+----------------+
§ 13. It is often convenient to obtain a formula to express the mean annual change of an element during a given period throughout an area of some size. The usual method is to assume that the change at a place whose latitude is l and longitude [lambda] is given by an expression of the type c + a(l - l0) + b([lambda] - [lambda]0), where a, b, c are constants, l0 and [lambda]0, denoting some fixed latitude and longitude which it is convenient to take as point of departure. Supposing observational data available from a series of stations throughout the area, a, b and c can be determined by least squares. As an example, we may take the following slightly modified formula given by Ad. Schmidt[15] as applicable to Northern Europe for the period 1890 to 1900. [Delta]D, [Delta]I and [Delta]H represent the mean annual changes during this period in westerly declination, in inclination and in horizontal force:--
´ ´ ´ [Delta]D = -5.24 - 0.071(l - 50) + 0.033([lambda] - 10), [Delta]I = -1.58 + 0.010(l - 50) + 0.036([lambda] - 10), [Delta]H = +23.5 - 0.59 (l - 50) - 0.35 ([lambda] - 10).
Longitude [lambda] is here counted positive to the east. The central position assumed here (lat. 50°, long. 10° E.) falls in the north of Bavaria. In the case of the horizontal force unity represents 1[gamma]. Schmidt found the above formulae to give results in very close agreement with the data at the eight stations which he had employed in determining the constants. These stations ranged from Pavlovsk to Perpignan, and from Stonyhurst to Ekaterinburg in Siberia. Formulae involving the second as well as the first powers of l - l0 and [lambda] - [lambda]0 have also been used, e.g., by A. Tanakadate in the Magnetic Survey of Japan.
Table V.--Declination at St Helena and Cape of Good Hope.
+----------------------+----------------------+ | St Helena. | Cape of Good Hope. | +--------+-------------+--------+-------------+ | Date. | Declination.| Date. | Declination.| +--------+-------------+--------+-------------+ | | ° ´ | | ° ´ | | 1610 | 7 13 E | 1605 | 0 30 E | | 1677 | 0 40 | 1609 | 0 12 W | | 1691 | 1 0 W | 1675 | 8 14 | | 1724 | 7 30 | 1691 | 11 0 | | 1775 | 12 18 | 1775 | 21 14 | | 1789 | 15 30 | 1792 | 24 31 | | 1796 | 15 48 | 1818 | 26 31 | | 1806 | 17 18 | 1839 | 29 9 | | 1839 | 22 17 | 1842 | 29 6 | | 1840 | 22 53 | 1846 | 29 9 | | 1846 | 23 11 | 1850 | 29 19 | | 1890 | 23 57 | 1857 | 29 34 | | | | 1874 | 30 4 | | | | 1890 | 29 32 | | | | 1903 | 28 44 | +--------+-------------+--------+-------------+
TABLE VI.--Secular Change of Declination in the United States (+ to the West).
+---------------------------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+ | Place. |Epoch | 1760 | 70 | 80 | 90 | 1800 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 1900 | 50 | +---------------------------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+ | | | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | | / Eastport, Maine | | -1.2 | 0.0 | +1.2 | +2.1 | +3.2 | +4.0 | +4.5 | +4.9 | +5.0 | +5.6 | +4.5 | +3.0 | +2.1 | +1.0 | +1.8 | +2.4 | | | Boston, Mass. | | -2.7 | -1.9 | -1.0 | 0.0 | +1.1 | +1.9 | +2.7 | +3.5 | +4.2 | +4.4 | +4.0 | +3.3 | +3.1 | +3.0 | +3.2 | +3.4 | | | Albany, New York | | -4.2 | -3.6 | -2.7 | -1.6 | -0.6 | +0.6 | +1.6 | +2.7 | +3.6 | +4.6 | +4.6 | +3.9 | +4.7 | +2.3 | +3.4 | +3.6 | | | Philadelphia, Penn. | | -4.6 | -4.2 | -3.5 | -2.3 | -1.3 | +0.1 | +1.3 | +2.5 | +3.4 | +4.3 | +4.2 | +4.6 | +4.4 | +3.4 | +3.5 | +3.4 | | | Baltimore, Maryland | | -3.9 | -3.4 | -2.7 | -2.0 | -0.9 | 0.0 | +0.9 | +2.0 | +2.7 | +3.4 | +3.9 | +4.0 | +3.9 | +3.6 | +3.5 | +3.2 | | | Richmond, Virginia | | -3.6 | -3.2 | -2.5 | -1.8 | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.1 | +3.6 | +3.9 | +3.8 | +3.7 | +3.4 | +3.2 | | | Columbia, S. Carolina | | -3.7 | -3.4 | -2.9 | -2.2 | -1.3 | -0.5 | +0.5 | +1.3 | +2.2 | +2.9 | +3.4 | +3.8 | +3.8 | +3.8 | +3.6 | +1.8 | | | Macon, Georgia | | -3.7 | -3.6 | -3.2 | -2.5 | -1.8 | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +3.9 | +3.5 | +3.1 | +1.2 | | \ Tampa, Florida | | -3.0 | -2.5 | -2.0 | -1.1 | -0.4 | +0.4 | +1.1 | +2.0 | +2.5 | +3.0 | +3.2 | +3.5 | +3.7 | +2.8 | +2.9 | +1.6 | | | | | | | | | | | | | | | | | | | | | / Marquette, Michigan | | | | | | | | | 0.0 | +1.4 | +2.6 | +3.7 | +4.7 | +5.1 | +4.9 | +3.8 | +2.4 | | | Columbus, Ohio | | | | | | | -0.9 | 0.0 | +0.9 | +2.0 | +2.9 | +3.4 | +3.6 | +3.7 | +3.9 | +4.0 | +2.4 | | | Bloomington, Illinois | | | | | | | -2.4 | -1.5 | -0.4 | +0.4 | +1.5 | +2.4 | +2.8 | +4.2 | +3.9 | +2.9 | +1.0 | | | Lexington, Kentucky | | | | | | | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +3.8 | +3.8 | +3.4 | +1.8 | | | Chattanooga, Tennessee | | | | | | | -0.9 | 0.0 | +0.9 | +1.8 | +2.5 | +3.2 | +3.6 | +4.0 | +3.5 | +3.1 | +1.6 | | | Little Rock, Arkansas | | | | | | | -2.3 | -1.5 | -0.9 | +0.1 | +0.8 | +1.7 | +2.0 | +3.6 | +3.7 | +2.3 | -1.2 | | | Montgomery, Alabama | | -3.6 | -3.5 | -3.1 | -2.8 | -2.2 | -1.5 | -0.8 | +0.1 | +0.8 | +1.6 | +2.2 | +2.8 | +3.8 | +3.9 | +2.6 | +0.2 | | \ Alexandria, Louisiana | | | | | | | -2.1 | -1.6 | -0.8 | +0.1 | +0.8 | +1.6 | +2.2 | +3.6 | +3.3 | +2.0 | -1.4 | | | | | | | | | | | | | | | | | | | | | / Northome, Minnesota | | | | | | | | | -1.7 | -0.6 | +0.6 | +1.7 | +2.8 | +4.2 | +4.4 | +3.5 | 0.0 | | | Jamestown, N. Dakota | | | | | | | | | | | | +1.0 | +1.9 | +3.1 | +4.8 | +1.9 | -2.2 | | | Des Moines, Iowa | | | | | | | | | -1.5 | -0.6 | +0.6 | +1.5 | +2.5 | +3.8 | +4.5 | +2.7 | -0.6 | | | Douglas, Wyoming | | | | | | | | | | | | -0.8 | 0.0 | +1.2 | +2.3 | +0.5 | -1.6 | | | Emporia, Kansas | | | | | | | | | | | | +0.6 | +1.6 | +2.7 | +3.8 | +1.7 | -1.8 | | | Pueblo, Colorado | | | | | | | | | | | | -0.3 | +0.4 | +1.5 | +3.1 | +0.7 | -2.2 | | | Okmulgee, Oklahoma | | | | | | | | | | | | +0.9 | +1.5 | +2.7 | +3.9 | +1.4 | -2.4 | | | Santa Rosa, New Mexico | | | | | | | | | | | | -0.4 | +0.4 | +1.4 | +2.6 | +0.4 | -2.4 | | \ San Antonio, Texas | | | | | | | | | | -1.1 | -0.5 | -0.5 | +1.1 | +1.8 | +2.7 | +0.9 | -2.4 | | | | | | | | | | | | | | | | | | | | | / Seattle, Washington | | | | | -3.3 | -3.5 | -3.7 | -3.7 | -3.5 | -3.3 | -3.0 | -2.6 | -2.1 | -1.3 | -1.9 | -2.0 | -3.2 | | | Wilson Creek, Washington| | | | | | | | | | | | -2.1 | -1.5 | -0.4 | -1.0 | -1.6 | -3.2 | | | Detroit, Oregon | | | | | | | -3.8 | -3.9 | -3.9 | -3.7 | -3.4 | -2.9 | -2.5 | -1.8 | -0.8 | -1.8 | -3.8 | | | Salt Lake, Utah | | | | | | | | | | | | -1.1 | -0.4 | +1.0 | +1.0 | -0.8 | -2.8 | | | Prescott, Arizona | | | | | | | | | | | | -1.4 | -0.7 | +0.4 | +0.4 | -1.2 | -3.2 | | | San José, California | | | | | -2.6 | -2.9 | -2.9 | -2.9 | -2.7 | -2.5 | -2.3 | -2.0 | -1.5 | -0.8 | -0.4 | -1.9 | -3.8 | | \ Los Angeles, " | | | | | -3.4 | -3.4 | -3.5 | -3.2 | -3.0 | -2.7 | -2.1 | -1.6 | -1.1 | -0.9 | -0.3 | -1.6 | -3.6 | +---------------------------+------+------+------+--------------------+------+------+------+------+------+------+------+------+------+------+------+
Formulae are also wanted to show how the value of an element, or the rate of change of an element, at a particular place has varied throughout a long period. For comparatively short periods it is best to use formulae of the type E = a + bt + ct², where E denotes the value of an element t years subsequent to some convenient epoch; a, b, c are constants to be determined from the observational data. For longer periods formulae of the type E = a + b sin (mt + n), where a, b, m and n are constants, have been used by Schott[16] and others with considerable success. The following examples, due to G. W. Littlehales,[17] for the Cape of Good Hope, will suffice for illustration:
Declination (West) = 14°.63 + 15°.00 sin {0.61(t - 1850) + 77°.8} Inclination (South) = 49°.11 + 8°.75 sin {0.8 (t - 1850) + 34°.3}.
Here t denotes the date. It is perhaps hardly necessary to point out that the extension of any of these empirical formulae--whether to places outside the surveyed area, or to times not included in the period of observation--is fraught with danger, which increases rapidly the further the extrapolation is pushed.
Table VII.--Inclination (northerly) and Horizontal Force at London.
+------+-------+------+---------+------+---------+--------+------+---------+--------+ | Date.| I. | Date.| I. | Date.| I. | H. | Date.| I. | H. | +------+-------+------+---------+------+---------+--------+------+---------+--------+ | | ° ´ | | ° ´ | | ° ´ | | | ° ´ | | | 1576 | 71 50 | 1801 | 70 36.0 | 1857 | 68 24.9 | .17474 | 1891 | 67 33.2 | .18193 | | 1600 | 72 0 | 1821 | 70 3.4 | 1860 | 69 19.8 | .17550 | 1895 | 67 25.4 | .18278 | | 1676 | 73 30 | 1830 | 69 38.0 | 1865 | 68 8.7 | .17662 | 1900 | 67 11.8 | .18428 | | 1723 | 74 42 | 1838 | 69 17.3 | 1870 | 67 58.6 | .17791 | 1905 | 67 3.8 | .18510 | | 1773 | 72 19 | 1854 | 68 31.1 | 1874 | 67 50.0 | .17903 | 1908 | 67 0.9 | .18515 | | 1786 | 72 9 | | | | | | | | | +------+-------+------+---------+------+---------+--------+------+---------+--------+
Bauer has employed a convenient graphical method of illustrating secular change. Radii are drawn from the centre of a sphere parallel to the direction of the freely dipping needle, and are produced to intersect the tangent plane drawn at the point which answers to the mean position of the needle during the epoch under consideration. The curve formed by the points of intersection shows the character of the secular change. Fig. 5 (slightly modified from _Nature_, vol. 57, p. 181) applies to London. The curve is being described in the clockwise direction. This, according to Bauer's[18] own investigation, is the normal mode of description. Schott and Littlehales have found, however, a considerable number of cases where it is difficult to say whether the motion is clockwise or not, while in some stations on both the east and west shores of the Pacific it was clearly anti-clockwise. Fritsche[19] dealing with the secular changes from 1600 to 1885--as given by his calculated values of the magnetic elements--at 204 points of intersection of equidistant lines of latitude and longitude, found only sixty-three cases in which the motion was unmistakably clockwise, while in twenty-one cases it was clearly the opposite.
Diurnal Variations.
§ 14. All the magnetic elements at any ordinary station show a regular variation in the solar day. To separate this from the irregular changes, means of the hourly readings must be formed making use of a number of days. The amplitude of the diurnal change usually varies considerably with the season of the year. Thus a diurnal inequality derived from all the days of the year combined, or from a smaller number of days selected equally from all the months of the year, can give only the average effect throughout the year. Also unless the hours of maxima and minima at a given station are but slightly variable with the season, the result obtained by combining data from all the months of the year may be a hybrid which does not very closely resemble the phenomena in the majority of individual months. This remark applies in particular to the declination at places within the tropics. One consequence is obviously to make the range of a diurnal inequality which answers to the year as a whole less than the arithmetic mean of the twelve ranges obtained for the constituent months. At stations in temperate latitudes, whilst minor differences of type do exist between the diurnal inequalities for different months of the year, the difference is mainly one of amplitude, and the mean diurnal inequality from all the months of the year gives a very fair idea of the nature of the phenomena in any individual month.
Table VIII.--Diurnal Inequality of Declination, mean from whole year (+ to West).
+----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+ | Station. | Jan Mayen. |St Petersburg| Greenwich.| Kew. | Parc | Tiflis. | Kolaba. | Batavia. | Mauritius.| South Vic- | | |and Pavlovsk.| | | St Maur. | | | | | toria Land. | +----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+ | Latitude.| 71° 0´ N. | 59° 41´ N. | 51° 28´ N.| 51° 28´ N. |48° 49´ N.| 41° 43´ N.| 18° 54´ N.| 6° 11´ S.| 20° 6´ S.| 77° 51´ S. | |Longitude.| 8° 28´ W. | 30° 29´ E. | 0° 0´. | 0° 19´ W. | 2° 29´ E.| 44° 48´ E.| 72° 49´ E.|106° 49´ E.| 57° 33´ E.| 166° 45´ E. | +----------+--------------+-------------+-----------+-------------+----------+-----------+-----------+-----------+-----------+---------------+ | Period. | 1882-1883. | 1873-1885. | 1890-1900.| 1890-1900. |1883-1897.| 1888-1898.| 1894-1901.| 1883-1894.| 1876-1890.| 1902-1903. | +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+ | | a. | q. | a. | q. | a. | a. | q. | a. | a. | q. | a. | a. | a. | q. | +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+ | Hour. | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | | 1 | -6.6 | -4.2 | -1.3 | -0.7 | -1.4 | -1.5 | -0.9 | -1.4 | -0.7 | -0.2 | +0.1 | +0.1 | +2.0 | +0.9 | | 2 | -10.5 | -6.4 | -1.2 | -0.8 | -1.3 | -1.4 | -0.9 | -1.2 | -0.6 | -0.1 | -0.1 | +0.1 | -2.1 | -1.8 | | 3 | -15.2 | -7.8 | -1.2 | -1.0 | -1.3 | -1.5 | -1.0 | -1.2 | -0.6 | -0.1 | -0.1 | +0.1 | -5.2 | -4.5 | | 4 | -16.9 | -8.4 | -1.4 | -1.3 | -1.4 | -1.7 | -1.3 | -1.2 | -0.5 | -0.1 | 0.0 | +0.2 | -9.4 | -6.8 | | 5 | -17.0 | -8.1 | -1.7 | -1.8 | -1.7 | -2.1 | -1.8 | -1.6 | -0.7 | -0.1 | 0.0 | +0.3 | -12.2 | -9.0 | | 6 | -13.7 | -7.0 | -1.9 | -2.3 | -2.1 | -2.4 | -2.3 | -1.9 | -1.2 | -0.6 | +0.1 | +0.4 | -15.3 | -11.7 | | 7 | -9.3 | -5.1 | -2.2 | -2.8 | -2.4 | -2.7 | -2.8 | -2.4 | -1.9 | -1.0 | +0.5 | +0.6 | -17.2 | -15.0 | | 8 | -6.8 | -3.2 | -2.5 | -3.2 | -2.5 | -2.8 | -3.1 | -2.7 | -2.4 | -1.2 | +1.3 | +1.1 | -21.5 | -17.3 | | 9 | -3.7 | -0.6 | -2.3 | -3.0 | -1.9 | -2.1 | -2.5 | -2.3 | -2.3 | -0.7 | +1.7 | +1.8 | -23.5 | -18.1 | | 10 | -2.4 | +2.1 | -1.0 | -1.7 | -0.2 | -0.3 | -0.7 | -0.5 | -0.9 | 0.0 | +1.5 | +1.9 | -21.2 | -15.8 | | 11 | -0.5 | +4.6 | +1.0 | +0.4 | +2.1 | +2.2 | +1.7 | +2.0 | +1.0 | +0.9 | +0.9 | +1.3 | -15.3 | -9.2 | | Noon | +2.5 | +6.5 | +3.1 | +2.7 | +4.2 | +4.3 | +3.9 | +4.2 | +2.6 | +1.4 | +0.1 | 0.0 | -9.8 | -4.9 | | 1 | +3.7 | +7.3 | +4.6 | +4.3 | +5.1 | +5.3 | +4.8 | +5.3 | +3.3 | +1.2 | -0.6 | -1.1 | -3.2 | -0.1 | | 2 | +6.4 | +7.1 | +4.9 | +4.5 | +4.7 | +4.9 | +4.4 | +4.9 | +3.1 | +0.6 | -1.1 | -2.0 | +3.8 | +5.9 | | 3 | +7.4 | +5.9 | +4.1 | +3.6 | +3.6 | +3.7 | +3.1 | +3.7 | +2.3 | +0.1 | -1.3 | -2.3 | +11.1 | +9.5 | | 4 | +8.5 | +4.3 | +2.7 | +2.3 | +2.2 | +2.4 | +1.8 | +2.3 | +1.3 | -0.2 | -1.2 | -1.8 | +16.6 | +12.9 | | 5 | +10.6 | +3.0 | +1.5 | +1.3 | +1.1 | +1.2 | +0.7 | +1.1 | +0.6 | -0.1 | -0.9 | -0.9 | +19.9 | +14.6 | | 6 | +14.2 | +2.3 | +0.6 | +0.7 | +0.3 | +0.4 | +0.2 | +0.2 | +0.2 | 0.0 | -0.6 | -0.1 | +22.0 | +15.5 | | 7 | +15.2 | +2.2 | 0.0 | +0.4 | -0.3 | -0.2 | -0.1 | -0.4 | +0.1 | +0.1 | -0.4 | +0.1 | +22.0 | +15.9 | | 8 | +15.8 | +2.6 | -0.4 | +0.2 | -0.9 | -0.6 | -0.3 | -0.9 | -0.1 | +0.2 | -0.2 | +0.1 | +19.9 | +14.6 | | 9 | +13.2 | +2.6 | -1.0 | 0.0 | -1.2 | -1.0 | -0.5 | -1.3 | -0.4 | +0.1 | 0.0 | +0.1 | +16.0 | +10.6 | | 10 | +7.4 | +2.0 | -1.4 | -0.2 | -1.5 | -1.3 | -0.7 | -1.5 | -0.6 | 0.0 | +0.1 | +0.1 | +11.6 | +7.2 | | 11 | +1.1 | +0.5 | -1.6 | -0.4 | -1.6 | -1.4 | -0.8 | -1.6 | -0.7 | 0.0 | +0.1 | +0.1 | +7.6 | +4.2 | | 12 | -3.6 | -1.8 | -1.5 | -0.6 | -1.6 | -1.5 | -0.9 | -1.6 | -0.8 | -0.1 | +0.1 | +0.1 | +3.3 | +1.9 | +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+ | Range | 32.8 | 15.7 | 7.4 | 7.7 | 7.6 | 8.1 | 7.9 | 8.0 | 5.7 | 2.6 | 3.0 | 4.2 | 45.5 | 34.0 | +----------+-------+------+------+------+-----------+------+------+----------+-----------+-----------+-----------+-----------+-------+-------+
Tables VIII. to XI. give mean diurnal inequalities derived from all the months of the year combined, the figures representing the algebraic excess of the hourly value over the mean for the twenty-four hours. The + sign denotes in Table VIII. that the north end of the needle is to the west of its mean position for the day; in Tables IX. to XI. it denotes that the element--the dip being the north or south as indicated--is numerically in excess of the twenty-four hour mean. The letter "a" denotes that all days have been included except, as a rule, those characterized by specially large disturbances. The letter "q" denotes that the results are derived from a limited number of days selected as being specially quiet, i.e. free from disturbance. In all cases the aperiodic or non-cyclic element--indicated by a difference between the values found for the first and second midnights of the day--has been eliminated in the usual way, i.e. by treating it as accumulating at a uniform rate throughout the twenty-four hours. The years from which the data were derived are indicated. The algebraically greatest and least of the hourly values are printed in heavy type; the range thence derived is given at the foot of the tables.
TABLE IX.--Diurnal Inequality of Horizontal Force, mean from whole year (Unit 1[gamma] = .00001 C.G.S.)
+--------+----------+-------------+----------+----------+----------+----------+----------+----------+----------+-----------+ |Station.|Jan Mayen.|St Petersburg|Greenwich.| Kew. | Parc | Tiflis. | Kolaba. | Batavia. |Mauritius.|S. Victoria| | | |and Pavlovsk.| | | St Maur. | | | | | Land. | +--------+----------+-------------+----------+----------+----------+----------+----------+----------+----------+-----------+ | Period.|1882-1883.| 1873-1885. |1890-1900.|1890-1900.|1883-1897.|1888-1898.|1894-1901.|1883-1894.|1883-1890.| 1902-1903.| +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+ | | a. | q. | a. | q. | a. | q. | a. | a. | q. | a. | a. | a. | +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+ | Hour. | | | | | | | | | | | | | | 1 | -57 |-22 | + 4 | + 5 | + 4 | + 4 | + 5 | + 3 | -10 | -11 | - 3 | -12 | | 2 | -64 |-24 | + 4 | + 4 | + 3 | + 4 | + 5 | + 3 | - 9 | -10 | - 1 | -13 | | 3 | -74 |-25 | + 4 | + 4 | + 3 | + 4 | + 5 | + 3 | - 9 | - 8 | + 1 | -14 | | 4 | -69 |-24 | + 4 | + 4 | + 3 | + 4 | + 5 | + 4 | - 9 | - 7 | + 2 | -15 | | 5 | -60 |-22 | + 5 | + 4 | + 3 | + 4 | + 6 | + 4 | - 9 | - 5 | + 3 | -15 | | 6 | -37 |-19 | + 4 | + 4 | + 1 | + 2 | + 4 | + 4 | - 7 | - 1 | + 4 | -12 | | 7 | -15 |-15 | + 2 | + 2 | - 3 | - 1 | + 1 | + 2 | - 1 | + 5 | + 7 | - 9 | | 8 | - 1 |-13 | - 3 | - 4 | - 9 | - 7 | - 5 | - 3 | + 8 | +14 | + 9 | - 7 | | 9 | + 8 |-12 | -10 | -10 | -16 | -13 | -12 | - 8 | -19 | +24 | + 9 | - 3 | | 10 | +17 |-12 | -16 | -16 | -20 | -18 | -17 | -10 | +26 | +31 | + 9 | + 3 | | 11 | +32 |-10 | -19 | -20 | -19 | -18 | -16 | - 7 | +30 | +35 | + 9 | + 7 | | Noon | +49 |- 4 | -17 | -18 | -13 | -12 | -12 | - 1 | +26 | +31 | + 8 | +12 | | 1 | +65 |+ 8 | -12 | -13 | - 7 | - 7 | - 7 | + 4 | +19 | +22 | + 7 | +18 | | 2 | +78 |+22 | - 6 | - 6 | - 1 | - 2 | - 4 | + 5 | +10 | +10 | + 2 | +20 | | 3 | +89 |+37 | 0 | 0 | + 2 | + 1 | - 1 | + 3 | + 2 | - 1 | - 2 | +19 | | 4 | +83 |+43 | + 3 | + 3 | + 5 | + 3 | 0 | - 1 | - 3 | - 9 | - 6 | +18 | | 5 | +68 |+49 | + 5 | + 5 | + 7 | + 5 | + 2 | - 4 | - 7 | -13 | - 7 | +15 | | 6 | +37 |+43 | + 6 | + 6 | + 9 | + 7 | + 4 | - 6 | - 8 | -14 | - 7 | +11 | | 7 | +13 |+30 | + 7 | + 7 | +10 | + 8 | + 6 | - 4 | - 9 | -15 | - 7 | + 5 | | 8 | -11 |+15 | + 8 | + 8 | +10 | + 8 | + 7 | - 1 | -10 | -16 | - 8 | + 0 | | 9 | -33 |+ 1 | + 9 | + 9 | + 8 | + 7 | + 7 | + 1 | -11 | -16 | - 8 | - 4 | | 10 | -36 |-10 | + 8 | + 9 | + 7 | + 6 | + 6 | + 2 | -11 | -16 | - 8 | - 7 | | 11 | -40 |-16 | + 7 | + 8 | + 6 | + 6 | + 6 | + 3 | -10 | -15 | - 7 | - 9 | | 12 | -51 |-20 | + 6 | + 6 | + 5 | + 5 | + 6 | + 3 | -10 | -13 | - 5 | -11 | +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+ | Range | 163 | 74 | 28 | 29 | 30 | 26 | 24 | 15 | 41 | 51 | 17 | 35 | +--------+-----+----+------+------+----------+----------+----------+----------+----------+----------+----------+-----------+
TABLE X.--Diurnal Inequality of Vertical Force, mean from whole year (Unit 1[gamma]).
+--------+-----------+-----------+-------+-------+--------+-------+-------+--------+-------+---------+ | | |St Peters- |Green- | | Parc St| | | |Maur- |South | |Station.| Jan Mayen.| burg and | wich. | Kew. | Maur. |Tiflis.|Kolaba.|Batavia.| itius.| Victoria| | | | Pavlovsk. | | | | | | | | Land. | +--------+-----------+-----------+-------+-------+--------+-------+-------+--------+-------+---------+ | Period.| 1882-1883.| 1873-1885.|1890 |1891 |1883 |1888 |1894 |1883 |1884 | 1902 | | | | | -1900.| -1900.| -1897. | -1898.| -1901.| -1894. | -1890.| -1903. | +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+ | Hour | a. | q. | a. | q. | a. | q. | a. | a. | q. | a. | a. | a. | +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+ | 1 | +65 | + 3 | - 7 | - 1 | - 3 | + 1 | 0 | + 2 | + 4 | + 7 | + 2 | +13 | | 2 | +65 | + 2 | - 7 | - 1 | - 4 | + 1 | 0 | + 2 | + 4 | + 5 | + 2 | +12 | | 3 | +56 | - 1 | - 7 | - 1 | - 4 | 0 | - 1 | + 1 | + 3 | + 4 | + 2 | +10 | | 4 | +37 | - 5 | - 6 | 0 | - 3 | 0 | 0 | + 1 | + 3 | + 3 | + 2 | + 8 | | 5 | +16 | - 7 | - 5 | 0 | - 2 | + 1 | 0 | + 2 | + 5 | + 2 | + 2 | + 3 | | 6 | - 7 | - 8 | - 4 | 0 | - 1 | + 1 | + 1 | + 3 | + 7 | + 1 | + 2 | 0 | | 7 | -17 | - 6 | - 3 | 0 | 0 | 0 | + 1 | + 3 | + 6 | 0 | + 3 | 0 | | 8 | -14 | - 4 | - 2 | 0 | 0 | - 1 | 0 | + 3 | 0 | - 3 | + 4 | - 2 | | 9 | - 9 | 0 | - 3 | - 1 | - 3 | - 4 | - 4 | - 1 | - 8 | -11 | + 5 | - 6 | | 10 | - 6 | + 5 | - 2 | - 2 | - 6 | - 8 | - 8 | - 7 | -14 | -20 | + 3 | -13 | | 11 | - 6 | +10 | - 3 | - 4 | - 9 | -11 | -12 | -11 | -15 | -26 | 0 | -17 | | Noon | -10 | +16 | - 3 | - 5 | -10 | -11 | -12 | -11 | -10 | -27 | - 4 | -20 | | 1 | -13 | +21 | - 1 | - 4 | - 6 | - 8 | - 9 | - 9 | - 3 | -21 | - 7 | -20 | | 2 | -24 | +23 | + 2 | - 1 | 0 | - 3 | - 3 | - 5 | + 1 | -13 | - 9 | -16 | | 3 | -31 | +20 | + 8 | + 2 | + 5 | + 2 | + 2 | - 1 | + 4 | - 4 | - 8 | -12 | | 4 | -40 | +13 | + 9 | + 3 | + 8 | + 5 | + 6 | + 1 | + 3 | + 4 | - 5 | - 6 | | 5 | -48 | + 2 | +10 | + 3 | + 9 | + 6 | + 7 | + 3 | 0 | +10 | - 3 | - 1 | | 6 | -53 | - 9 | +10 | + 3 | +10 | + 7 | + 8 | + 4 | 0 | +13 | 0 | + 3 | | 7 | -47 | -18 | + 9 | + 3 | + 9 | + 6 | + 7 | + 3 | 0 | +14 | 0 | + 6 | | 8 | -36 | -20 | + 8 | + 3 | + 7 | + 5 | + 6 | + 3 | + 1 | +14 | + 1 | + 9 | | 9 | - 7 | -19 | + 6 | + 2 | + 5 | + 5 | + 5 | + 3 | + 2 | +14 | + 2 | +11 | | 10 | +18 | -13 | + 3 | + 2 | + 3 | + 4 | + 3 | + 3 | + 3 | +13 | + 2 | +12 | | 11 | +42 | - 5 | - 2 | 0 | 0 | + 3 | + 2 | + 3 | + 3 | +11 | + 2 | +12 | | 12 | +54 | 0 | - 5 | - 1 | - 2 | + 2 | + 1 | + 2 | + 3 | + 9 | + 2 | +13 | +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+ | Range | 118 | 43 | 17 | 8 | 20 | 18 | 20 | 15 | 22 | 41 | 14 | 33 | +--------+-----+-----+-----+-----+-------+-------+--------+-------+-------+--------+-------+---------+
When comparing results from different stations, it must be remembered that the disturbing forces required to cause a change of 1´ in declination and in dip vary directly, the former as the horizontal force, the latter as the total force. Near a magnetic pole the horizontal force is relatively very small, and this accounts, at least partly, for the difference between the declination phenomena at Jan Mayen and South Victoria Land on the one hand and at Kolaba, Batavia and Mauritius on the other. There is, however, another cause, already alluded to, viz. the variability in the type of the diurnal inequality in tropical stations. With a view to illustrating this point Table XII. gives diurnal inequalities of declination for June and December for a number of stations lying between 45° N. and 45° S. latitude. Some of the results are represented graphically in fig. 6, plus ordinates representing westerly deflection. At the northmost station, Toronto, the difference between the two months is mainly a matter of amplitude, the range being much larger at midsummer than at midwinter. The conspicuous phenomenon at both seasons is the rapid swing to the west from 8 or 9 a.m. to 1 or 2 p.m. At the extreme southern station, Hobart--at nearly equal latitude--the rapid diurnal movement is to the east, and so in the opposite direction to that in the northern hemisphere, but it again takes place at nearly the same hours in June (midwinter) as in December. If, however, we take a tropical station such as Trivandrum or Kolaba, the phenomena in June and December are widely different in type. At Trivandrum--situated near the magnetic equator in India--we have in June the conspicuous forenoon swing to the west seen at Toronto, occurring it is true slightly earlier in the day; but in December at the corresponding hours the needle is actually swinging to the east, just as it is doing at Hobart. In June the diurnal inequality of declination at tropical stations--whether to the north of the equator like Trivandrum, or to the south of it like Batavia--is on the whole of the general type characteristic of temperate regions in the northern hemisphere; whereas in December the inequality at these stations resembles that of temperate regions in the southern hemisphere. Comparing the inequalities for June in Table XII. amongst themselves, and those for December amongst themselves, one can trace a gradual transformation from the phenomena seen at Toronto to those seen at Hobart. At a tropical station the change from the June to the December type is probably in all cases more or less gradual, but at some stations the transition seems pretty rapid.
TABLE XI.--Diurnal Inequality of Inclination mean from whole year.
+--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+ | | | St Peters- |Green- | | Parc St| | | |Maur- |South | |Station.| Jan Mayen. | burg and | wich. | Kew. | Maur. |Tiflis.|Kolaba.|Batavia.| itius.| Victoria| | | | Pavlovsk. | | | | | | | | Land. | +--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+ | End | North. | North. | North.| North.| North. | North.| North.| South. | South.| South. | |Dipping | | | | | | | | | | | +--------+-------------+-------------+-------+-------+--------+-------+-------+--------+-------+---------+ | Period.| 1882-1883. | 1873-1885. |1890 |1891 |1883 |1888 |1894 |1883 |1884 | 1902 | | | | | -1900.| -1900.| -1897. | -1898.| -1901.| -1894. | -1890.| -1903. | +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+ | | a. | q. | a. | q. | a. | q. | a. | a. | q. | a. | a. | a. | +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+ | Hour | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | | 1 | +4.6 | +1.5 | -0.5 | -0.3 | -0.4 | -0.3 | -0.3 | -0.1 | +0.6 | +0.9 | +0.3 | +0.6 | | 2 | +5.0 | +1.6 | -0.5 | -0.3 | -0.3 | -0.2 | -0.3 | -0.1 | +0.6 | +0.8 | +0.2 | +0.7 | | 3 | +5.6 | +1.6 | -0.5 | -0.3 | -0.3 | -0.2 | -0.3 | -0.1 | +0.5 | +0.6 | 0.0 | +0.7 | | 4 | +5.0 | +1.5 | -0.4 | -0.3 | -0.3 | -0.2 | -0.4 | -0.2 | +0.5 | +0.5 | -0.0 | +0.7 | | 5 | +4.2 | +1.4 | -0.5 | -0.3 | -0.2 | -0.2 | -0.4 | -0.2 | +0.7 | +0.3 | -0.1 | +0.7 | | 6 | +2.4 | +1.2 | -0.4 | -0.3 | -0.1 | -0.1 | -0.3 | -0.1 | +0.8 | +0.1 | -0.2 | +0.5 | | 7 | +0.7 | +0.9 | -0.2 | -0.1 | +0.2 | +0.1 | 0.0 | 0.0 | +0.5 | -0.2 | -0.3 | +0.4 | | 8 | -0.1 | +0.8 | +0.1 | +0.3 | +0.6 | +0.4 | +0.4 | +0.3 | -0.2 | -0.8 | -0.4 | +0.3 | | 9 | -0.7 | +0.8 | +0.6 | +0.6 | +1.0 | +0.8 | +0.7 | +0.5 | -1.2 | -1.7 | -0.4 | +0.1 | | 10 | -1.2 | +0.9 | +1.0 | +1.0 | +1.1 | +1.0 | +0.9 | +0.3 | -1.9 | -2.7 | -0.5 | -0.2 | | 11 | -2.2 | +0.8 | +1.2 | +1.2 | +1.0 | +0.9 | +0.7 | 0.0 | -2.1 | -3.3 | -0.6 | -0.4 | | Noon | -3.4 | +0.4 | +1.1 | +1.1 | +0.6 | +0.6 | +0.4 | -0.5 | -1.6 | -3.1 | -0.7 | -0.7 | | 1 | -4.5 | -0.2 | +0.7 | +0.7 | +0.3 | +0.2 | +0.2 | -0.6 | -0.8 | -2.4 | -0.8 | -0.9 | | 2 | -5.6 | -1.2 | +0.4 | +0.4 | +0.1 | +0.1 | +0.2 | -0.5 | -0.2 | -1.3 | -0.6 | -1.0 | | 3 | -6.3 | -2.2 | +0.2 | +0.1 | 0.0 | 0.0 | +0.2 | -0.3 | +0.3 | -0.2 | -0.3 | -1.0 | | 4 | -6.1 | -2.9 | 0.0 | -0.1 | -0.1 | -0.1 | +0.2 | +0.1 | +0.3 | +0.7 | +0.1 | -0.9 | | 5 | -5.1 | -3.2 | -0.1 | -0.3 | -0.2 | -0.2 | +0.1 | +0.4 | +0.2 | +1.3 | +0.4 | -0.7 | | 6 | -3.1 | -2.9 | -0.2 | -0.3 | -0.3 | -0.3 | 0.0 | +0.5 | +0.2 | +1.5 | +0.5 | -0.5 | | 7 | -1.7 | -2.2 | -0.3 | -0.4 | -0.4 | -0.4 | -0.2 | +0.4 | +0.3 | +1.6 | +0.5 | -0.2 | | 8 | +0.3 | -1.3 | -0.3 | -0.5 | -0.4 | -0.4 | -0.3 | +0.2 | +0.4 | +1.6 | +0.6 | 0.0 | | 9 | +2.0 | -0.3 | -0.4 | -0.6 | -0.4 | -0.4 | -0.3 | +0.1 | +0.5 | +1.6 | +0.6 | +0.2 | | 10 | +2.5 | +0.5 | -0.5 | -0.6 | -0.4 | -0.3 | -0.3 | 0.0 | +0.6 | +1.5 | +0.6 | +0.4 | | 11 | +3.0 | +1.0 | -0.5 | -0.6 | -0.4 | -0.3 | -0.3 | 0.0 | +0.6 | +1.4 | +0.5 | +0.5 | | 12 | +4.0 | +1.3 | -0.5 | -0.4 | -0.4 | -0.3 | -0.3 | -0.1 | +0.6 | +1.2 | +0.4 | +0.6 | +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+ | Range | 11.9 | 4.8 | 1.7 | 1.8 | 1.5 | 1.4 | 1.3 | 1.1 | 2.9 | 4.9 | 1.4 | 1.7 | +--------+------+------+------+------+-------+-------+--------+-------+-------+--------+-------+---------+
TABLE XII.--Diurnal Inequality of Declination (+ to West).
+--------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+ |Station.| Toronto. | Kolaba. |Trivandrum.| Batavia. | St Helena.| Mauritius.| Cape. | Hobart. | +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | Month. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. |June.|Dec. | +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | Hour | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | | 1 |-0.4 |-0.1 |-0.3 | 0.0 |-0.3 |-0.1 |+0.1 |+0.1 |-0.1 |-0.4 | 0.0 |+0.1 |-0.4 |-0.7 |+0.8 |+1.1 | | 2 |-0.2 |+0.4 |-0.3 |+0.1 |-0.4 |+0.1 |-0.1 |+0.1 |-0.2 |-0.1 |-0.2 |+0.2 |-0.5 |-0.4 |+0.3 |+1.1 | | 3 |-0.2 |-0.1 |-0.3 |+0.1 |-0.4 |+0.3 |-0.2 |+0.2 |-0.2 |+0.1 |-0.2 |+0.4 |-0.7 |-0.1 |-0.1 |+1.0 | | 4 |-1.2 |-0.4 |-0.3 |+0.3 |-0.5 |+0.5 |-0.3 |+0.3 |-0.3 |+0.3 |-0.2 |+0.7 |-0.6 |+0.3 |-0.1 |+1.1 | | 5 |-2.9 |-0.6 |-0.7 |+0.4 |-0.7 |+0.7 |-0.3 |+0.5 |-0.5 |+0.6 |-0.3 |+1.0 |-0.7 |+1.0 | 0.0 |+1.7 | | 6 |-5.2 |-0.6 |-1.6 |+0.5 |-1.6 |+1.1 |-0.5 |+1.2 |-1.0 |+0.9 |-0.4 |+1.7 |-1.0 |+2.2 | 0.0 |+2.7 | | 7 |-6.2 |-0.9 |-2.2 |+0.7 |-1.7 |+1.4 |-1.1 |+2.0 |-2.2 |+1.9 |-1.1 |+2.6 |-1.6 |+3.3 |-0.1 |+4.4 | | 8 |-6.0 |-1.2 |-2.1 |+0.2 |-1.1 |+0.9 |-0.4 |+2.3 |-1.5 |+2.2 |-1.0 |+2.4 |-0.8 |+3.6 |+0.1 |+5.6 | | 9 |-4.4 |-1.8 |-1.1 |-0.1 |-0.2 |+0.5 |+0.5 |+2.0 |-0.3 |+1.3 |+0.2 |+2.0 |+0.7 |+3.1 |+0.6 |+5.6 | | 10 |-1.5 |-1.1 | 0.0 |-0.2 |+0.6 |+0.3 |+0.9 |+1.3 |+0.3 |+0.2 |+1.2 |+1.1 |+1.6 |+1.6 |+1.2 |+3.6 | | 11 |+2.1 |+0.6 |+1.2 | 0.0 |+1.2 |+0.1 |+1.0 |+0.4 |+0.5 |-1.0 |+1.4 | 0.0 |+1.5 |+0.1 |+1.0 |+0.7 | | Noon |+4.8 |+2.2 |+2.1 | 0.0 |+1.4 |-0.4 |+0.7 |-0.6 |+0.3 |-1.4 |+1.0 |-1.4 |+0.8 |-1.0 |-0.1 |-2.6 | | 1 |+6.1 |+3.2 |+2.0 |-0.2 |+1.1 |-0.8 |+0.3 |-1.4 |+0.3 |-1.2 |+0.1 |-2.2 |+0.3 |-1.8 |-1.4 |-5.1 | | 2 |+6.1 |+3.2 |+1.6 |-0.3 |+0.7 |-0.9 |-0.2 |-1.8 |+0.2 |-0.4 |-0.9 |-2.5 |-0.3 |-1.9 |-2.2 |-6.2 | | 3 |+5.2 |+2.4 |+0.9 |-0.3 |+0.3 |-0.9 |-0.7 |-1.9 |+0.2 |+0.4 |-1.5 |-2.2 |-0.3 |-1.4 |-2.4 |-5.8 | | 4 |+3.6 |+1.5 |+0.2 |-0.3 |+0.1 |-0.8 |-0.8 |-1.6 |+0.7 |+0.6 |-1.3 |-1.6 |+0.2 |-0.8 |-1.6 |-4.8 | | 5 |+1.8 |+0.5 | 0.0 |-0.2 | 0.0 |-0.4 |-0.5 |-1.2 |+1.1 |+0.4 |-0.3 |-1.0 |+0.5 |-0.8 |-0.7 |-3.3 | | 6 |+0.7 |-0.1 |+0.1 |-0.2 |+0.2 |-0.4 |-0.1 |-0.7 |+1.0 |+0.1 |+0.5 |-0.5 |+0.5 |-0.6 |-0.4 |-1.9 | | 7 | 0.0 |-0.8 |+0.3 |-0.2 |+0.5 |-0.4 |+0.1 |-0.6 |+0.6 |-0.4 |+0.7 |-0.3 |+0.4 |-0.8 | 0.0 |-1.0 | | 8 | 0.0 |-1.2 |+0.4 |-0.1 |+0.5 |-0.3 |+0.2 |-0.5 |+0.5 |-0.7 |+0.7 |-0.3 |+0.3 |-0.9 |+0.5 |-0.3 | | 9 |-0.5 |-1.4 |+0.3 |-0.1 |+0.4 |-0.2 |+0.4 |-0.3 |+0.4 |-0.9 |+0.6 |-0.2 |+0.2 |-0.9 |+1.1 | 0.0 | | 10 |-0.5 |-1.7 |+0.1 | 0.0 |+0.2 |-0.1 |+0.4 |-0.1 |+0.2 |-1.0 |+0.4 |-0.1 |+0.1 |-1.0 |+1.3 |+0.6 | | 11 |-0.7 |-1.1 |-0.1 |-0.1 | 0.0 |-0.1 |+0.3 | 0.0 |+0.1 |-0.8 |+0.3 | 0.0 | 0.0 |-1.0 |+1.3 |+0.9 | | 12 |-0.6 |-0.7 |-0.2 |-0.1 |-0.2 |-0.1 |+0.2 |+0.1 |-0.1 |-0.6 |+0.1 |+0.1 |-0.2 |-1.0 |+1.1 |+1.2 | +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | Range |12.3 | 5.0 | 4.3 | 1.0 | 3.1 | 2.3 | 2.1 | 4.2 | 3.3 | 3.6 | 2.9 | 5.1 | 3.2 | 5.5 | 3.7 |11.8 | +--------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
§ 15. In the case of the horizontal force there are, as Table IX. shows, two markedly different types of diurnal inequality. In the one type, exemplified by Pavlovsk or Greenwich, the force is below its mean value in the middle of the day; it has a principal minimum about 10 or 11 a.m., and morning and evening maxima, the latter usually the largest. In the other type, exemplified by Kolaba or Batavia, the horizontal force is above its mean in the middle of the day, and has a maximum about 11 a.m. The second type may be regarded as the tropical type. At tropical stations, such as Kolaba, Batavia, Manila and St Helena, the type is practically the same in summer as in winter, and is the same whether the station is north or south of the equator. Similarly, what we may call the temperate type is seen--with comparatively slight modifications--both in summer and winter at stations such as Greenwich or Pavlovsk. In winter, it is true, the pronounced daily minimum is a little later and the early morning maximum is relatively more important than in summer. There is not, as in the case of the declination, any essential difference between the phenomena at temperate stations in the northern and southern hemispheres.
With diminishing latitude, there is a gradual transition from the temperate to the tropical type of horizontal force diurnal variation, and at stations whose latitude is under 45° there is a very appreciable variation in type with the season. The mean diurnal variation for the year at Tiflis in Table IX. really represents a struggle between the two types, in which on the whole the temperate type prevails. If we take the diurnal variations at Tiflis for midsummer and midwinter, we find the former essentially of the temperate, the latter essentially of the tropical type. A similar conflict may be seen in the mean diurnal inequality for the year at the Cape of Good Hope, but there the tropical type on the whole predominates, and it prevails more at midwinter than at midsummer. Toronto and Hobart, though similar in latitude to Tiflis, show a closer approach to the temperate type. Still at both stations the hours during which the force is below its mean value tend to extend back towards midnight, especially at midsummer. The amplitude of the horizontal force range appears less at intermediate stations, such as Tiflis, than at stations in either higher or lower latitudes. There is a very great difference in this respect between the north and the south of India.
§ 16. In the case of the vertical force in higher temperate latitudes--at Pavlovsk for instance--the diurnal inequalities from "all" and from "quiet" days differ somewhat widely in amplitude and slightly even in type. In mean latitudes, e.g. at Tiflis, there is often a well marked double period in the mean diurnal inequality for the whole year; but even at Tiflis this is hardly, if at all, apparent in the winter months. In the summer months the double period is distinctly seen at Kew and Greenwich, though the evening maximum is always pre-eminent. Speaking generally, the time of the minimum, or principal minimum, varies much less with the season than that of the maximum. At Kew, for instance, on quiet days the minimum falls between 11 a.m. and noon in almost all the months of the year, but the time of the maximum varies from about 4 p.m. in December to 7 p.m. in June. At Kolaba the time of the minimum is nearly independent of the season; but the changes from positive to negative in the forenoon and from negative to positive in the afternoon are some hours later in winter than in summer. At Batavia the diurnal inequality varies very little in type with the season, and there is little evidence of more than one maximum and minimum in the day. At Batavia, as at Kolaba, negative values occur near noon; but it must be remembered that while at Kolaba and more northern stations vertical force urges the north pole of a magnet downwards, the reverse is true of Batavia, as the dip is southerly. At St Helena vertical force is below its mean value in the forenoon, but the change from - to + occurs at noon, or but little later, both in winter and summer. At the Cape of Good Hope the phenomena at midsummer are similar to those at Kolaba, the force being below its mean value from about 9 a.m. to 3 p.m. and above it throughout the rest of the day; but at midwinter there is a conspicuous double period, the force being below its mean from 1 a.m. to 7 a.m. as well as from 11 a.m. to 3 p.m., and thus resembling the all-day annual results at Greenwich. At Hobart vertical force is below its mean value from 1 a.m. to 9 a.m. at midsummer, and from 4 a.m. to noon at midwinter; while the force is above its mean persistently throughout the afternoon both in summer and winter, there is at midwinter a well marked secondary minimum about 6 p.m., almost the same hour as that at which the maximum for the day is observed in summer.
TABLE XIII.--Range of the Diurnal Inequality of Declination.
+-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+ | Place. | Period. | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. | +-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+ | | | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | | Pavlovsk | 1890-1900 a | 4.93 | 6.15 | 8.58 |10.93 |12.18 |12.27 |11.82 |11.38 | 8.70 | 6.87 | 5.54 | 4.63 | | " | " q | 2.96 | 4.20 | 8.73 |11.28 |12.89 |13.28 |12.31 |11.70 | 9.37 | 6.91 | 3.95 | 2.66 | | Ekatarinburg| 1890-1900 a | 3.33 | 4.32 | 7.63 |11.19 |11.82 |11.58 |11.09 |10.45 | 8.13 | 5.60 | 3.73 | 3.14 | | Greenwich | 1865-1896 a | 5.87 | 7.07 | 9.40 |11.42 |10.55 |10.90 |10.82 |10.93 | 9.66 | 8.15 | 6.41 | 5.15 | | Kew | 1890-1900 a | 4.92 | 6.06 | 9.08 |10.95 |10.66 |10.92 |10.59 |11.01 | 9.49 | 7.73 | 5.37 | 4.46 | | " | " q | 4.07 | 4.76 | 8.82 |10.57 |10.92 |10.62 |10.18 |11.01 | 9.76 | 7.51 | 4.75 | 3.34 | | Toronto | 1842-1848 a | 5.96 | 6.05 | 9.18 | 9.94 |11.55 |12.34 |12.21 |13.14 |10.76 | 6.96 | 6.32 | 4.97 | | Manila | 1890-1900 a | 1.79 | 1.09 | 2.13 | 3.02 | 3.84 | 3.94 | 4.21 | 4.89 | 4.53 | 1.83 | 0.85 | 1.33 | | Trivandrum | 1853-1864 a | 2.06 | 1.48 | 0.79 | 1.67 | 2.90 | 3.06 | 3.06 | 3.64 | 3.31 | 1.27 | 2.14 | 2.33 | | Batavia | 1884-1899 a | 4.18 | 4.64 | 3.57 | 2.93 | 2.38 | 2.03 | 2.31 | 3.16 | 3.80 | 4.51 | 4.50 | 4.19 | | St Helena | 1842-1847 a | 3.72 | 5.19 | 4.93 | 3.30 | 2.64 | 3.24 | 3.42 | 3.59 | 2.40 | 4.43 | 4.05 | 3.54 | | Mauritius | 1876-1890 a | 5.2 | 6.1 | 6.3 | 4.7 | 4.1 | 2.9 | 3.4 | 4.9 | 5.0 | 5.5 | 5.6 | 5.1 | | Cape | 1841-1846 a | 5.14 | 8.21 | 7.27 | 5.00 | 3.91 | 3.21 | 3.54 | 4.98 | 4.33 | 5.96 | 6.36 | 5.47 | | Hobart | 1841-1848 a |11.66 |11.80 | 9.50 | 7.26 | 4.56 | 3.70 | 4.61 | 5.89 | 8.24 |11.01 |12.05 |11.81 | +-------------+-------------+------+------+------+------+------+------+------+------+------+------+------+------+
§ 17. Variations of inclination are connected with those of horizontal and vertical force by the relation
[delta]I = ½ sin 2I {V^-1 [delta]V - H^-1 [delta]H}.
Thus in temperate latitudes where V is considerably in excess of H, whilst diurnal changes in V are usually less than those in H, it is the latter which chiefly dominate the diurnal changes in inclination. When the H influence prevails, I has its highest values at hours when H is least. This explains why the dip is above its mean value near midday at stations in Table XI. from Pavlovsk to Parc St Maur. Near the magnetic equator the vertical force has the greater influence. This alone would tend to make a minimum dip in the late forenoon, and this minimum is accentuated owing to the altered type of the horizontal force diurnal variation, whose maximum now coincides closely with the minimum in the vertical force. This accounts for the prominence of the minimum in the diurnal variation of the inclination at Kolaba and Batavia, and the large amplitude of the range. Tiflis shows an intermediate type of diurnal variation; there is a minimum near noon, as in tropical stations, but inclination is also below its mean for some hours near midnight. The type really varies at Tiflis according to the season of the year. In June--as in the mean equality from the whole year--there is a well marked double period; there is a principal minimum at 2 p.m. and a secondary one about 4 a.m.; a principal maximum about 9 a.m. and a secondary one about 6 p.m. In December, however, only a single period is recognizable, with a minimum about 8 a.m. and a maximum about 7 p.m. The type of diurnal inequality seen at the Cape of Good Hope does not differ much from that seen at Batavia. Only a single period is clearly shown. The maximum occurs about 8 or 9 p.m. throughout the year. The time of the minimum is more variable; at midsummer it occurs about 11 a.m., but at midwinter three or four hours later. At Hobart the type varies considerably with the season. In June (midwinter) a double period is visible. The principal minimum occurs about 8 a.m., as at the Cape. But, corresponding to the evening maximum seen at the Cape, there is now only a secondary maximum, the principal maximum occurring about 1 p.m. At midsummer the principal maximum is found--as at Kew or Greenwich--about 10 or 11 a.m., the principal minimum about 4 p.m.
§ 18. Even at tropical stations a considerable seasonal change is usually seen in the amplitude of the diurnal inequality in at least one of the magnetic elements. At stations in Europe, and generally in temperate latitudes, the amplitude varies notably in all the elements. Table XIII. gives particulars of the inequality range of declination derived from hourly readings at selected stations, arranged in order of latitude from north to south. The letters "a" and "q" are used in the same sense as before. At temperate stations in either hemisphere--e.g. Pavlovsk, Greenwich or Hobart--the range is conspicuously larger in summer than in winter. In northern temperate stations a decided minimum is usually apparent in December. There is, on the other hand, comparatively little variation in the range from April to August. Sometimes, as at Kew and Greenwich, there is at least a suggestion of a secondary minimum at midsummer. Manila and Trivandrum show a transition from the December minimum, characteristic of the northern stations, to the June minimum characteristic of the southern, there being two conspicuous minima in February or March and in November or October. At St Helena there are two similar minima in May and September, while a third apparently exists in December. It will be noticed that at both Pavlovsk and Kew the annual variation in the range is specially prominent in the quiet day results.
Table XIV. gives a smaller number of data analogous to those of Table XIII., comprising inequality ranges for horizontal force, vertical force and inclination. In some cases the number of years from which the data were derived seems hardly sufficient to give a smooth annual variation. It should also be noticed that unless the same group of years is employed the data from two stations are not strictly comparable. The difference between the all and quiet day vertical force data at Pavlovsk is remarkably pronounced. The general tendency in all the elements is to show a reduced range at midwinter; but in some cases there is also a distinct reduction in the range at midsummer. This double annual period is particularly well marked at Batavia.
TABLE XIV.--Ranges in the Diurnal Inequalities.
+-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+ | | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. | +-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+ | H (unit 1[gamma]) | | | | | | | | | | | | | | Pavlovsk 1890-1900 a | 12 | 20 | 32 | 46 | 47 | 49 | 49 | 44 | 39 | 32 | 17 | 11 | | " " q | 12 | 17 | 31 | 42 | 45 | 45 | 42 | 40 | 37 | 31 | 17 | 10 | | Ekatarinburg " a | 11 | 15 | 29 | 37 | 40 | 40 | 39 | 36 | 33 | 27 | 13 | 9 | | Kew " q | 15 | 17 | 26 | 36 | 38 | 39 | 38 | 38 | 35 | 27 | 20 | 11 | | Toronto 1843-1848 a | 23 | 21 | 24 | 28 | 29 | 29 | 26 | 28 | 41 | 25 | 21 | 20 | | Batavia 1883-1898 a | 49 | 47 | 54 | 60 | 51 | 48 | 50 | 53 | 58 | 52 | 43 | 40 | | St Helena 1843-1847 a | 43 | 41 | 48 | 53 | 46 | 40 | 40 | 45 | 41 | 40 | 40 | 32 | | Mauritius 1883-1890 a | 21 | 15 | 21 | 23 | 20 | 21 | 20 | 22 | 20 | 21 | 21 | 20 | | Cape of Good Hope 1841-1846 a | 13 | 10 | 13 | 13 | 15 | 16 | 14 | 18 | 21 | 14 | 17 | 20 | | Hobart 1842-1848 a | 42 | 43 | 34 | 28 | 19 | 17 | 22 | 23 | 23 | 35 | 39 | 42 | | | | | | | | | | | | | | | | V (unit 1[gamma]) | | | | | | | | | | | | | | Pavlovsk 1890-1900 a | 15 | 27 | 29 | 24 | 26 | 20 | 23 | 19 | 23 | 20 | 18 | 14 | | " " q | 4 | 5 | 9 | 13 | 13 | 12 | 13 | 10 | 9 | 7 | 5 | 4 | | Ekatarinburg " a | 10 | 15 | 17 | 21 | 22 | 19 | 20 | 16 | 14 | 13 | 11 | 9 | | Kew 1891-1900 q | 7 | 10 | 20 | 25 | 31 | 27 | 28 | 23 | 20 | 15 | 9 | 6 | | Toronto 1843-1848 a | 12 | 14 | 17 | 23 | 26 | 14 | 27 | 32 | 34 | 25 | 19 | 18 | | Batavia 1883-1898 a | 42 | 48 | 48 | 45 | 31 | 31 | 32 | 29 | 41 | 50 | 40 | 33 | | St Helena 1843-1847 a | 16 | 13 | 12 | 14 | 13 | 11 | 17 | 11 | 17 | 11 | 15 | 18 | | Mauritius 1884-1890 a | 12 | 16 | 18 | 15 | 14 | 13 | 15 | 21 | 20 | 16 | 13 | 11 | | Cape of Good Hope 1841-1846 a | 29 | 47 | 41 | 38 | 21 | 12 | 14 | 19 | 19 | 35 | 33 | 28 | | Hobart 1842-1848 a | 25 | 27 | 22 | 23 | 24 | 21 | 22 | 28 | 26 | 22 | 23 | 27 | | | | | | | | | | | | | | | | _Inclination_ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | | Pavlovsk 1890-1900 a | 0.97 | 1.24 | 2.07 | 2.79 | 2.72 | 2.88 | 2.85 | 2.64 | 2.52 | 2.18 | 1.20 | 0.89 | | Ekatarinburg " a | 0.79 | 0.94 | 1.70 | 2.08 | 2.25 | 2.19 | 2.18 | 2.08 | 2.00 | 1.70 | 0.88 | 0.69 | | Kew " q | 0.98 | 1.01 | 1.38 | 1.86 | 2.05 | 2.02 | 2.05 | 2.15 | 1.98 | 1.57 | 1.27 | 0.63 | | Toronto 1843-1848 a | 1.15 | 0.94 | 1.19 | 1.23 | 1.31 | 1.37 | 1.13 | 1.26 | 1.87 | 1.16 | 1.09 | 1.05 | | Batavia 1883-1898 a | 4.88 | 5.22 | 5.56 | 5.62 | 4.21 | 4.05 | 4.24 | 4.17 | 5.13 | 5.58 | 4.51 | 3.85 | | Cape of Good Hope 1842-1846 a | 1.55 | 2.29 | 2.23 | 2.23 | 1.60 | 1.41 | 1.54 | 1.70 | 1.86 | 2.03 | 1.55 | 2.04 | | Hobart 1842-1848 a | 1.95 | 2.16 | 1.72 | 1.62 | 1.23 | 1.16 | 1.28 | 1.42 | 1.39 | 1.75 | 2.04 | 2.10 | +-------------------------------+------+------+------+------+------+------+------+------+------+------+------+------+
§ 19. When discussing diurnal inequalities it is sometimes convenient to consider the components of the horizontal force in and perpendicular to the astronomical meridian, rather than the horizontal force and declination. If N and W be the components of H to astronomical north and west, and D the westerly declination, N = H cos D, W = H sin D. Thus corresponding small variations in N, W, H and D are connected by the relations:--
[delta]N = cos D[delta]H - H sin D[delta]D, [delta]W = sin D[delta]H + H cos D[delta]D.
If [delta]H and [delta]D denote the departures of H and D at any hour of the day from their mean values, then [delta]N and [delta]W represent the corresponding departures of N and W from their mean values. In this way diurnal inequalities may be calculated for N and W when those for H and D are known. The formulae suppose [delta]D to be expressed in absolute measure, i.e. 1´ of arc has to be replaced by 0.0002909. If we take as an example a station at which H is .185 then H[delta]D = .0000538 (number of minutes in [delta]D). In other words, employing 1[gamma] as unit of force, one replaces H[delta]D by 5.38[delta]D, where [delta]D represents declination change expressed as usual in minutes of arc. In calculating diurnal inequalities for N and W, one ought, strictly speaking, to assign to H and D the exact mean values belonging to these elements for the month or the year being dealt with. For practical purposes, however, a slight departure from the true mean values is immaterial, and one can make use of a constant value for several successive years without sensible error. As an example, Table XV. gives the mean diurnal inequality for the whole year in N and W at Falmouth, as calculated from the 12 years 1891 to 1902. The unit employed is 1[gamma].
The data in Table XV. are closely similar to corresponding Kew data, and are presumably fairly applicable to the whole south of England for the epoch considered. At Falmouth there is comparatively little seasonal variation in the type of the diurnal variation in either N or W. The amplitude of the diurnal range varies, however, largely with the season, as will appear from Table XVI., which is based on the same 12 years as Table XV.
Diurnal inequalities in N and W lend themselves readily to the construction of what are known as _vector diagrams_. These are curves showing the direction and intensity at each hour of the day of the horizontal component of the disturbing force to which the diurnal inequality may be regarded as due. Figs. 7 and 8, taken from the _Phil. Trans._ vol. 204A, will serve as examples. They refer to the mean diurnal inequalities for the months stated at Kew (1890 to 1900) and Falmouth (1891 to 1902), thick lines relating to Kew, thin to Falmouth. NS and EW represent the geographical north-south and east-west directions; their intersection answers to the origin (thick lines for Kew, thin for Falmouth). The line from the origin to M represents the magnetic meridian. The line from the origin to any cross--the number indicating the corresponding hour counted from midnight as 0--represents the magnitude and direction at that hour of the horizontal component of the disturbing force to which the diurnal inequality may be assigned. The cross marks the point whose rectangular co-ordinates are the values of [delta]N and [delta]W derived from the diurnal inequalities of these elements. In figs. 7 and 8 the distances of the points N, E, S, W from their corresponding origin represents 10[gamma]. The tendency to form a loop near midnight, seen in the November and December curves, is characteristic of the winter months at Kew and Falmouth. The shape is less variable in summer than in winter; but even in summer the portion answering to the hours 6 p.m. to 6 a.m. varies a good deal. The object of presenting the Kew and Falmouth curves side by side is to emphasize the close resemblance between the magnetic phenomena at places in similar latitudes, though over 200 miles apart and exhibiting widely different ranges for their meteorological elements. With considerable change of latitude however the shape of vector diagrams changes largely.
TABLE XV.--Diurnal Inequalities in N. and W. at Falmouth (unit 1[gamma]).
+---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | Hour. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | +---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ |N. /a.m. | + 6 | + 5 | + 5 | + 5 | + 6 | + 6 | + 5 | + 1 | - 6 | -14 | -20 | -20 | | \p.m. | -17 | -12 | - 6 | - 1 | + 3 | + 6 | + 9 | + 9 | + 9 | + 8 | + 7 | + 7 | |W. /a.m. | - 2 | - 2 | - 3 | - 4 | - 6 | - 9 | -13 | -17 | -19 | -13 | - 3 | +11 | | \p.m. | +20 | +22 | +17 | +11 | + 6 | + 4 | + 2 | + 1 | 0 | - 1 | - 2 | - 2 | +---------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
Fourier Series.
§ 20. Any diurnal inequality can be analysed into a series of harmonic terms whose periods are 24 hours and submultiples thereof. The series may be expressed in either of the equivalent forms:--
a1 cos t + b1 sin t + a2 cos 2t + b2 sin 2t + ... (i)
c1 sin (t + [alpha]1) + c2 sin (2t + [alpha]2) + .... (ii)
TABLE XVI.--Ranges in Diurnal Inequalities at Falmouth (unit 1[gamma]).
+----+------+------+------+------+------+------+------+------+------+------+------+------+ | | Jan. | Feb. |March.|April.| May. | June.| July.| Aug. | Sept.| Oct. | Nov. | Dec. | +----+------+------+------+------+------+------+------+------+------+------+------+------+ | N. | 21 | 23 | 30 | 39 | 39 | 37 | 37 | 39 | 36 | 32 | 24 | 15 | | W. | 20 | 24 | 46 | 54 | 55 | 55 | 54 | 56 | 51 | 39 | 24 | 15 | +----+------+------+------+------+------+------+------+------+------+------+------+------+
In both forms t denotes time, counted usually from midnight, one hour of time being interpreted as 15° of angle. Form (i) is that utilized in actually calculating the constants a, b, ... Once the a, b, ... constants are known, the c, [alpha], ... constants are at once derivable from the formulae:--
tan [alpha]_n = a_n/b_n; c_n = a_n/sin [alpha]_n = b_n/cos [alpha]_n = [root](a_n² + b_n²).
The a, b, c, [alpha] constants are called sometimes Fourier, sometimes Bessel coefficients.
By taking a sufficient number of terms a series can always be obtained which will represent any set of diurnal inequality figures; but unless one can obtain a close approach to the observational figures from the terms possessing the periods 24, 12, 8 and 6 hours the physical significance and general utility of the analysis is somewhat problematical. In the case of the magnetic elements, the 24 and 12 hour terms are usually much the more important; the 24-hour term is generally, but by no means always, the larger of the two. The c constants give the amplitudes of the harmonic terms or waves, the [alpha] constants the phase angles. An advance of 1 hour in the time of occurrence of the first (and subsequent, if any) maximum and minimum answers to an _increase_ of 15° in [alpha]1 of 30° in [alpha]2, of 45° in [alpha]3, of 60° in [alpha]4 and so on. In the case of magnetic elements the phase angles not infrequently possess a somewhat large annual variation. It is thus essential for a minute study of the phenomena at any station to carry out the analysis for the different seasons of the year, and preferably for the individual months. If the a and b constants are known for all the individual months of one year, or for all the Januarys of a series of years, we have only to take their arithmetic means to obtain the corresponding constants for the mean diurnal inequality of the year, or for the diurnal inequality of the average January of the series of years. This, however, is obviously not true of the c or [alpha] constants, unless the phase angle is absolutely unchanged throughout the contributory months or years. This is a point requiring careful attention, because when giving values of c and [alpha] for the whole year some authorities give the arithmetic mean of the c's and [alpha]'s calculated from the diurnal inequalities of the individual months of the year, others give the values obtained for c and [alpha] from the mean diurnal inequality of the whole year. The former method inevitably supplies a larger value for c than the latter, supposing [alpha] to vary with the season. At some observatories, e.g. Greenwich and Batavia, it has long been customary to publish every year values of the Fourier coefficients for each month, and to include other elements besides the declination. For a thoroughly satisfactory comparison of different stations, it is necessary to have data from one and the same epoch; and preferably that epoch should include at least one 11-year period. There are, however, few stations which can supply the data required for such a comparison and we have to make the best of what is available. Information is naturally most copious for the declination. For this element E. Engelenburg[20] gives values of C1, C2, C3, C4, and of [alpha]1, [alpha]2, [alpha]3, [alpha]4 for each month of the year for about 50 stations, ranging from Fort Rae (62° 6´ N. lat.) to Cape Horn (55° 5´ S. lat.). From the results for individual stations, Engelenburg derives a series of means which he regards as representative of 11 different zones of latitude. His data for individual stations refer to different epochs, and some are based on only one year's observations. The original observations also differ in reliability; thus the results are of somewhat unequal value. The mean results for Engelenburg's zones must naturally have some of the sources of uncertainty reduced; but then the fundamental idea represented by the arrangement in zones is open to question. The majority of the data in Table XVII. are taken from Engelenburg, but the phase angles have been altered so as to apply to westerly declination. The stations are arranged in order of latitude from north to south; in a few instances results are given for quiet days. The figures represent in all cases arithmetic means derived from the 12 monthly values. In the table, so far as is known, the local mean time of the observatory has been employed. This is a point requiring attention, because most observatories employ Greenwich time, or time based on Greenwich or some other national observatory, and any departure from local time enters into the values of the constants. The data for Victoria Land refer to the "Discovery's" 1902-1903 winter quarters, where the declination, taken westerly, was about 207°.5.
As an example of the significance of the phase angles in Table XVII., take the ordinary day data for Kew. The times of occurrence of the maxima are given by t + 234° = 450° for the 24-hour term, 2t + 39°.7 = 90° or = 450° for the 12-hour term, and so on, taking an hour in t as equivalent to 15°.
Thus the times of the maxima are:--
24-hour term, 2 h. 24 m. p.m.; 12-hour term, 1 h. 41 m. a.m. and p.m.
8-hour term, 4 h. 41 m. a.m., 0 h. 41 m. p.m., and 8 h. 41 m. p.m.
6-hour term, 0 h. 33 m. a.m. and p.m., and 6 h. 33 m. a.m. and p.m.
The minima, or extreme easterly positions in the waves, lie midway between successive maxima. All four terms, it will be seen, have maxima at some hour between 0h. 30m. and 2h. 30m. p.m. They thus reinforce one another strongly from 1 to 2 p.m., accounting for the prominence of the maximum in the early afternoon.
The utility of a Fourier analysis depends largely on whether the several terms have a definite physical significance. If the 24-hour and 12-hour terms, for instance, represent the action of forces whose distribution over the earth or whose seasonal variation is essentially different, then the analysis helps to distinguish these forces, and may assist in their being tracked to their ultimate source. Suppose, for example, one had reason to think the magnetic diurnal variation due to some meteorological phenomenon, e.g. heating of the earth's atmosphere, then a comparison of Fourier coefficients, if such existed, for the two sets of phenomena would be a powerful method of investigation.
TABLE XVII.--Amplitudes and Phase Angles for Diurnal Inequality of Declination.
+---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ | Place. | Epoch. | c1. | c2. | c3. | c4. | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. | +---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ | | | ´ | ´ | ´ | ´ | ° | ° | ° | ° | | Fort Rae (all) | 1882-1883 | 18.49 | 8.22 | 1.99 | 2.07 | 156.5 | 41.9 | 308 | 104 | | " (quiet) | " | 9.09 | 4.51 | 1.32 | 0.73 | 166.5 | 37.5 | 225 | 350 | | Ekatarinburg | 1841-1862 | 2.57 | 1.81 | 0.73 | 0.22 | 223.3 | 7.4 | 204 | 351 | | Potsdam | 1890-1899 | 2.81 | 1.90 | 0.83 | 0.31 | 239.9 | 32.6 | 237 | 49 | | Kew (ordinary) | 1890-1900 | 2.91 | 1.79 | 0.79 | 0.27 | 234.0 | 39.7 | 239 | 57 | | Kew (quiet) | " | 2.37 | 1.82 | 0.90 | 0.30 | 227.3 | 42.1 | 240 | 55 | | Falmouth (quiet) | 1891-1902 | 2.18 | 1.82 | 0.91 | 0.29 | 226.2 | 40.5 | 238 | 56 | | Parc St Maur | 1883-1899 | 2.70 | 1.87 | 0.85 | 0.30 | 238.6 | 32.5 | 235 | 95 | | Toronto | 1842-1848 | 2.65 | 2.34 | 1.00 | 0.33 | 213.7 | 34.9 | 238 | 350 | | Washington | 1840-1842 | 2.38 | 1.86 | 0.65 | 0.33 | 223.0 | 26.6 | 223 | 53 | | Manila | 1890-1900 | 0.53 | 0.58 | 0.43 | 0.17 | 266.3 | 50.7 | 226 | 89 | | Trivandrum | 1853-1864 | 0.54 | 0.46 | 0.29 | 0.10 | 289.0 | 49.6 | | 114 | | Batavia | 1883-1899 | 0.80 | 0.88 | 0.43 | 0.13 | 332.0 | 163.2 | 5 | 236 | | St. Helena | 1842-1847 | 0.68 | 0.61 | 0.63 | 0.34 | 275.8 | 171.4 | 27 | 244 | | Mauritius | 1876-1890 | 0.86 | 1.11 | 0.76 | 0.22 | 21.6 | 172.7 | 350 | 161 | | C. of G. Hope | 1841-1846 | 1.15 | 1.13 | 0.80 | 0.35 | 287.7 | 156.0 | 351 | 193 | | Melbourne | 1858-1863 | 2.52 | 2.45 | 1.23 | 0.35 | 27.4 | 176.7 | 9 | 193 | | Hobart | 1841-1848 | 2.29 | 2.15 | 0.87 | 0.32 | 33.6 | 170.8 | 349 | 185 | | S. Georgia | 1882-1883 | 2.13 | 1.28 | 0.76 | 0.31 | 30.3 | 185.3 | 7 | 180 | | Victoria Land (all) | 1902-1903 | 20.51 | 4.81 | 1.21 | 1.32 | 158.7 | 306.9 | 292 | 303 | | " (quieter) | " | 15.34 | 4.05 | 1.24 | 1.18 | 163.8 | 312.9 | 261 | | +---------------------+-----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
§ 21. Fourier coefficients of course often vary much with the season of the year. In the case of the declination this is especially true of the phase angles at tropical stations. To enter on details for a number of stations would unduly occupy space. A fair idea of the variability in the case of declination in temperate latitudes may be derived from Table XVIII., which gives monthly values for Kew derived from ordinary days of an 11-year period 1890-1900.
Fourier analysis has been applied to the diurnal inequalities of the other magnetic elements, but more sparingly. Such results are illustrated by Table XIX., which contains data derived from quiet days at Kew from 1890 to 1900. _Winter_ includes November to February, _Summer_ May to August, and _Equinox_ the remaining four months. In this case the data are derived from mean diurnal inequalities for the season specified. In the case of the c or amplitude coefficients the unit is 1´ for I (inclination), and 1[gamma] for H and V (horizontal and vertical force). At Kew the seasonal variation in the amplitude is fairly similar for all the elements. The 24-hour and 12-hour terms tend to be largest near midsummer, and least near midwinter; but the 8-hour and 6-hour terms have two well-marked maxima near the equinoxes, and a clearly marked minimum near midsummer, in addition to one near midwinter. On the other hand, the phase angle phenomena vary much for the different elements. The 24-hour term, for instance, has its maximum earlier in winter than in summer in the case of the declination and vertical force, but the exact reverse holds for the inclination and the horizontal force.
TABLE XVIII.--Kew Declination: Amplitudes and Phase Angles (local mean time).
+----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ | Month. | C1. | C2. | C3. | C4. | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. | +----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ | | ´ | ´ | ´ | ´ | ° | ° | ° | ° | | January | 1.79 | 0.86 | 0.41 | 0.27 | 251.2 | 29.8 | 254 | 64 | | February | 2.41 | 1.11 | 0.57 | 0.30 | 242.0 | 27.7 | 235 | 39 | | March | 3.05 | 1.98 | 1.11 | 0.45 | 233.2 | 36.1 | 223 | 49 | | April | 3.35 | 2.48 | 1.17 | 0.39 | 224.8 | 39.2 | 228 | 61 | | May | 3.57 | 2.38 | 0.87 | 0.17 | 221.3 | 50.8 | 245 | 89 | | June | 3.83 | 2.39 | 0.74 | 0.05 | 212.6 | 46.7 | 239 | 72 | | July | 3.72 | 2.30 | 0.77 | 0.11 | 214.6 | 48.1 | 233 | 8 | | August | 3.64 | 2.43 | 1.05 | 0.18 | 228.2 | 57.2 | 244 | 51 | | September| 3.35 | 2.02 | 1.04 | 0.35 | 236.9 | 55.3 | 245 | 70 | | October | 2.69 | 1.69 | 0.92 | 0.48 | 240.1 | 35.6 | 235 | 65 | | November | 1.94 | 1.06 | 0.51 | 0.32 | 248.3 | 28.3 | 247 | 61 | | December | 1.61 | 0.81 | 0.35 | 0.20 | 255.1 | 22.0 | 243 | 56 | +----------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
Annual Inequality.
§ 22. If secular change proceeded uniformly throughout the year, the value E_n of any element at the middle of the nth month of the year would be connected with E, the mean value for the whole year, by the formula E_n = E + (2n - 13)s/24, where s is the secular change per annum. For the present purpose, difference in the lengths of the months may be neglected. If one applies to E_n - E the correction -(2n - 13)s/24 one eliminates a regularly progressive secular change; what remains is known as the _annual inequality_. If only a short period of years is dealt with, irregularities in the secular change from year to year, or errors of observation, may obviously simulate the effect of a real annual inequality. Even when a long series of years is included, there is always a possibility of a spurious inequality arising from annual variation in the instruments, or from annual change in the conditions of observation. J. Liznar,[21] from a study of data from a number of stations, arrived at certain mean results for the annual inequalities in declination and inclination in the northern and southern hemispheres, and J. Hann[22] has more recently dealt with Liznar's and newer results. Table XX. gives a variety of data, including the mean results given by Liznar and Hann. In the case of declination + denotes westerly position; in the case of inclination it denotes a larger dip (whether the inclination be north or south). According to Liznar declination in summer is to the west of the normal position in both hemispheres. The phenomena, however, at Parc St Maur are, it will be seen, the exact opposite of what Liznar regards as normal; and whilst the Potsdam results resemble his mean in type, the range of the inequality there, as at Parc St Maur, is relatively small. Of the three sets of data given for Kew the first two are derived in a similar way to those for other stations; the first set are based on quiet days only, the second on all but highly disturbed days. Both these sets of results are fairly similar in type to the Parc St Maur results, but give larger ranges; they are thus even more opposed to Liznar's normal type. The last set of data for Kew is of a special kind. During the 11 years 1890 to 1900 the Kew declination magnetograph showed to within 1´ the exact secular change as derived from the absolute observations; also, if any annual variation existed in the position of the base lines of the curves it was exceedingly small. Thus the accumulation of the daily non-cyclic changes shown by the curves should closely represent the combined effects of secular change and annual inequality. Eliminating the secular change, we arrive at an annual inequality, based on all days of the year including the highly disturbed. It is this annual inequality which appears under the heading s. It is certainly very unlike the annual inequality derived in the usual way. Whether the difference is to be wholly assigned to the fact that highly disturbed days contribute in the one case, but not in the other, is a question for future research.
TABLE XIX.--Kew Diurnal Inequality: Amplitudes and Phase Angles (local mean time).
+-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ | Month. | C1. | C2. | C3. | C4. | [alpha]1. | [alpha]2. | [alpha]3. | [alpha]4. | +-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+ | | ´ | ´ | ´ | ´ | ° | ° | ° | ° | | /Winter | 0.240 | 0.222 | 0.104 | 0.076 | 250.0 | 91.8 | 344 | 194 | | I < Equinox | 0.601 | 0.290 | 0.213 | 0.127 | 290.3 | 135.5 | 4 | 207 | | \Summer | 0.801 | 0.322 | 0.172 | 0.070 | 312.5 | 155.5 | 39 | 238 | | | | | | | | | | | | /Winter | 3.62 | 3.86 | 1.81 | 1.13 | 82.9 | 277.3 | 154 | 6 | | H < Equinox | 10.97 | 5.87 | 3.32 | 1.84 | 109.6 | 303.5 | 167 | 16 | | \Summer | 14.85 | 6.23 | 2.35 | 0.95 | 130.3 | 316.5 | 199 | 41 | | | | | | | | | | | | /Winter | 2.46 | 1.67 | 0.86 | 0.42 | 153.9 | 300.8 | 108 | 280 | | V < Equinox | 6.15 | 4.70 | 2.51 | 0.94 | 117.2 | 272.3 | 99 | 289 | | \Summer | 8.63 | 6.45 | 2.24 | 0.55 | 122.0 | 272.4 | 100 | 285 | +-------------+-------+-------+-------+-------+-----------+-----------+-----------+-----------+
In the case of the inclination, Liznar found that in both hemispheres the dip (north in the northern, south in the southern hemisphere) was larger than the normal when the sun was in perihelion, corresponding to an enhanced value of the horizontal force in summer in the northern hemisphere.
In the case of annual inequalities, at least that of the declination, it is a somewhat suggestive fact that the range seems to become less as we pass from older to more recent results, or from shorter to longer periods of years. Thus for Paris from 1821 to 1830 Arago deduced a range of 2´ 9´´. Quiet days at Kew from 1890 to 1894 gave a range of 1´.2, while at Potsdam Lüdeling got a range 30% larger than that in Table XX. when considering the shorter period 1891-1899. Up to the present, few individual results, if any, can claim a very high degree of certainty. With improved instruments and methods it may be different in the future.
TABLE XX.--Annual Inequality.
+---------------------------------------------------------------------------------------------+-------------------------------------+ | Declination. | Inclination. | +-----------+---------+-----------+-----------+-----------------------+-----------+-----------+---------+---------+---------+-------+ | | Liznar, | Potsdam, | Parc St | Kew (1890-1900). | Batavia, | | Liznar &| | Parc St.| | | | N. Hemi-| 1891-1906.| Maur, +-------+-------+-------+ 1883-1893.| Mauritius.| Hann's | Potsdam.| Maur. | Kew. | | | sphere. | | 1888-1897.| q. | o. | s. | | | mean. | | | | +-----------+---------+-----------+-----------+-------+-------+-------+-----------+-----------+---------+---------+---------+-------+ | | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | | January | -0.25 | +0.04 | +0.01 | +0.08 | +0.03 | +0.32 | +0.23 | +0.06 | +0.49 | +0.32 | +0.44 | -0.03 | | February | -0.54 | -0.11 | 0.00 | +0.48 | +0.25 | -0.20 | +0.19 | +0.29 | +0.39 | +0.56 | +0.29 | -0.07 | | March | -0.27 | +0.04 | +0.17 | +0.03 | +0.05 | -1.02 | -0.12 | +0.27 | +0.20 | +0.38 | +0.13 | +0.53 | | April | -0.03 | +0.10 | +0.12 | -0.31 | -0.14 | -0.90 | -0.11 | +0.30 | -0.08 | -0.02 | -0.13 | +0.18 | | May | +0.19 | +0.07 | -0.11 | -0.39 | -0.28 | +0.29 | -0.30 | +0.08 | -0.43 | -0.29 | -0.37 | -0.15 | | June | +0.46 | +0.13 | -0.14 | -0.47 | -0.39 | +0.78 | -0.13 | -0.19 | -0.70 | -0.77 | -0.59 | -0.35 | | July | +0.48 | +0.14 | -0.17 | -0.30 | -0.13 | +0.44 | -0.08 | -0.44 | -0.72 | -0.67 | -0.27 | -0.13 | | August | +0.47 | +0.11 | +0.01 | +0.08 | +0.05 | +0.52 | -0.18 | -0.38 | -0.47 | -0.23 | -0.05 | -0.19 | | September | +0.31 | +0.01 | 0.00 | +0.29 | +0.24 | -0.02 | +0.06 | -0.06 | -0.06 | +0.16 | +0.01 | +0.20 | | October | -0.07 | -0.11 | +0.09 | +0.06 | +0.01 | -0.26 | +0.03 | -0.04 | +0.31 | +0.27 | +0.19 | 0.00 | | November | -0.30 | -0.28 | -0.05 | +0.17 | +0.11 | -0.02 | +0.08 | -0.01 | +0.51 | +0.30 | +0.43 | +0.18 | | December | -0.36 | -0.14 | +0.05 | +0.26 | +0.23 | +0.05 | +0.35 | +0.06 | +0.55 | +0.19 | +0.24 | -0.29 | +-----------+---------+-----------+-----------+-------+-------+-------+-----------+-----------+---------+---------+---------+-------+ | Range | 1.02 | 0.42 | 0.34 | 0.95 | 0.64 | 1.80 | 0.65 | 0.74 | 1.27 | 1.33 | 1.03 | 0.88 | +-----------+---------+-----------+-----------+-------+-------+-------+-----------+-----------+---------+---------+---------+-------+
Annual Variation Fourier Coefficients.
§ 23. The inequalities in Table XX. may be analysed--as has in fact been done by Hann--in a series of Fourier terms, whose periods are the year and its submultiples. Fourier series can also be formed representing the annual variation in the amplitudes of the regular diurnal inequality, and its component 24-hour, 12-hour, &c. waves, or of the amplitude of the absolute daily range (§ 24). To secure the highest theoretical accuracy, it would be necessary in calculating the Fourier coefficients to allow for the fact that the "months" from which the observational data are derived are not of uniform length. The mid-times, however, of most months of the year are but slightly displaced from the position they would occupy if the 12 months were exactly equal, and these displacements are usually neglected. The loss of accuracy cannot be but trifling, and the simplification is considerable.
The Fourier series may be represented by
P1 sin (t + [theta]1) + P2 sin (2t + [theta]2) + ...,
where t is time counted from the beginning of the year, one month being taken as the equivalent of 30°, P1, P2 represent the amplitudes, and [theta]1, [theta]2 the phase angles of the first two terms, whose periods are respectively 12 and 6 months. Table XXI. gives the values of these coefficients in the case of the range of the regular diurnal inequality for certain specified elements and periods at Kew[23] and Falmouth.[23a] In the case of P1 and P2 the unit is 1´ for D and I, and 1[gamma] for H and V. M denotes the mean value of the range for the 12 months. The letters q and o represent quiet and ordinary day results. S max. means the years 1892-1895, with a mean sun spot frequency of 75.0. S min. for Kew means the years 1890, 1899 and 1900 with a mean sun spot frequency of 9.6; for Falmouth it means the years 1899-1902 with a mean sun spot frequency of 7.25.
Increase in [theta]1 or [theta]2 means an earlier occurrence of the maximum or maxima, 1° answering roughly to one day in the case of the 12-month term, and to half a day in the case of the 6-month term. P1/M and P2/M both increase decidedly as we pass from years of many to years of few sun spots; i.e. _relatively_ considered the range of the regular diurnal inequality is more variable throughout the year when sun spots are few than when they are many.
The tendency to an earlier occurrence of the maximum as we pass from quiet days to ordinary days, or from years of sun spot minimum to years of sun spot maximum, which appears in the table, appears also in the case of the horizontal force--at least in the case of the annual term--both at Kew and Falmouth. The phenomena at the two stations show a remarkably close parallelism. At both, and this is true also of the absolute ranges, the maximum of the annual term falls in all cases near midsummer, the minimum near midwinter. The maxima of the 6-month terms fall near the equinoxes.
TABLE XXI.--Annual Variation of Diurnal Inequality Range. Fourier Coefficients.
+---------------------+--------+--------+-----------+-----------+-------+-------+ | | P1. | P2. | [theta]1. | [theta]2. | P1/M. | P2/M. | +-----------+---------+--------+--------+-----------+-----------+-------+-------+ | Kew | D_0 | 3.36 | 0.94 | 279° | 280° | 0.40 | 0.11 | | 1890-1900 | D_q | 3.81 | 1.22 | 275° | 273° | 0.47 | 0.15 | | | I_q | 0.67 | 0.16 | 264° | 269° | 0.42 | 0.10 | | | H_q | 13.6 | 3.0 | 269° | 261° | 0.48 | 0.11 | | | V_q | 11.7 | 2.2 | 282° | 242° | 0.63 | 0.12 | +-----------+---------+--------+--------+-----------+-----------+-------+-------+ | S max. | Kew | 4.50 | 1.26 | 277° | 282° | 0.47 | 0.13 | | D_q | Falmouth| 4.10 | 1.40 | 277° | 286° | 0.43 | 0.15 | +-----------+---------+--------+--------+-----------+-----------+-------+-------+ | S min. | Kew | 3.35 | 1.10 | 274° | 269° | 0.49 | 0.16 | | D_q | Falmouth| 3.19 | 1.14 | 275° | 277° | 0.49 | 0.17 | +-----------+---------+--------+--------+-----------+-----------+-------+-------+
Absolute Range.
§ 24. Allusion has already been made in § 14 to one point which requires fuller discussion. If we take a European station such as Kew, the general character of, say, the declination does not vary very much with the season, but still it does vary. The principal minimum of the day, for instance, occurs from one to two hours earlier in summer than in winter. Let us suppose for a moment that all the days of a month are exactly alike, the difference in type between successive months coming in _per saltum._ Suppose further that having formed twelve diurnal inequalities from the days of the individual months of the year, we deduce a mean diurnal inequality for the whole year by combining these twelve inequalities and taking the mean. The hours of maximum and minimum being different for the twelve constituents, it is obvious that the resulting maximum will normally be less than the arithmetic mean of the twelve maxima, and the resulting minimum (arithmetically) less than the arithmetic mean of the twelve minima. The range--or algebraic excess of the maximum over the minimum--in the mean diurnal inequality for the year is thus normally less than the arithmetic mean of the twelve ranges from diurnal inequalities for the individual months. Further, as we shall see later, there are differences in type not merely between the different months of the year, but even between the same months in different years. Thus the range of the mean diurnal inequality for, say, January based on the combined observations of, say, eleven Januarys may be and generally will be slightly less than the arithmetic mean of the ranges obtained from the Januarys separately. At Kew, for instance, taking the ordinary days of the 11 years 1890-1900, the arithmetic mean of the diurnal inequality ranges of declination from the 132 months treated independently was 8´.52, the mean range from the 12 months of the year (the eleven Januarys being combined into one, and so on) was 8´.44, but the mean range from the whole 4,000 odd days superposed was only 8´.03. Another consideration is this: a diurnal inequality is usually based on hourly readings, and the range deduced is thus an under-estimate unless the absolute maximum and minimum both happen to come exactly at an hour. These considerations would alone suffice to show that the _absolute range_ in individual days, i.e. the difference between the algebraically largest and least values of the element found any time during the 24 hours, must on the average exceed the range in the mean diurnal inequality for the year, however this latter is formed. Other causes, moreover, are at work tending in the same direction. Even in central Europe, the magnetic curves for individual days of an ordinary month often differ widely amongst themselves, and show maxima and minima at different times of the day. In high latitudes, the variation from day to day is sometimes so great that mere eye inspection of magnetograph curves may leave one with but little idea as to the probable shape of the resultant diurnal curve for the month. Table XXII. gives the arithmetic mean of the absolute daily ranges from a few stations. The values which it assigns to the year are the arithmetic means of the 12 monthly values. The Mauritius data are for different periods, viz. declination 1875, 1880 and 1883 to 1890, horizontal force 1883 to 1890, vertical force 1884 to 1890. The other data are all for the period 1890 to 1900.
TABLE XXII.--Mean Absolute Daily Ranges (Units 1´ for Declination, 1[gamma] for H and V).
+--------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | Jan. | Feb. | Mar. | April.| May. | June. | July. | Aug. | Sept. | Oct. | Nov. | Dec. | Year. | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ | _Declination._ | | | | | | | | | | | | | | | Pavlovsk | 13.42 | 17.20 | 18.22 | 17.25 | 17.76 | 15.91 | 16.89 | 16.57 | 16.75 | 15.70 | 13.87 | 12.37 | 15.99 | | Ekatarinburg | 7.33 | 9.54 | 11.90 | 12.89 | 13.63 | 13.03 | 12.78 | 12.21 | 11.23 | 9.44 | 7.86 | 6.85 | 10.72 | | Kew. All days | 11.16 | 13.69 | 15.93 | 15.00 | 14.90 | 13.65 | 14.13 | 14.22 | 14.57 | 14.07 | 11.71 | 9.80 | 13.57 | | " Ordinary days| 10.14 | 11.87 | 14.19 | 14.24 | 13.85 | 13.26 | 13.47 | 13.67 | 13.71 | 13.10 | 10.40 | 9.00 | 12.58 | | " Quiet " | 6.12 | 7.57 | 10.59 | 11.84 | 12.09 | 11.95 | 11.60 | 11.93 | 10.86 | 9.16 | 6.54 | 5.08 | 9.61 | | Zi-ka-wei | 3.88 | 3.25 | 6.22 | 7.04 | 7.15 | 7.40 | 7.77 | 8.06 | 6.73 | 4.68 | 2.91 | 2.52 | 5.63 | | Mauritius | 6.93 | 7.79 | 7.11 | 5.75 | 4.87 | 4.03 | 4.36 | 6.00 | 6.28 | 6.71 | 6.99 | 6.78 | 6.13 | | | | | | | | | | | | | | | | | _Horizontal force._| | | | | | | | | | | | | | | Pavlovsk | 52.4 | 74.5 | 79.1 | 80.1 | 86.2 | 79.0 | 86.7 | 77.6 | 76.7 | 67.3 | 55.7 | 45.9 | 71.8 | | Ekatarinburg | 33.2 | 43.1 | 48.4 | 51.7 | 56.2 | 54.1 | 56.7 | 51.7 | 49.3 | 44.1 | 34.1 | 29.3 | 46.0 | | Mauritius | 37.9 | 35.0 | 36.2 | 37.6 | 35.0 | 34.1 | 33.8 | 34.5 | 36.6 | 37.4 | 37.8 | 35.3 | 35.9 | | | | | | | | | | | | | | | | | _Vertical force._ | | | | | | | | | | | | | | | Pavlovsk | 27.0 | 50.4 | 54.7 | 43.2 | 45.3 | 34.8 | 42.1 | 35.5 | 42.5 | 37.5 | 33.5 | 25.5 | 39.3 | | Ekatarinburg | 17.4 | 26.6 | 29.2 | 30.1 | 29.6 | 27.6 | 29.6 | 26.1 | 25.2 | 22.1 | 19.6 | 16.4 | 24.9 | | Mauritius | 17.1 | 19.5 | 20.1 | 17.3 | 16.5 | 15.5 | 17.1 | 22.0 |22.7 | 19.4 | 16.7 | 15.2 | 18.2 | +--------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
A comparison of the absolute ranges in Table XXII. with the inequality ranges for the same stations derivable from Tables VIII. to X. is most instructive. At Mauritius the ratio of the absolute to the inequality range is for D 1.38, for H 1.76, and for V 1.19. At Pavlovsk the corresponding ratios are much larger, viz. 2.16 for D, 2.43 for H, and 2.05 for V. The declination data for Kew in Table XXII. illustrate other points. The first set of data are derived from all days of the year. The second omit the highly disturbed days. The third answer to the 5 days a month selected as typically quiet. The yearly mean absolute range from ordinary days at Kew in Table XXII. is 1.49 times the mean inequality range in Table VIII.; comparing individual months the ratio of the absolute to the inequality range varies from 2.06 in January to 1.21 in June. Even confining ourselves to the quiet days at Kew, which are free from any but the most trifling disturbances, we find that the mean absolute range for the year is 1.20 times the arithmetic mean of the inequality ranges for the individual months of the year, and 1.22 times the range from the mean diurnal inequality for the year. In this case the ratio of the absolute to the inequality range varies from 1.55 in December to only 1.09 in May.
§ 25. The variability of the absolute daily range of declination is illustrated by Table XXIII., which contains data for Kew[24] derived from all days of the 11-year period 1890-1900. It gives the total number of times during the 11 years when the absolute range lay within the limits specified at the heads of the first nine columns of figures. The two remaining columns give the arithmetic means of the five largest and the five least absolute ranges encountered each month. The mean of the twelve monthly diurnal inequality ranges from ordinary days was only 8´.44, but the absolute range during the 11 years exceeded 20´ on 492 days, 15´ on 1196 days, and 10´ on 2784 days, i.e. on 69 days out of every 100.
Table XXIII.--Absolute Daily Range of Declination at Kew.
+------------------------------------------------------------------------------------------------------------------+---------------------+ | | Means from the 5 | | | largest and 5 least | | Number of occasions during 11 years when absolute range was:-- | ranges of the month | | | on the average of | | | 11 years. | +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+ | |0´ to 5´.|5´ to 10´.|10´ to 15´.|15´ to 20´.|20´ to 25´.|25´ to 30´.|30´ to 35´.|35´ to 40´.|over 40´.| 5 largest.| 5 least.| +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+ | | | | | | | | | | | ´ | ´ | | January | 51 | 145 | 69 | 37 | 24 | 7 | 4 | 3 | 1 | 22.90 | 5.07 | | February | 26 | 99 | 84 | 51 | 226 | 10 | 4 | 2 | 8 | 27.21 | 6.55 | | March | 1 | 72 | 138 | 61 | 232 | 21 | 8 | 1 | 7 | 29.87 | 8.93 | | April | 0 | 43 | 167 | 73 | 227 | 10 | 6 | 3 | 1 | 23.69 | 10.31 | | May | 0 | 57 | 157 | 85 | 220 | 12 | 3 | 0 | 7 | 25.36 | 9.50 | | June | 0 | 56 | 185 | 67 | 215 | 1 | 3 | 1 | 2 | 19.92 | 9.89 | | July | 0 | 59 | 185 | 70 | 214 | 5 | 2 | 2 | 4 | 22.49 | 9.96 | | August | 0 | 37 | 202 | 75 | 222 | 1 | 2 | 0 | 2 | 21.27 | 10.05 | | September | 1 | 68 | 153 | 71 | 219 | 5 | 4 | 5 | 4 | 24.55 | 9.52 | | October | 3 | 103 | 111 | 67 | 234 | 10 | 11 | 2 | 0 | 23.92 | 8.01 | | November | 42 | 140 | 81 | 28 | 214 | 9 | 8 | 5 | 3 | 23.58 | 5.64 | | December | 64 | 166 | 56 | 29 | 214 | 7 | 1 | 1 | 3 | 20.43 | 4.36 | +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+ | Totals | 188 | 1045 | 1588 | 714 | 261 | 98 | 56 | 25 | 42 | | | +-----------+---------+----------+-----------+-----------+-----------+-----------+-----------+-----------+---------+-----------+---------+
Relations to Sun-spot Frequency.
§ 26. Magnetic phenomena, both regular and irregular, at any station vary from year to year. The extent of this variation is illustrated in Tables XXIV. and XXV., both relating to the period 1890 to 1900.[25] Table XXIV. gives the amplitudes of the regular diurnal inequality in the elements stated at the head of the columns. The ordinary day declination data (D0) for Kew represent arithmetic means from the twelve months of the year; the other data all answer to the mean diurnal inequality for the whole year. Table XXV. gives the arithmetic means for each year of the absolute daily range, of the monthly range (or difference between the highest and lowest values in the month), and of the yearly range (or difference between the highest and lowest values of the year). The numerals attached to the years in these tables indicate their order as regards sun-spot frequency according to Wolf and Wolfer (see Aurora Polaris), 1893 being the year of largest frequency, and 1890 that of least. The difference in sun-spot frequency between 1897 and 1898 was microscopic; the differences between 1890, 1900 and 1899 were small, and those between 1893, 1894 and 1892 were not very large.
The years 1892-1895 represent high sun-spot frequency, while 1890, 1899 and 1900 represent low frequency. Table XXIV. shows that 1892 to 1895 were in all cases distinguished by the large size of the inequality ranges, and 1890, 1899 and 1900 by the small size. The range in 1893 is usually the largest, and though the H and V ranges at Ekaterinburg are larger in 1892 than in 1893, the excess is trifling. The phenomena apparent in Table XXIV. are fairly representative; other stations and other periods associate large inequality ranges with high sun-spot frequency. The diurnal inequality range it should be noticed is comparatively little influenced by irregular disturbances. Coming to Table XXV., we have ranges of a different character. The absolute range at Kew on quiet days is almost as little influenced by irregularities as is the range of the diurnal inequality, and in its case the phenomena are very similar to those observed in Table XXIV. As we pass from left to right in Table XXV., the influence of disturbance increases. Simultaneously with this, the parallelism with sun-spot frequency is less close. The entries relating to 1892 and 1894 become more and more prominent compared to those for 1893. The yearly range may depend on but a single magnetic storm, the largest disturbance of the year possibly far outstripping any other. But taking even the monthly ranges the values for 1893 are, speaking roughly, only half those for 1892 and 1894, and very similar to those of 1898, though the sun-spot frequency in the latter year was less than a third of that in 1893. Ekatarinburg data exactly analogous to those for Pavlovsk show a similar prominence in 1892 and 1894 as compared to 1893. The retirement of 1893 from first place, seen in the absolute ranges at Kew, Pavlovsk and Ekatarinburg, is not confined to the northern hemisphere. It is visible, for instance, in the amplitudes of the Batavia disturbance results. Thus though the variation from year to year in the amplitude of the absolute ranges is relatively not less but greater than that of the inequality ranges, and though the general tendency is for all ranges to be larger in years of many than in years of few sun-spots, still the parallelism between the changes in sun-spot frequency and in magnetic range is not so close for the absolute ranges and for disturbances as for the inequality ranges.
TABLE XXIV.--Ranges of Diurnal Inequalities.
+----------+-------------------------+-----------------------------------+---------------------------------+ | | Pavlovsk. | Ekatarinburg. | Kew. | +----------+-------+-------+---------+-------+-------+---------+---------+-------+-------+---------+-------+ | | D. | I. | H. | D. | I. | H. | V. | D_q. | I_q. | H_q. | D_0. | | +-------+-------+---------+-------+-------+---------+---------+-------+-------+---------+-------+ | | ´ | ´ | [gamma] | ´ | ´ | [gamma] | [gamma] | ´ | ´ | [gamma] | ´ | | 1890_11 | 6.32 | 1.33 | 22 | 5.83 | 1.05 | 18 | 9 | 6.90 | | 20 | 7.32 | | 1891_6 | 7.31 | 1.79 | 30 | 6.85 | 1.38 | 25 | 14 | 8.04 | 1.52 | 28 | 8.48 | | 1892_3 | 8.75 | 2.21 | 37 | 7.74 | 1.72 | 32 | 19 | 9.50 | 1.66 | 31 | 9.85 | | 1893_1 | 9.64 | 2.24 | 38 | 8.83 | 1.80 | 31 | 17 | 10.06 | 1.96 | 35 | 10.74 | | 1894_2 | 8.58 | 2.17 | 38 | 7.80 | 1.73 | 30 | 17 | 9.32 | 1.94 | 34 | 9.80 | | 1895_4 | 8.22 | 2.08 | 33 | 7.29 | 1.64 | 28 | 15 | 8.59 | 1.66 | 30 | 9.54 | | 1896_5 | 7.39 | 1.77 | 29 | 6.50 | 1.38 | 25 | 15 | 7.77 | 1.31 | 25 | 8.50 | | 1897_6 | 6.79 | 1.59 | 26 | 6.01 | 1.16 | 21 | 12 | 6.71 | 1.14 | 22 | 7.76 | | 1898_7 | 6.25 | 1.56 | 26 | 5.76 | 1.19 | 21 | 11 | 6.85 | 1.07 | 21 | 7.59 | | 1899_9 | 6.02 | 1.44 | 24 | 5.33 | 1.12 | 20 | 11 | 6.69 | 1.01 | 21 | 7.30 | | 1900_10 | 6.20 | 1.28 | 22 | 5.88 | 0.93 | 17 | 8 | 6.52 | 1.06 | 21 | 6.83 | +----------+-------+-------+---------+-------+-------+---------+---------+-------+-------+---------+-------+
TABLE XXV.--Absolute Ranges.
+---------+-----------------------+-----------------------------------------------------------------------------------+ | | Kew Declination. | Pavlovsk. | | | Daily. +---------------------------+---------------------------+---------------------------+ | | | Daily. | Monthly. | Yearly. | +---------+-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+ | | q. | o. | a. | D. | H. | V. | D. | H. | V. | D. | H. | V. | | +-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+ | | ´ | ´ | ´ | ´ | [gamma] | [gamma] | ´ | [gamma] | [gamma] | ´ | [gamma] | [gamma] | | 1890_11 | 8.3 | 10.5 | 10.7 | 12.1 | 49 | 21 | 28.2 | 118 | 80 | 42.1 | 169 | 179 | | 1891_6 | 10.0 | 12.8 | 13.7 | 16.0 | 70 | 39 | 46.3 | 218 | 233 | 92.3 | 550 | 614 | | 1892_3 | 12.3 | 15.4 | 17.7 | 21.0 | 111 | 73 | 93.6 | 698 | 575 | 194.0 | 2416 | 1385 | | 1893_1 | 11.8 | 15.2 | 15.6 | 17.8 | 79 | 41 | 48.3 | 241 | 210 | 87.1 | 514 | 457 | | 1894_2 | 11.3 | 14.7 | 16.5 | 20.4 | 97 | 62 | 84.1 | 493 | 493 | 145.6 | 1227 | 878 | | 1895_4 | 10.6 | 14.8 | 15.6 | 18.1 | 80 | 46 | 47.4 | 220 | 223 | 73.9 | 395 | 534 | | 1896_5 | 9.5 | 12.9 | 14.5 | 17.5 | 74 | 43 | 52.4 | 232 | 236 | 88.7 | 574 | 608 | | 1897_8 | 8.2 | 11.5 | 12.1 | 14.6 | 61 | 30 | 43.8 | 201 | 170 | 101.1 | 449 | 480 | | 1898_7 | 8.2 | 11.2 | 12.3 | 14.7 | 67 | 35 | 46.6 | 276 | 242 | 118.9 | 1136 | 888 | | 1899_9 | 7.9 | 10.5 | 11.3 | 13.1 | 58 | 27 | 38.3 | 178 | 150 | 63.8 | 382 | 527 | | 1900_10 | 7.4 | 8.9 | 9.2 | 10.5 | 44 | 16 | 32.8 | 134 | 89 | 94.2 | 457 | 365 | +---------+-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+ | Means | 9.6 | 12.6 | 13.6 | 16.0 | 72 | 39 | 51.1 | 274 | 246 | 100.2 | 752 | 629 | +---------+-------+-------+-------+-------+---------+---------+-------+---------+---------+-------+---------+---------+
§ 27. The relationship between magnetic ranges and sun-spot frequency has been investigated in several ways. W. Ellis[26] has employed a graphical method which has advantages, especially for tracing the general features of the resemblance, and is besides independent of any theoretical hypothesis. Taking time for the axis of abscissae, Ellis drew two curves, one having for its ordinates the sun-spot frequency, the other the inequality range of declination or of horizontal force at Greenwich. The value assigned in the magnetic curve to the ordinate for any particular month represents a mean from 12 months of which it forms a central month, the object being to eliminate the regular annual variation in the diurnal inequality. The sun-spot data derived from Wolf and Wolfer were similarly treated. Ellis originally dealt with the period 1841 to 1877, but subsequently with the period 1878 to 1896, and his second paper gives curves representing the phenomena over the whole 56 years. This period covered five complete sun-spot periods, and the approximate synchronism of the maxima and minima, and the general parallelism of the magnetic and sun-spot changes is patent to the eye. Ellis[27] has also applied an analogous method to investigate the relationship between sun-spot frequency and the number of days of magnetic disturbance at Greenwich. A decline in the number of the larger magnetic storms near sun-spot minimum is recognizable, but the application of the method is less successful than in the case of the inequality range. Another method, initiated by Professor Wolf of Zurich, lends itself more readily to the investigation of numerical relationships. He started by supposing an exact proportionality between corresponding changes in sun-spot frequency and magnetic range. This is expressed mathematically by the formula
R = a + bS [equiv] a{1 + (b/a)S},
where R denotes the magnetic range, S the corresponding sun-spot frequency, while a and b are constants. The constant a represents the range for zero sun-spot frequency, while b/a is the proportional increase in the range accompanying unit rise in sun-spot frequency. Assuming the formula to be true, one obtains from the observed values of R and S numerical values for a and b, and can thus investigate whether or not the sun-spot influence is the same for the different magnetic elements and for different places. Of course, the usefulness of Wolf's formula depends largely on the accuracy with which it represents the facts. That it must be at least a rough approximation to the truth in the case of the diurnal inequality at Greenwich might be inferred from Ellis's curves. Several possibilities should be noticed. The formula may apply with high accuracy, a and b having assigned values, for one or two sun-spot cycles, and yet not be applicable to more remote periods. There are only three or four stations which have continuous magnetic records extending even 50 years back, and, owing to temperature correction uncertainties, there is perhaps no single one of these whose earlier records of horizontal and vertical force are above criticism. Declination is less exposed to uncertainty, and there are results of eye observations of declination before the era of photographic curves. A change, however, of 1´ in declination has a significance which alters with the intensity of the horizontal force. During the period 1850-1900 horizontal force in England increased about 5%, so that the force requisite to produce a declination change of 19´ in 1900 would in 1850 have produced a deflection of 20´. It must also be remembered that secular changes of declination must alter the angle between the needle and any disturbing force acting in a fixed direction. Thus secular alteration in a and b is rather to be anticipated, especially in the case of the declination. Wolf's formula has been applied by Rajna[28] to the yearly mean diurnal declination ranges at Milan based on readings taken twice daily from 1836 to 1894, treating the whole period together, and then the period 1871 to 1894 separately. During two sub-periods, 1837-1850 and 1854-1867, Rajna's calculated values for the range differ very persistently in one direction from those observed; Wolf's formula was applied by C. Chree[25] to these two periods separately. He also applied it to Greenwich inequality ranges for the years 1841 to 1896 as published by Ellis, treating the whole period and the last 32 years of it separately, and finally to all (a) and quiet (q) day Greenwich ranges from 1889 to 1896. The results of these applications of Wolf's formula appear in Table XXVI.
The Milan results are suggestive rather of heterogeneity in the material than of any decided secular change in a or b. The Greenwich data are suggestive of a gradual fall in a, and rise in b, at least in the case of the declination.
Table XXVII. gives values of a, b and b/a in Wolf's formula calculated by Chree[25] for a number of stations. There are two sets of data, the first set relating to the range from the mean diurnal inequality for the year, the second to the arithmetic mean of the ranges in the mean diurnal inequalities for the twelve months. It is specified whether the results were derived from all or from quiet days.
TABLE XXVI.--Values of a and b in Wolf's Formula.
+--------------------------+------------------------------------------------+ | Milan. | Greenwich. | |---------+----------------+------------+----------------+------------------+ | | Declination | | Declination | Horizontal Force | | | (unit 1´). | | (unit 1´). | (unit 1[gamma]). | | Epoch. |--------+-------+ Epoch. +--------+-------+---------+--------+ | | a. | b. | | a. | b. | a. | b. | +---------+--------+-------+------------+--------+-------+---------+--------+ | 1836-94 | 5.31 | .047 | 1841-96 | 7.29 | .0377 | 26.4 | .190 | | 1871-94 | 5.39 | .047 | 1865-96 | 7.07 | .0396 | 23.6 | .215 | | 1837-50 | 6.43 | .041 | 1889-96(a) | 6.71 | .0418 | 23.7 | .218 | | 1854-67 | 4.62 | .047 | 1889-96(q) | 6.36 | .0415 | 25.0 | .213 | +---------+--------+-------+------------+--------+-------+---------+--------+
As explained above, a would represent the range in a year of no sun-spots, while 100 b would represent the excess over this shown by the range in a year when Wolf's sun-spot frequency is 100. Thus b/a seems the most natural measure of sun-spot influence. Accepting it, we see that sun-spot influence appears larger at most places for inclination and horizontal force than for declination. In the case of vertical force there is at Pavlovsk, and probably in a less measure at other northern stations, a large difference between all and quiet days, which is not shown in the other elements. The difference between the values of b/a at different stations is also exceptionally large for vertical force. Whether this last result is wholly free from observational uncertainties is, however, open to some doubt, as the agreement between Wolf's formula and observation is in general somewhat inferior for vertical force. In the case of the declination, the mean numerical difference between the observed values and those derived from Wolf's formula, employing the values of a and b given in Table XXVII., represented on the average about 4% of the mean value of the element for the period considered, the probable error representing about 6% of the difference between the highest and lowest values observed. The agreement was nearly, if not quite, as good as this for inclination and horizontal force, but for vertical force the corresponding percentages were nearly twice as large.
TABLE XXVII.--Values of a and b in Wolf's Formula.
+---------------------------------+----------------------+----------------------+----------------------+----------------------+ | | Declination | Inclination | Horizontal Force | Vertical Force | | | (unit 1´). | (unit 1´). | (unit 1[gamma]). | (unit 1[gamma]). | +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+ | Diurnal Inequality for the Year.| a. | b. |100 b/a.| a. | b. |100 b/a.| a. | b. |100 b/a.| a. | b. |100 b/a.| +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+ | Pavlovsk, 1890-1900 all | 5.74 |.0400 | .70 | 1.24 |.0126 | 1.01 | 20.7 | .211 | 1.02 | 8.1 | .265 | 3.26 | | Pavlovsk, 1890-1900 quiet | 6.17 |.0424 | .69 | .. | .. | .. | 20.6 | .195 | 0.95 | 5.9 | .027 | 0.46 | | Ekatarinburg, 1890-1900 all | 5.29 |.0342 | .65 | 0.93 |.0105 | 1.13 | 16.8 | .182 | 1.09 | 8.6 | .117 | 1.37 | | Irkutsk " " all | 4.82 |.0358 | .74 | 0.97 |.0087 | 0.90 | 18.2 | .190 | 1.04 | 6.5 | .071 | 1.09 | | Kew " " quiet | 6.10 |.0433 | .71 | 0.87 |.0125 | 1.45 | 18.1 | .194 | 1.07 | 14.3 | .081 | 0.56 | | Falmouth, 1891-1902 quiet | 5.90 |.0451 | .76 | .. | .. | .. | 20.1 | .233 | 1.16 | .. | .. | .. | | Kolaba, 1894-1901 quiet | 2.37 |.0066 | .28 | .. | .. | .. | 31.6 | .281 | 0.89 | 19.4 | .072 | 0.37 | | Batavia, 1887-1898 all | 2.47 |.0179 | .72 | 3.60 |.0218 | 0.61 | 38.7 | .274 | 0.71 | 30.1 | .156 | 0.52 | | Mauritius / 1875-1880 \ all | 4.06 |.0164 | .40 | .. | .. | .. | 15.0 | .096 | 0.64 | 11.9 | .069 | 0.58 | | \ 1883-1890 / | | | | | | | | | | | | | +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+ | _Mean from individual months:--_| | | | | | | | | | | | | | Pavlovsk, 1890-1900 all | 6.81 |.0446 | .66 | 1.44 |.0151 | 1.05 | 22.8 | .243 | 1.07 | 9.7 | .287 | 2.97 | | " " " quiet | 6.52 |.0442 | .68 | .. | .. | .. | 22.2 | .208 | 0.94 | 7.0 | .044 | 0.63 | | Ekatarinburg, 1890-1900 all | 6.18 |.0355 | .58 | 1.12 |.0120 | 1.06 | 19.2 | .195 | 1.01 | 9.2 | .156 | 1.70 | | Greenwich, 1865-1896 all | 7.07 |.0396 | .56 | .. | .. | .. | 23.6 | .215 | 0.91 | .. | .. | .. | | Kew, 1890-1900 all | 6.65 |.0428 | .64 | .. | .. | .. | .. | .. | .. | .. | .. | .. | | " " " quiet | 6.49 |.0410 | .63 | 1.17 |.0130 | 1.11 | 21.5 | .191 | 0.89 | 16.0 | .072 | 0.45 | | Falmouth, 1891-1902 quiet | 6.16 |.0450 | .73 | .. | .. | .. | 20.9 | .236 | 1.13 | .. | .. | .. | +---------------------------------+------+------+--------+------+------+--------+------+------+--------+------+------+--------+
Applying Wolf's formula to the diurnal ranges for different months of the year, Chree found, as was to be anticipated, that the constant a had an annual period, with a conspicuous minimum at midwinter; but whilst b also varied, it did so to a much less extent, the consequence being that b/a showed a minimum at midsummer. The annual variation in b/a alters with the place, with the element, and with the type of day from which the magnetic data are derived. Thus, in the case of Pavlovsk declination, whilst the mean value of 100 b/a for the 12 months is, as shown in Table XXVII., 0.66 for all and 0.68 for quiet days--values practically identical--if we take the four midwinter and the four midsummer months separately, we have 100 b/a, varying from 0.81 in winter to 0.52 in summer on all days, but from 1.39 in winter to 0.52 in summer on quiet days. In the case of horizontal force at Pavlovsk the corresponding figures to these are for all days--winter 1.77, summer 0.98, but for quiet days--winter 1.83, summer 0.71.
Wolf's formula has also been applied to the absolute daily ranges, to monthly ranges, and to various measures of disturbance. In these cases the values found for b/a are usually larger than those found for diurnal inequality ranges, but the accordance between observed values and those calculated from Wolf's formula is less good. If instead of the range of the diurnal inequality we take the sum of the 24-hourly differences from the mean for the day--or, what comes to the same thing, the average departure throughout the 24 hours from the mean value for the day--we find that the resulting Wolf's formula gives at least as good an agreement with observation as in the case of the inequality range itself. The formulae obtained in the case of the 24 differences, at places as wide apart as Kew and Batavia, agreed in giving a decidedly larger value for b/a than that obtained from the ranges. This indicates that the inequality curve is relatively less peaked in years of many than in years of few sun-spots.
§ 28. The applications of Ellis's and Wolf's methods relate directly only to the amplitude of the diurnal changes. There is, however, a change not merely in amplitude but in type. This is clearly seen when we compare the values found in years of many and of few sun-spots for the Fourier coefficients in the diurnal inequality. Such a comparison is carried out in Table XXVIII. for the declination on ordinary days at Kew. Local mean time is used. The heading S max. (sun-spot maximum) denotes mean average results from the four years 1892-1895, having a mean sun-spot frequency of 75.0, whilst S min. (sun-spot minimum) applies similarly to the years 1890, 1899 and 1900, having a mean sun-spot frequency of only 9.6. The data relate to the mean diurnal inequality for the whole year or for the season stated. It will be seen that the difference between the c, or amplitude, coefficients in the S max. and S min. years is greater for the 24-hour term than for the 12-hour term, greater for the 12-hour than for the 8-hour term, and hardly apparent in the 6-hour term. Also, _relatively considered_, the difference between the amplitudes in S max. and S min. years is greatest in winter and least in summer. Except in the case of the 6-hour term, where the differences are uncertain, the phase angle is larger, i.e. maxima and minima occur earlier in the day, in years of S min. than in years of S max. Taking the results for the whole year in Table XXVIII., this advance of phase in the S min. years represents in time 15.6 minutes for the 24-hour term, 9.4 minutes for the 12-hour term, and 14.7 minutes for the 8-hour term. The difference in the phase angles, as in the amplitudes, is greatest in winter. Similar phenomena are shown by the horizontal force, and at Falmouth[24] as well as Kew.
TABLE XXVIII.--Fourier Coefficients in Years of many and few Sun-spots.
+---------+-------------+-------------+-------------+-------------+ | | Year. | Winter. | Equinox. | Summer. | | +------+------+------+------+------+------+------+------+ | |S max.|S min.|S max.|S min.|S max.|S min.|S max.|S min.| +---------+------+------+------+------+------+------+------+------+ | | ´ | ´ | ´ | ´ | ´ | ´ | ´ | ´ | | c1 | 3.47 | 2.21 | 2.41 | 1.43 | 3.76 | 2.41 | 4.38 | 2.98 | | c2 | 2.04 | 1.51 | 1.15 | 0.78 | 2.33 | 1.71 | 2.73 | 2.06 | | c3 | 0.89 | 0.72 | 0.55 | 0.42 | 1.16 | 0.97 | 0.97 | 0.77 | | c4 | 0.28 | 0.27 | 0.30 | 0.27 | 0.42 | 0.42 | 0.11 | 0.11 | +---------+------+------+------+------+------+------+------+------+ | | ° | ° | ° | ° | ° | ° | ° | ° | |[alpha]1 | 228.5| 232.4| 243.0| 256.0| 231.3| 233.7| 218.2| 220.3| |[alpha]2 | 41.7| 46.6| 23.5| 36.9| 40.6| 43.9| 50.6| 52.5| |[alpha]3 | 232.6| 243.6| 234.0| 257.6| 228.4| 236.2| 236.8| 245.4| |[alpha]4 | 58.0| 57.3| 52.3| 60.8| 62.0| 58.2| 57.4| 45.2| +---------+------+------+------+------+------+------+------+------+
Quiet Day Phenomena.
§ 29. There have already been references to _quiet_ days, for instance in the tables of diurnal inequalities. It seems to have been originally supposed that quiet days differed from other days only in the absence of irregular disturbances, and that mean annual values, or secular change data, or diurnal inequalities, derived from them might be regarded as truly normal or representative of the station. It was found, however, by P. A. Müller[29] that mean annual values of the magnetic elements at St Petersburg and Pavlovsk from 1873 to 1885 derived from quiet days alone differed in a systematic fashion from those derived from all days, and analogous results were obtained by Ellis[30] at Greenwich for the period 1889-1896. The average excesses for the quiet-day over the all-day means in these two cases were as follows:--
+---------------+--------------+--------------+------------+-------------+ | | Westerly | Inclination. | Horizontal | Vertical | | | Declination. | | Force. | Force. | +---------------+--------------+--------------+------------+-------------+ | St Petersburg | +0.24 | -0.23 | +3.2[gamma]| -0.8[gamma] | | Greenwich | +0.08 | | +3.2[gamma]| -0.9[gamma] | +---------------+--------------+--------------+------------+-------------+
The sign of the difference in the case of D, I and H was the same in each year examined by Müller, and the same was true of H at Greenwich. In the case of V, and of D at Greenwich, the differences are small and might be accidental. In the case of D at Greenwich 1891 differed from the other years, and of two more recent years examined by Ellis[31] one, 1904, agreed with 1891. At Kew, on the average of the 11 years 1890 to 1900, the quiet-day mean annual value of declination exceeded the ordinary day value, but the apparent excess 0´.02 is too small to possess much significance.
Non-cyclic Change.
Another property more recently discovered in quiet days is the non-cyclic change. The nature of this phenomenon will be readily understood from the following data from the 11-year period 1890 to 1900 at Kew[32]. The mean daily change for all days is calculated from the observed annual change.
+------------------------------+--------+--------+--------------+--------------+ | | D. | I. | H. | V. | +------------------------------+--------+--------+--------------+--------------+ | | ´ | ´ | | | | Mean annual change | -5.79 | -2.38 | +25.9[gamma] | -22.6[gamma] | | Mean daily change, all days | -0.016 | -0.007 | +0.07[gamma] | -0.06[gamma] | | Mean daily change, quiet days| +0.044 | -0.245 | +3.34[gamma] | -0.84[gamma] | +------------------------------+------------------+-------------+--------------+
Thus the changes during the representative quiet day differed from those of the average day. Before accepting such a phenomenon as natural, instrumental peculiarities must be carefully considered. The secular change is really based on the absolute instruments, the diurnal changes on the magnetographs, and the first idea likely to occur to a critical mind is that the apparent abnormal change on quiet days represents in reality change of zero in the magnetographs. If, however, the phenomenon were instrumental, it should appear equally on days other than quiet days, and we should thus have a shift of zero amounting in a year to over 1,200[gamma] in H, and to about 90´ in I. Under such circumstances the curve would be continually drifting off the sheet. In the case of the Kew magnetographs, a careful investigation showed that if any instrumental change occurred in the declination magnetograph during the 11 years it did not exceed a few tenths of a minute. In the case of the H and V magnetographs at Kew there is a slight drift, of instrumental origin, due to weakening of the magnets, but it is exceedingly small, and in the case of H is in the opposite direction to the non-cyclic change on quiet days. It only remains to add that the hypothesis of instrumental origin was positively disproved by measurement of the curves on ordinary days.
It must not be supposed that every quiet day agrees with the average quiet day in the order of magnitude, or even in the sign, of the non-cyclic change. In fact, in not a few months the sign of the non-cyclic change on the mean of the quiet days differs from that obtained for the average quiet day of a period of years. At Kew, between 1890 and 1900, the number of months during which the mean non-cyclic change for the five quiet days selected by the astronomer royal (Sir W. H. M. Christie) was plus, zero, or minus, was as follows:--
+-----------+------+------+------+------+ | Element. | D. | I. | H. | V. | +-----------+------+------+------+------+ | Number + | 63 | 13 | 112 | 47 | | " 0 | 14 | 16 | 11 | 9 | | " - | 55 | 101 | 9 | 74 | +-----------+------+------+------+------+
The + sign denotes westerly movement in the declination, and increasing dip of the north end of the needle. In the case of I and H the excess in the number of months showing the normal sign is overwhelming. The following mean non-cyclic changes on quiet days are from other sources:--
+-----------+--------------+-------------+--------------+ | | Greenwich | Falmouth | Kolaba | | Element. | (1890-1895). | (1898-1902).| (1894-1901). | +-----------+--------------+-------------+--------------+ | | ´ | ´ | ´ | | D | + 0.03 | + 0.05 | + 0.07 | | H | + 4.3[gamma] | + 3.0[gamma]| + 3.9[gamma] | +-----------+--------------+-------------+--------------+
The results are in the same direction as at Kew, + meaning in the case of D movement to the west. At Falmouth[32], as at Kew, the non-cyclic change showed a tendency to be small in years of few sun-spots.
§ 30. In calculating diurnal inequalities from quiet days the non-cyclic effect must be eliminated, otherwise the result would depend on the hour at which the "day" is supposed to commence. If the value recorded at the second midnight of the average day exceeds that at the first midnight by N, the elimination is effected by applying to each hourly value the correction N(12 - n)/24, where n is the hour counted from the first midnight (0 hours). This assumes the change to progress uniformly throughout the 24 hours. Unless this is practically the case--a matter difficult either to prove or disprove--the correction may not secure exactly what is aimed at. This method has been employed in the previous tables. The fact that differences do exist between diurnal inequalities derived from quiet days and all ordinary days was stated explicitly in § 4, and is obvious in Tables VIII. to XI. An extreme case is represented by the data for Jan Mayen in these tables. Figs. 9 and 10 are vector diagrams for this station, for all and for quiet days during May, June and July 1883, according to data got out by Lüdeling. As shown by the arrows, fig. 10 (quiet days) is in the main described in the normal or clockwise direction, but fig. 9 (all days) is described in the opposite direction. Lüdeling found this peculiar difference between all and quiet days at all the north polar stations occupied in 1882-1883 except Kingua Fjord, where both diagrams were described clockwise.
In temperate latitudes the differences of type are much less, but still they exist. A good idea of their ordinary size and character in the case of declination may be derived from Table XXIX., containing data for Kew, Greenwich and Parc St Maur.
The data for Greenwich are due to W. Ellis[30], those for Parc St Maur to T. Moureaux[33]. The quantity tabulated is the algebraic excess of the all or ordinary day mean hourly value over the corresponding quiet day value in the mean diurnal inequality for the year. At Greenwich and Kew days of extreme disturbance have been excluded from the ordinary days, but apparently not at Parc St Maur. The number of highly disturbed days at the three stations is, however, small, and their influence is not great. The differences disclosed by Table XXIX. are obviously of a systematic character, which would not tend to disappear however long a period was utilized. In short, while the diurnal inequality from quiet days may be that most truly representative of undisturbed conditions, it does not represent the average state of conditions at the station. To go into full details respecting the differences between all and quiet days would occupy undue space, so the following brief summary of the differences observed in declination at Kew must suffice. While the inequality range is but little different for the two types of days, the mean of the hourly differences from the mean for the day is considerably reduced in the quiet days. The 24-hour term in the Fourier analysis is of smaller amplitude in the quiet days, and its phase angle is on the average about 6°.75 smaller than on ordinary days, implying a retardation of about 27 minutes in the time of maximum. The diurnal inequality range is more variable throughout the year in quiet days than on ordinary days, and the same is true of the absolute ranges. The tendency to a secondary minimum in the range at midsummer is considerably more decided on ordinary than on quiet days. When the variation throughout the year in the diurnal inequality range is expressed in Fourier series, whose periods are the year and its submultiples, the 6-month term is notably larger for ordinary than for quiet days. Also the date of the maximum in the 12-month term is about three days earlier for ordinary than for quiet days. The exact size of the differences between ordinary and quiet day phenomena must depend to some extent on the criteria employed in selecting quiet days and in excluding disturbed days. This raises difficulties when it comes to comparing results at different stations. For stations near together the difficulty is trifling. The astronomer royal's quiet days have been used for instance at Parc St. Maur, Val Joyeux, Falmouth and Kew, as well as at Greenwich. But when stations are wide apart there are two obvious difficulties: first, the difference of local time; secondly, the fact that a day may be typically quiet at one station but appreciably disturbed at the other.
If the typical quiet day were simply the antithesis of a disturbed day, it would be natural to regard the non-cyclic change on quiet days as a species of recoil from some effect of disturbance. This view derives support from the fact, pointed out long ago by Sabine[34], that the horizontal force usually, though by no means always, is lowered by magnetic disturbances. Dr van Bemmelen[35] who has examined non-cyclic phenomena at a number of stations, seems disposed to regard this as a sufficient explanation. There are, however, difficulties in accepting this view. Thus, whilst the non-cyclic effect in horizontal force and inclination at Kew and Falmouth appeared on the whole enhanced in years of sun-spot maximum, the difference between years such as 1892 and 1894 on the one hand, and 1890 and 1900 on the other, was by no means proportional to the excess of disturbance in the former years. Again, when the average non-cyclic change of declination was calculated at Kew for 207 days, selected as those of most marked irregular disturbance between 1890 and 1900, the sign actually proved to be the same as for the average quiet day of the period.
TABLE XXIX.--All or Ordinary, less Quiet Day Hourly Values (+ to the West).
+-----+--------------------------------------+-------------------------------------+ | | Forenoon. | Afternoon. | |Hour.+------------+-----------+-------------+-----------+-----------+-------------+ | | Kew | Greenwich |Parc St Maur | Kew | Greenwich |Parc St Maur | | | 1890-1900. | 1890-1894.| 1883-1897. | 1890-1900.| 1890-1894.| 1893-1897. | +-----+------------+-----------+-------------+-----------+-----------+-------------+ | | ´ | ´ | ´ | ´ | ´ | ´ | | 1 | -0.58 | -0.59 | -0.63 | +0.42 | +0.44 | +0.40 | | 2 | -0.54 | -0.47 | -0.47 | +0.52 | +0.45 | +0.50 | | 3 | -0.51 | -0.31 | -0.32 | +0.57 | +0.52 | +0.59 | | 4 | -0.41 | -0.23 | -0.16 | +0.60 | +0.51 | +0.55 | | 5 | -0.28 | -0.10 | -0.01 | +0.46 | +0.34 | +0.38 | | 6 | -0.08 | +0.12 | +0.18 | +0.21 | +0.04 | +0.07 | | 7 | +0.13 | +0.30 | +0.34 | -0.06 | -0.24 | -0.25 | | 8 | +0.29 | +0.48 | +0.47 | -0.27 | -0.50 | -0.54 | | 9 | +0.40 | +0.56 | +0.53 | -0.47 | -0.68 | -0.74 | | 10 | +0.44 | +0.58 | +0.51 | -0.61 | -0.78 | -0.79 | | 11 | +0.48 | +0.50 | +0.44 | -0.62 | -0.77 | -0.79 | | 12 | +0.45 | +0.44 | +0.38 | -0.54 | -0.61 | -0.67 | +-----+------------+-----------+-------------+-----------+-----------+-------------+
Magnetic Disturbances.
§ 31. A satisfactory definition of magnetic disturbance is about as difficult to lay down as one of heterodoxy. The idea in its generality seems to present no difficulty, but it is a very different matter when one comes to details. Amongst the chief disturbances recorded since 1890 are those of February 13-14 and August 12, 1892; July 20 and August 20, 1894; March 15-16, and September 9, 1898; October 31, 1903; February 9-10, 1907; September 11-12, 1908 and September 25, 1909. On such days as these the oscillations shown by the magnetic curves are large and rapid, aurora is nearly always visible in temperate latitudes, earth currents are prominent, and there is interruption--sometimes very serious--in the transmission of telegraph messages both in overhead and underground wires. At the other end of the scale are days on which the magnetic curves show practically no movement beyond the slow regular progression of the regular diurnal inequality. But between these two extremes there are an infinite variety of intermediate cases. The first serious attempt at a precise definition of disturbance seems due to General Sabine[35a]. His method had once an extensive vogue, and still continues to be applied at some important observatories. Sabine regarded a particular observation as disturbed when it differed from the mean of the observations at that hour for the whole month by not less than a certain limiting value. His definition takes account only of the extent of the departure from the mean, whether the curve is smooth at the time or violently oscillating makes no difference. In dealing with a particular station Sabine laid down separate limiting values for each element. These limits were the same, irrespective of the season of the year or of the sun-spot frequency. A departure, for example, of 3´.3 at Kew from the mean value of declination for the hour constituted a disturbance, whether it occurred in December in a year of sun-spot minimum, or in June in a year of sun-spot maximum, though the regular diurnal inequality range might be four times as large in the second case as in the first. The limiting values varied from station to station, the size depending apparently on several considerations not very clearly defined. Sabine subdivided the disturbances in each element into two classes: the one tending to increase the element, the other tending to diminish it. He investigated how the numbers of the two classes varied throughout the day and from month to month. He also took account of the aggregate value of the disturbances of one sign, and traced the diurnal and annual variations in these aggregate values. He thus got two sets of diurnal variations and two sets of annual variations of disturbance, the one set depending only on the number of the disturbed hours, the other set considering only the aggregate value of the disturbances. Generally the two species of disturbance variations were on the whole fairly similar. The aggregates of the + and - disturbances for a particular hour of the day were seldom equal, and thus after the removal of the disturbed values the mean value of the element for that hour was generally altered. Sabine's complete scheme supposed that after the criterion was first applied, the hourly means would be recalculated from the undisturbed values and the criterion applied again, and that this process would be repeated until the disturbed observations all differed by not less than the accepted limiting value from the final mean based on undisturbed values alone. If the disturbance limit were so small that the disturbed readings formed a considerable fraction of the whole number, the complete execution of Sabine's scheme would be exceedingly laborious. As a matter of fact, his disturbed readings were usually of the order of 5% of the total number, and unless in the case of exceptionally large magnetic storms it is of little consequence whether the first choice of disturbed readings is accepted as final or is reconsidered in the light of the recalculated hourly means.
Sabine applied his method to the data obtained during the decade 1840 to 1850 at Toronto, St Helena, Cape of Good Hope and Hobart, also to data for Pekin, Nertchinsk, Point Barrow, Port Kennedy and Kew. C. Chambers[36] applied it to data from Bombay. The yearly publication of the Batavia observatory gives corresponding results for that station, and Th. Moureaux [33] has published similar data for Parc St Maur. Tables XXX. to XXXII. are based on a selection of these data. Tables XXX. and XXXI. show the annual variation in Sabine's disturbances, the monthly values being expressed as percentages of the arithmetic mean value for the 12 months. The Parc St Maur and Batavia data, owing to the long periods included, are especially noteworthy. Table XXX. deals with the east (E) and west (W) disturbances of declination separately. Table XXXI., dealing with disturbances in horizontal and vertical force, combines the + and - disturbances, treated numerically. At Parc St Maur the limits required to qualify for disturbance were 3´.0 in D, 20[gamma] in H, and 12[gamma] in V; the corresponding limits for Batavia were 1´.3, 11[gamma] and 11[gamma]. The limits for D at Toronto, Bombay and Hobart were respectively 3´.6, 1´.4 and 2´.4.
At Parc St Maur the disturbance data from all three elements give distinct maxima near the equinoxes; a minimum at midwinter is clearly shown, and also one at midsummer, at least in D and H. A decline in disturbance at midwinter is visible at all the stations, but at Batavia the equinoctial values for D and V are inferior to those at midsummer.
TABLE XXX.--Annual Variation of Disturbances (Sabine's numbers).
+-----------+-------------+-------------+-------------+-------------+-------------+ | | Parc St Maur| Toronto | Bombay | Batavia | Hobart | | | 1883-97. | 1841-48. | 1859-65. | 1883-99. | 1843-48. | +-----------+------+------+------+------+------+------+------+------+------+------+ | Month. | E. | W. | E. | W. | E. | W. | E. | W. | E. | W. | +-----------+------+------+------+------+------+------+------+------+------+------+ | January | 78 | 60 | 55 | 66 | 89 | 89 | 180 | 223 | 165 | 182 | | February | 116 | 92 | 75 | 86 | 94 | 67 | 138 | 144 | 121 | 116 | | March | 126 | 107 | 92 | 94 | 129 | 97 | 102 | 87 | 114 | 104 | | April | 105 | 113 | 115 | 114 | 106 | 129 | 67 | 73 | 110 | 102 | | May | 101 | 118 | 101 | 101 | 63 | 99 | 72 | 71 | 62 | 53 | | June | 77 | 89 | 95 | 72 | 78 | 81 | 45 | 27 | 32 | 37 | | July | 82 | 104 | 140 | 126 | 121 | 173 | 62 | 46 | 50 | 49 | | August | 88 | 113 | 137 | 133 | 154 | 131 | 69 | 69 | 86 | 78 | | September | 134 | 137 | 163 | 139 | 111 | 108 | 135 | 144 | 135 | 114 | | October | 119 | 115 | 101 | 111 | 140 | 128 | 95 | 88 | 124 | 123 | | November | 99 | 94 | 73 | 85 | 43 | 43 | 106 | 91 | 79 | 111 | | December | 75 | 58 | 51 | 72 | 72 | 55 | 124 | 137 | 123 | 130 | +-----------+------+------+------+------+------+------+------+------+------+------+
Table XXXII. shows in some cases a most conspicuous diurnal variation in Sabine's disturbances. The data are percentages of the totals for the whole 24 hours. But whilst at Batavia the easterly and westerly disturbances in D vary similarly, at Parc St Maur they follow opposite laws, the easterly showing a prominent maximum near noon, the westerly a still more prominent maximum near midnight. The figures in the second last line of the table, if divided by 0.24, will give the percentage of hours which show the species of disturbance indicated. For instance, at Parc St Maur, out of 100 hours, 3 show disturbances to the west and 3.7 to the east; or in all 6.7 show disturbances of declination. The last line gives the average size of a disturbance of each type, the unit being 1´ in D and 1[gamma] in H and V.
TABLE XXXI.--Annual Variation of Disturbances.
+-----------+-------------+-------------+---------------------------+ | |Parc St Maur.| Toronto. | Batavia. | +-----------+-------------+-------------+-------------+-------------+ | Month. | Numbers. | Aggregates. | Numbers. | Aggregates. | +-----------+------+------+------+------+------+------+------+------+ | | H. | V. | H. | V. | H. | V. | H. | V. | | +------+------+------+------+------+------+------+------+ | January | 81 | 51 | 58 | 56 | 96 | 151 | 89 | 154 | | February | 96 | 133 | 94 | 74 | 105 | 123 | 110 | 125 | | March | 126 | 118 | 94 | 108 | 116 | 105 | 117 | 103 | | April | 94 | 111 | 150 | 149 | 104 | 76 | 105 | 73 | | May | 108 | 133 | 90 | 112 | 101 | 92 | 105 | 95 | | June | 90 | 85 | 36 | 50 | 82 | 69 | 79 | 66 | | July | 99 | 128 | 61 | 71 | 90 | 83 | 95 | 81 | | August | 113 | 92 | 75 | 108 | 91 | 91 | 98 | 91 | | September | 119 | 122 | 171 | 160 | 113 | 111 | 114 | 115 | | October | 101 | 94 | 148 | 129 | 114 | 89 | 104 | 86 | | November | 104 | 81 | 98 | 75 | 99 | 102 | 100 | 101 | | December | 70 | 51 | 128 | 100 | 89 | 108 | 84 | 110 | +-----------+------+------+------+------+------+------+------+------+
At Batavia disturbances increasing and decreasing the element are about equally numerous, but this is exceptional. Easterly disturbances of declination predominated at Toronto, Point Barrow, Fort Kennedy, Kew, Parc St Maur, Bombay and the Falkland Islands whilst the reverse was true of St Helena, Cape of Good Hope, Pekin and Hobart. At Kew and Parc St Maur the ratios borne by the eastern to the western disturbances were 1.19 and 1.23 respectively, and so not much in excess of unity; but the preponderance of easterly disturbances at the North American[37] stations was considerably larger than this.
TABLE XXXII.--Diurnal Variation of Disturbances (Sabine's numbers).
+-------------+-----------------------------------------+-----------------------------------------+ | | Parc St Maur. | Batavia. | | +-------------+-------------+-------------+-------------+-------------+-------------+ | Hour. | D. | H. | V. | D. | H. | V. | | +------+------+------+------+------+------+------+------+------+------+------+------+ | | E. | W. | + | - | + | - | E. | W. | + | - | + | - | +-------------+------+------+------+------+------+------+------+------+------+------+------+------+ | 0-3 | 10.1 | 20.3 | 9.0 | 8.3 | 5.7 | |9.2 | 1.1 | 5.8 | 13.1 | 6.6 | 4.0 | 7.4 | | 3-6 | 12.3 | 8.2 | 8.4 | 8.0 | 6.4 | 10.4 | 7.6 | 7.3 | 14.2 | 4.8 | 6.3 | 10.0 | | 6-9 | 15.7 | 3.8 | 14.1 | 12.5 | 7.2 | 9.0 | 24.9 | 16.8 | 12.1 | 9.9 | 21.2 | 21.7 | | 9-noon | 16.2 | 5.1 | 18.0 | 15.6 | 12.9 | 15.4 | 38.5 | 33.0 | 8.6 | 15.8 | 19.8 | 16.4 | | noon-3 | 19.3 | 6.7 | 15.3 | 16.5 | 18.2 | 18.3 | 18.8 | 24.7 | 16.8 | 21.1 | 23.5 | 22.1 | | 3-6 | 14.8 | 9.7 | 12.5 | 15.4 | 22.9 | 21.8 | 6.4 | 5.4 | 13.3 | 16.9 | 12.6 | 12.7 | | 6-9 | 5.7 | 21.2 | 11.4 | 13.2 | 18.9 | 11.2 | 2.3 | 3.4 | 9.9 | 13.6 | 7.1 | 4.1 | | 9-12 | 5.9 | 25.0 | 11.2 | 10.5 | 7.8 | 4.7 | 0.4 | 3.8 | 12.0 | 11.1 | 5.6 | 5.4 | +-------------+------+------+------+------+------+------+------+------+------+------+------+------+ | Mean number | | | | | | | | | | | | | | per day | 0.88| 0.72| 1.15| 1.56| 1.04| 0.96| 0.46| 0.44| 1.62| 1.61| 1.19| 1.13| | Mean size | .. | .. | .. | .. | .. | .. | 1.72| 1.69| 18.0| 19.5 | 16.7 | 15.5 | +-------------+------+------+------+------+------+------+------+------+------+------+------+------+
§ 32. From the point of view of the surveyor there is a good deal to be said for Sabine's definition of disturbance, but it is less satisfactory from other standpoints. One objection has been already indicated, viz. the arbitrariness of applying the same limiting value at a station irrespective of the size of the normal diurnal range at the time. Similarly it is arbitrary to apply the same limit between 10 a.m. and noon, when the regular diurnal variation is most rapid, as between 10 p.m. and midnight, when it is hardly appreciable. There seems a distinct difference of phase between the diurnal inequalities on different types of days at the same season; also the phase angles in the Fourier terms vary continuously throughout the year, and much more rapidly at some stations and at some seasons than at others. Thus there may be a variety of phenomena which one would hesitate to regard as disturbances which contribute to the annual and diurnal variations in Tables XXX. to XXXII.
Sabine, as we have seen, confined his attention to the departure of the hourly reading from the mean for that hour. Another and equally natural criterion is the apparent character of the magnetograph curve. At Potsdam curves are regarded as "1" quiet, "2" moderately disturbed, or "3" highly disturbed. Any hourly value to which the numeral 3 is attached is treated as disturbed, and the annual Potsdam publication contains tables giving the annual and diurnal variations in the number of such disturbed hours for D, H and V. According to this point of view, the extent to which the hourly value departs from the mean for that hour is immaterial to the results. It is the greater or less sinuosity and irregularity of the curve that counts. Tables XXXIII. and XXXIV. give an abstract of the mean Potsdam results from 1892 to 1901. The data are percentages: in Table XXXIII. of the mean monthly total, in Table XXXIV. of the total for the day. So far as the annual variation is concerned, the results in Table XXXIII. are fairly similar to those in Table XXX. for Parc St Maur. There are pronounced maxima near the equinoxes, especially the spring equinox. The diurnal variations, however, in Tables XXXII. and XXXIV. are dissimilar. Thus in the case of H the largest disturbance numbers at Parc St Maur occurred between 6 a.m. and 6 p.m., whereas in Table XXXIV. they occur between 4 p.m. and midnight. Considering the comparative proximity of Parc St Maur and Potsdam, one must conclude that the apparent differences between the results for these two stations are due almost entirely to the difference in the definition of disturbance.
TABLE XXXIII.--Annual Variation of Potsdam Disturbances.
+---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+ | Element.| Jan.| Feb.| Mar.| April.| May.| June.| July.| Aug.| Sept.| Oct.| Nov.| Dec.| +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+ | D | 129 | 170 | 149 | 90 | 86 | 57 | 62 | 64 | 59 | 118 | 94 | 82 | | H | 109 | 133 | 131 | 102 | 109 | 82 | 94 | 91 | 89 | 101 | 75 | 84 | | V | 106 | 171 | 170 | 108 | 121 | 56 | 64 | 74 | 93 | 87 | 78 | 70 | +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+ | Mean | 115 | 158 | 150 | 100 | 105 | 65 | 73 | 76 | 94 | 102 | 82 | 79 | +---------+-----+-----+-----+-------+-----+------+------+-----+------+-----+------+-----+
TABLE XXXIV.--Diurnal Variation of Potsdam Disturbances.
+--------+------+------+-----+---------+------+------+------+-------+ | Hours. | 1-3. | 4-6. | 7-9.| 10-noon.| 1-3. | 4-6. | 7-9. | 10-12.| +--------+------+------+-----+---------+------+------+------+-------+ | D | 14.9 | 11.1 | 8.0 | 5.2 | 5.7 | 13.1 | 22.5 | 19.5 | | H | 10.5 | 8.4 | 8.0 | 8.5 | 11.3 | 17.6 | 19.2 | 16.5 | | V | 13.5 | 9.7 | 5.7 | 4.7 | 8.5 | 17.2 | 21.5 | 19.2 | +--------+------+------+-----+---------+------+------+------+-------+ | Mean | 13.0 | 9.7 | 7.2 | 6.1 | 8.5 | 16.0 | 21.1 | 18.4 | +--------+------+------+-----+---------+------+------+------+-------+
TABLE XXXV.--Disturbed Day less ordinary Day Inequality (Unit 1´, + to West).
+------+------+------+------+------+------+------+------+------+------+------+------+------+ | Hour.| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | +------+------+------+------+------+------+------+------+------+------+------+------+------+ | a.m. | -3.4 | -2.6 | -2.0 | -0.3 | +1.6 | +1.9 | +2.3 | +2.0 | +2.1 | +2.0 | +1.6 | +1.8 | | p.m. | +1.8 | +2.2 | +2.1 | +1.7 | +1.4 | 0.0 | -1.3 | -2.8 | -3.5 | -2.6 | -3.5 | -2.4 | +------+------+------+------+------+------+------+------+------+------+------+------+------+
One difficulty in the Potsdam procedure is the maintenance of a uniform standard. Unless very frequent reference is made to the curves of some standard year there must be a tendency to enter under "3" in quiet years a number of hours which would be entered under "2" in a highly disturbed year. Still, such a source of uncertainty is unlikely to have much influence on the diurnal, or even on the annual, variation.
§ 33. A third method of investigating a diurnal period in disturbances is to form a diurnal inequality from disturbed days alone, and compare it with the corresponding inequalities from ordinary or from quiet days. Table XXXV. gives some declination data for Kew, the quantity tabulated being the algebraic excess of the disturbed day hourly value over that for the ordinary day in the mean diurnal inequality for the year, as based on the 11 years 1890 to 1900.
The disturbed day inequality was corrected for non-cyclic change in the usual way. Fig. 11 shows the results of Table XXXV. graphically. The irregularities are presumably due to the limited number, 209, of disturbed days employed; to get a smooth curve would require probably a considerably longer period of years. The differences between disturbed and ordinary days at Kew are of the same general character as those between ordinary and quiet days in Table XXIX.; they are, however, very much larger, the range in Table XXXV. being fully 5½ times that in Table XXIX. If quiet days had replaced ordinary days in Table XXXV., the algebraic excess of the disturbed day would have varied from +2´.7 at 2 p.m. to -4´.1 at 11 p.m., or a range of 6´.8.
§ 34. When the mean diurnal inequality in declination for the year at Kew is analysed into Fourier waves, the chief difference, it will be remembered, between ordinary and quiet days was that the amplitude of the 24-hour term was enhanced in the ordinary days, whilst its phase angle indicated an earlier occurrence of the maximum. Similarly, the chief difference between the Fourier waves for the disturbed and ordinary day inequalities at Kew is the increase in the amplitude of the 24-hour term in the former by over 70%, and the earlier occurrence of its maximum by about 1 hour 50 minutes. It is clear from these results for Kew, and it is also a necessary inference from the differences obtained by Sabine's method between east and west or + and - disturbances, that there is present during disturbances some influence which affects the diurnal inequality in a regular systematic way, tending to make the value of the element higher during some hours and lower during others than it is on days relatively free from disturbance. At Kew the consequence is a notable increase in the range of the regular diurnal inequality on disturbed days; but whether this is the general rule or merely a local peculiarity is a subject for further research.
§ 35. There are still other ways of attacking the problem of disturbances. W. Ellis[27] made a complete list of disturbed days at Greenwich from 1848 onwards, arranging them in classes according to the amplitude of the disturbance shown on the curves. Of the 18,000 days which he considered, Ellis regarded 2,119, or only about 12%, as undisturbed. On 11,898 days, or 66%, the disturbance movement in declination was under 10´; on 3614, or 20%, the disturbance, though exceeding 10´, was under 30´; on 294 days it lay between 30´ and 60´; while on 75 days it exceeded 60´. Taking each class of disturbances separately, Ellis found, except in the case of his "minor" disturbances--those under 10´--a distinct double annual period, with maxima towards the equinoxes. Subsequently C. W. Maunder,[38] making use of these same data, and of subsequent data up to 1902, put at his disposal by Ellis, came to similar conclusions. Taking all the days with disturbances of declination over 10´, and dealing with 15-day periods, he found the maxima of frequency to occur the one a little before the spring equinox, the other apparently after the autumnal equinox; the two minima were found to occur early in June and in January. When the year is divided into three seasons--winter (November to February), summer (May to August), and equinox--Maunder's figures lead to the results assigned to Greenwich disturbed days in Table XXXVI. The frequency in winter, it will be noticed, though less than at equinox, is considerably greater than in summer. This greater frequency in winter is only slightly apparent in the disturbances over 60´, but their number is so small that this may be accidental. The next figures in Table XXXVI. relate to highly disturbed days at Kew. The larger relative frequency at Kew in winter as compared to summer probably indicates no real difference from Greenwich, but is simply a matter of definition. The chief criterion at Kew for classifying the days was not so much the mere amplitude of the largest movement, as the general character of the day's curve and its departure from the normal form. The data in Table XXXVI. as to magnetic storms at Greenwich are based on the lists given by Maunder[39] in the _Monthly Notices_, R.A.S. A storm may last for any time from a few hours to several days, and during part of its duration the disturbance may not be very large; thus it does not necessarily follow that the frequencies of magnetic storms and of disturbed days will follow the same laws. The table shows, however, that so far as Greenwich is concerned the annual variations in the two cases are closely alike. In addition to mean data for the whole 56 years, 1848 to 1903, Table XXXVI. contains separate data for the 14 years of that period which represented the highest sun-spot frequency, and the 15 years which represented lowest sun-spot frequency. It will be seen that relatively considered the seasonal frequencies of disturbance are more nearly equal in the years of many than in those of few sun-spots. Storms are more numerous as a whole in the years of many sun-spots, and this preponderance is especially true of storms of the largest size. This requires to be borne in mind in any comparisons between larger and smaller storms selected promiscuously from a long period. An unduly large proportion of the larger storms will probably come from years of large sun-spot frequency, and there is thus a risk of assigning to differences between the laws obeyed by large and small storms phenomena that are due in whole or in part to differences between the laws followed in years of many and of few sun-spots. The last data in Table XXXVI. are based on statistics for Batavia given by W. van Bemmelen,[40] who considers separately the storms which commence suddenly and those which do not. These sudden movements are recorded over large areas, sometimes probably all over the earth, if not absolutely simultaneously, at least too nearly so for differences in the time of occurrence to be shown by ordinary magnetographs. It is ordinarily supposed that these sudden movements, and the storms to which they serve as precursors, arise from some source extraneous to the earth, and that the commencement of the movement intimates the arrival, probably in the upper atmosphere, of some form of energy transmitted through space. In the storms which commence gradually the existence of a source external to the earth is not so prominently suggested, and it has been sometimes supposed that there is a fundamental difference between the two classes of storms. Table XXXVI. shows, however, no certain difference in the annual variation at Batavia. At the same time, this possesses much less significance than it would have if Batavia were a station like Greenwich, where the annual variation in magnetic storms is conspicuous.
Besides the annual period, there seems to be also a well-marked diurnal period in magnetic disturbances. This is apparent in Tables XXXVII. and XXXVIII., which contain some statistics for Batavia due to van Bemmelen, and some for Greenwich derived from the data in Maunder's papers referred to above. Table XXXVII. gives the relative frequency of occurrence for two hour intervals, starting with midnight, treating separately the storms of gradual (g) and sudden (s) commencement. In Table XXXVIII. the day is subdivided into three equal parts. Batavia and Greenwich agree in showing maximum frequency of beginnings about the time of minimum frequency of endings and conversely; but the hours at which the respective maxima and minima occur at the two places differ rather notably.
§ 36. There are peculiarities in the sudden movements ushering in magnetic storms which deserve fuller mention. According to van Bemmelen the impulse consists usually at some stations of a sudden slight jerk of the magnet in one direction, followed by a larger decided movement in the opposite direction, the former being often indistinctly shown. Often we have at the very commencement but a faint outline, and thereafter a continuous movement which is only sometimes distinctly indicated, resulting after some minutes in the displacement of the trace by a finite amount from the position it occupied on the paper before the disturbance began. This may mean, as van Bemmelen supposes, a small preliminary movement in the opposite direction to the clearly shown displacement; but it may only mean that the magnet is initially set in vibration, swinging on both sides of the position of equilibrium, the real displacement of the equilibrium position being all the time in the direction of the displacement apparent after a few minutes. To prevent misconception, the direction of the displacement apparent after a few minutes has been termed the direction of the first _decided_ movement in Table XXXIX., which contains some data as to the direction given by Ellis[41] and van Bemmelen.[40] The + sign means an increase, the - sign a decrease of the element. The sign is not invariably the same, it will be understood, but there are in all cases a marked preponderance of changes in the direction shown in the table. The fact that all the stations indicated an increase in horizontal force is of special significance.
TABLE XXXVI.--Disturbances, and their Annual Distribution.
+-------------------------------+-------+---------------------------+ | | Total | Percentages. | | |Number.+--------+---------+--------+ | | | Winter.| Equinox.| Summer.| +-------------------------------+-------+--------+---------+--------+ | Greenwich disturbed days, | | | | | | all, 1848-1902 | 4,214 | 33.9 | 39.2 | 26.9 | | Greenwich disturbed days, | | | | | | range 10´ to 30´, 1848-1902 | 3,830 | 33.9 | 39.0 | 27.1 | | Greenwich disturbed days, | | | | | | range 30´ to 60´, 1848-1902 | 307 | 34.5 | 41.0 | 24.4 | | Greenwich disturbed days, | | | | | | range over 60´, 1848-1902 | 77 | 29.9 | 41.6 | 28.6 | | Kew highly disturbed days, | | | | | | 1890-1900 | 209 | 38.3 | 41.6 | 20.1 | | Greenwich magnetic storms, | | | | | | all, 1848-1903 | 726 | 32.1 | 42.3 | 25.6 | | Greenwich magnetic storms, | | | | | | range 20´ to 30´, 1848-1903 | 392 | 30.1 | 43.6 | 26.3 | | Greenwich magnetic storms, | | | | | | range over 30´, 1848-1903 | 334 | 34.4 | 40.7 | 24.9 | | Greenwich magnetic storms, | | | | | | all, 14 years of S. max. | 258 | 35.3 | 38.0 | 26.7 | | Greenwich magnetic storms, | | | | | | all, 15 years of S. min. | 127 | 28.4 | 48.0 | 23.6 | | Batavia magnetic storms, | | | | | | all, 1883-1899 | 1,008 | 32.9 | 34.9 | 32.2 | | Batavia magnetic storms of | | | | | | gradual commencement | 679 | 32.4 | 34.8 | 32.8 | | Batavia magnetic storms of | | | | | | sudden commencement | 329 | 33.7 | 35.3 | 31.0 | +-------------------------------+-------+--------+---------+--------+
TABLE XXXVII.--Batavia Magnetic Storms, Diurnal Distribution (percentages).
+--------------+----+----+----+----+----+----+----+----+----+----+----+----+ | Hour. | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | +--------------+----+----+----+----+----+----+----+----+----+----+----+----+ | Beginning /g | 5 | 5 | 5 | 6 | 20 | 16 | 7 | 5 | 6 | 9 | 8 | 8 | | \s | 7 | 5 | 7 | 10 | 10 | 11 | 10 | 8 | 8 | 9 | 8 | 7 | | Maximum /g | 12 | 10 | 6 | 5 | 4 | 9 | 9 | 6 | 6 | 6 | 12 | 15 | | \s | 14 | 7 | 5 | 2 | 2 | 9 | 9 | 5 | 8 | 10 | 13 | 16 | | End all | 15 | 16 | 19 | 13 | 5 | 3 | 6 | 5 | 4 | 5 | 4 | 5 | +--------------+----+----+----+----+----+----+----+----+----+----+----+----+
TABLE XXXVIII.--Greenwich Magnetic Storms, Diurnal Distribution.
+------------------------+--------+-------+-----------------------------+ | | | | Percentages. | | Epoch. | Class. | Total +---------+---------+---------+ | | |Number.| 1-8 p.m.| 9 p.m.- | 5 a.m.- | | | | | | 4 a.m. | noon. | +------------------------+--------+-------+---------+---------+---------+ | / 1848-1903 | all | 721 | 60.1 | 21.9 | 18.0 | | Beginning < 1882-1903 | " | 276 | 58.0 | 18.8 | 23.2 | | \ " " | sudden | 77 | 45.4 | 27.3 | 27.3 | | | | | | | | | / 1848-1903 | all | 720 | 9.4 | 44.6 | 46.0 | | End < 1882-1903 | " | 276 | 7.2 | 41.7 | 51.1 | | \ " " | sudden | 77 | 11.7 | 35.1 | 53.2 | +------------------------+--------+-------+---------+---------+---------+
§ 37. That large magnetic disturbances occur simultaneously over large areas was known in the time of Gauss, on whose initiative observations were taken at 5-minute intervals at a number of stations on prearranged _term days_. During March 1879 and August 1880 some large magnetic storms occurred, and the magnetic curves showing these at a number of stations fitted with Kew pattern magnetographs were compared by W. G. Adams.[42] He found the more characteristic movements to be, so far as could be judged, simultaneous at all the stations. At comparatively near stations such as Stonyhurst and Kew, or Coimbra and Lisbon, the curves were in general almost duplicates. At Kew and St Petersburg there were usually considerable differences in detail, and the movements were occasionally in opposite directions. The differences between Toronto, Melbourne or Zi-ka-wei and the European stations were still more pronounced. In 1896, on the initiative of M. Eschenhagen,[43] eye observations of declination and horizontal force were taken at 5-second intervals during prearranged hours at Batavia, Manila, Melbourne and nine European stations. The data from one of these occasions when appreciable disturbance prevailed were published by Eschenhagen, and were subsequently analysed by Ad. Schmidt.[44] Taking the stations in western Europe, Schmidt drew several series of lines, each series representing the disturbing forces at one instant of time as deduced from the departure of the elements at the several stations from their undisturbed value. The lines answering to any one instant had a general sameness of direction with more or less divergence or convergence, but their general trend varied in a way which suggested to Schmidt the passage of a species of vortex with large but finite velocity.
TABLE XXXIX.--Direction of First Decided Movement.
+-----------+-------------+------------------+----------------+ | Place. | Declination.| Horizontal Force.| Vertical Force.| +-----------+-------------+------------------+----------------+ | Pavlovsk | West | + | + | | Potsdam | West | + | - | | Greenwich | West | + | + | | Zi-ka-wei | East | + | - | | Kolaba | East | + | - | | Batavia | West | + | - | | Mauritius | East | + | + | | Cape Horn | West | + | - | +-----------+-------------+------------------+----------------+
The conclusion that magnetic disturbances tend to follow one another at nearly equal intervals of time has been reached by several independent observers. J. A. Broun[45] pronounced for a period of about 26 days, and expressed a belief that a certain zone, or zones, of the sun's surface might exert a prepotent influence on the earth's magnetism during several solar rotations. Very similar views were advanced in 1904 by E. W. Maunder,[39] who was wholly unaware of Broun's work. Maunder concluded that the period was 27.28 days, coinciding with the sun's rotation period relative to an observer on the earth. Taking magnetic storms at Greenwich from 1882 to 1903, he found the interval between the commencement of successive storms to approach closely to the above period in a considerably larger number of instances than one would have expected from mere chance. He found several successions of three or four storms, and in one instance of as many as six storms, showing his interval. In a later paper Maunder reached similar results for magnetic storms at Greenwich from 1848 to 1881. Somewhat earlier than Maunder, Arthur Harvey[46] deduced a period of 27.246 days from a consideration of magnetic disturbances at Toronto. A. Schuster,[47] examining Maunder's data mathematically, concluded that they afforded rather strong evidence of a period of about ½ (27.28) or 13.6 days. Maunder regarded his results as _demonstrating_ that magnetic disturbances originate in the sun. He regarded the solar action as arising from active areas of limited extent on the sun's surface, and as propagated along narrow, well defined streams. The active areas he believed to be also the seats of the formation of sun-spots, but believed that their activity might precede and outlive the visible existence of the sun-spot.
Maunder did not discuss the physical nature of the phenomenon, but his views are at least analogous to those propounded somewhat earlier by Svante Arrhenius,[48] who suggested that small negatively charged particles are driven from the sun by the repulsion of light and reach the earth's atmosphere, setting up electrical currents, manifest in aurora and magnetic disturbances. Arrhenius's calculations, for the size of particle which he regarded as most probable, make the time of transmission to the earth slightly under two days. Amongst other theories which ascribe magnetic storms to direct solar action may be mentioned that of Kr. Birkeland,[49] who believes the vehicle to be cathode rays. Ch. Nordmann[50] similarly has suggested Röntgen rays. Supposing the sun the ultimate source, it would be easier to discriminate between the theories if the exact time of the originating occurrence could be fixed. For instance, a disturbance that is propagated with the velocity of light may be due to Röntgen rays, but not to Arrhenius's particles. In support of his theory, Nordmann mentions several cases when conspicuous visual phenomena on the sun have synchronized with magnetic movements on the earth--the best known instance being the apparent coincidence in time of a magnetic disturbance at Kew on the 1st of September 1859 with a remarkable solar outburst seen by R. C. Carrington. Presumably any electrical phenomenon on the sun will set up waves in the aether, so transmission of electric and magnetic disturbances from the sun to the earth with the velocity of light is a certainty rather than a hypothesis; but it by no means follows that the energy thus transmitted can give rise to sensible magnetic disturbances. Also, when considering Nordmann's coincidences, it must be remembered that magnetic movements are so numerous that it would be singular if no apparent coincidences had been noticed. Another consideration is that the movements shown by ordinary magnetographs are seldom very rapid. During some storms, especially those accompanied by unusually bright and rapidly varying auroral displays, large to and fro movements follow one another in close succession, the changes being sometimes too quick to be registered distinctly on the photographic paper. This, however, is exceptional, even in polar regions where disturbances are largest and most numerous. As a rule, even when the change in the direction of movement in the declination needle seems quite sudden, the movement in one direction usually lasts for several minutes, often for 10, 15 or 30 minutes. Thus the cause to which magnetic disturbances are due seems in many cases to be persistent in one direction for a considerable time.
§ 38. Attempts have been made to discriminate between the theories as to magnetic storms by a critical examination of the phenomena. A general connexion between sun-spot frequency and the amplitude of magnetic movements, regular and irregular, is generally admitted. If it is a case of cause and effect, and the interval between the solar and terrestrial phenomena does not exceed a few hours, then there should be a sensible connexion between corresponding daily values of the sun-spot frequency and the magnetic range. Even if only some sun-spots are effective, we should expect when we select from a series of years two groups of days, the one containing the days of most sun-spots, the other the days of least, that a prominent difference will exist between the mean values of the absolute daily magnetic ranges for the two groups. Conversely, if we take out the days of small and the days of large magnetic range, or the days that are conspicuously quiet and those that are highly disturbed, we should expect a prominent difference between the corresponding mean sun-spot areas. An application of this principle was made by Chree[23] to the five quiet days a month selected by the astronomer royal between 1890 and 1900. These days are very quiet relative to the average day and possess a much smaller absolute range. One would thus have expected on Birkeland's or Nordmann's theory the mean sun-spot frequency derived from Wolfer's provisional values for these days to be much below his mean value, 41.22, for the eleven years. It proved, however, to be 41.28. This practical identity was as visible in 1892 to 1895, the years of sun-spot maximum, as it was in the years of sun-spot minimum. Use was next made of the Greenwich _projected_ sun-spot areas, which are the result of exact measurement. The days of each month were divided into three groups, the first and third--each normally of ten days--containing respectively the days of largest and the days of least sun-spot area. The mean sun-spot area from group 1 was on the average about five times that for group 3. It was then investigated how the astronomer royal's quiet days from 1890 to 1900, and how the most disturbed days of the period selected from the Kew[24] magnetic records, distributed themselves among the three groups of days. Nineteen months were excluded, as containing more than ten days with no sun-spots. The remaining 113 months contained 565 quiet and 191 highly disturbed days, whose distribution was as follows:
+----------------+---------+---------+---------+ | | Group 1.| Group 2.| Group 3.| | +---------+---------+---------+ | Quiet days | 179 | 195 | 191 | | Disturbed days | 68 | 65 | 58 | +----------------+---------+---------+---------+
The group of days of largest sun-spot area thus contained slightly under their share of quiet days and slightly over their share of disturbed days. The differences, however, are not large, and in three years, viz. 1895, 1897 and 1899, the largest number of disturbed days actually occurred in group 3, while in 1895, 1896 and 1899 there were fewer quiet days in group 3 than in group 1. Taking the same distribution of days, the mean value of the absolute daily range of declination at Kew was calculated for the group 1 and the group 3 days of each month. The mean range from the group 1 days was the larger in 57% of the individual months as against 43% in which it was the smaller. When the days of each month were divided into groups according to the absolute declination range at Kew, the mean sun-spot area for the group 1 days (those of largest range) exceeded that for the group 3 days (those of least range) in 55% of the individual months, as against 45% of cases in which it was the smaller.
Taking next the five days of largest and the five days of least range in each month, sun-spot areas were got out not merely for these days themselves, but also for the next subsequent day and the four immediately preceding days in each case. On Arrhenius's theory we should expect the magnetic range to vary with the sun-spot area, not on the actual day but two days previously. The following figures give the percentage excess or deficiency of the mean sun-spot area for the respective groups of days, relative to the average value for the whole epoch dealt with. n denotes the day to which the magnetic range belongs, n + 1 the day after, n - 1 the day before, and so on. Results are given for 1894 and 1895, the years which were on the whole the most favourable and the least favourable for Arrhenius's hypothesis, as well as for the whole eleven years.
TABLE XL.
+-------------------------+-------+-------+-------+-------+--------+-------+ | Day. | n - 4 | n - 3 | n - 2 | n - 1 | n | n + 1 | +-------------------------+-------+-------+-------+-------+--------+-------+ | Five days of \ 1894 | +12 | + 9 | +11 | +12 | +11 | + 6 | | largest range > 1895 | -16 | -17 | -15 | -12 | -11 | -10 | | / 11 yrs. | + 9 | + 8 | + 8 | + 7 | + 5 | + 0.5| | Five days of \ 1894 | -15 | -17 | -19 | -21 | -21 | -19 | | least range > 1895 | +17 | +10 | + 1 | - 2 | - 2 | - 4 | | / 11 yrs. | - 4 | - 4 | - 7 | - 7 | - 7 | - 6 | +-------------------------+-------+-------+-------+-------+--------+-------+
Taking the 11-year-means we have the sun-spot area practically normal on the day subsequent to the representative day of large magnetic range, but sensibly above its mean on that day and still more so on the four previous days. This suggests an emission from the sun taking a highly variable time to travel to the earth. The 11-year mean data for the five days of least range seem at first sight to point to the same conclusion, but the fact that the deficiency in sun-spot area is practically as prominent on the day after the representative day of small magnetic range as on that day itself, or the previous days, shows that the phenomenon is probably a secondary one. On the whole, taking into account the extraordinary differences between the results from individual years, we seem unable to come to any very positive conclusion, except that in the present state of our knowledge little if any clue is afforded by the extent of the sun's spotted area on any particular day as to the magnetic conditions on the earth on that or any individual subsequent day. Possibly some more definite information might be extracted by considering the extent of spotted area on different zones of the sun. On theories such as those of Arrhenius or Maunder, effective bombardment of the earth would be more or less confined to spotted areas in the zones nearest the centre of the visible hemisphere, whilst all spots on this hemisphere contribute to the total spotted area. Still the _projected_ area of a spot rapidly diminishes as it approaches the edge of the visible hemisphere, i.e. as it recedes from the most effective position, so that the method employed above gives a preponderating weight to the central zones. One rather noteworthy feature in Table XL. is the tendency to a sequence in the figures in any one row. This seems to be due, at least in large part, to the fact that days of large and days of small sun-spot area tend to occur in groups. The same is true to a certain extent of days of large and days of small magnetic range, but it is unusual for the range to be much above the average for more than 3 or 4 successive days.
Pulsations.
§ 39. The records from ordinary magnetographs, even when run at the usual rate and with normal sensitiveness, not infrequently show a repetition of regular or nearly regular small rhythmic movements, lasting sometimes for hours. The amplitude and period on different occasions both vary widely. Periods of 2 to 4 minutes are the most common. W. van Bemmelen[51] has made a minute examination of these movements from several years' traces at Batavia, comparing the results with corresponding statistics sent him from Zi-ka-wei and Kew. Table XLI. shows the diurnal variation in the frequency of occurrence of these small movements--called _pulsations_ by van Bemmelen--at these three stations. The Batavia results are from the years 1885 and 1892 to 1898. Of the two sets of data for Zi-ka-wei (i) answers to the years 1897, 1898 and 1900, as given by van Bemmelen, while (ii) answers to the period 1900-1905, as given in the Zi-ka-wei _Bulletin_ for 1905. The Kew data are for 1897. The results are expressed as percentages of the total for the 24 hours. There is a remarkable contrast between Batavia and Zi-ka-wei on the one hand and Kew on the other, pulsations being much more numerous by night than by day at the two former stations, whereas at Kew the exact reverse holds. Van Bemmelen decided that almost all the occasions of pulsation at Zi-ka-wei were also occasions of pulsations at Batavia. The hours of commencement at the two places usually differed a little, occasionally by as much as 20 minutes; but this he ascribed to the fact that the earliest oscillations were too small at one or other of the stations to be visible on the trace. Remarkable coincidence between pulsations at Potsdam and in the north of Norway has been noted by Kr. Birkeland.[49]
With magnetographs of greater sensitiveness and more open time scales, waves of shorter period become visible. In 1882 F. Kohlrausch[52] detected waves with a period of about 12 seconds. Eschenhagen[53] observed a great variety of short period waves, 30 seconds being amongst the most common. Some of the records he obtained suggest the superposition of regular sine waves of different periods. Employing a very sensitive galvanometer to record changes of magnetic induction through a coil traversed by the earth's lines of force, H. Ebert[54] has observed vibrations whose periods are but a small fraction of a second. The observations of Kohlrausch and Eschenhagen preceded the recent great development of applications of electrical power, while longer period waves are shown in the Kew curves of 50 years ago, so that the existence of natural waves with periods of from a few seconds up to several minutes can hardly be doubted. Whether the much shorter period waves of Ebert are also natural is more open to doubt, as it is becoming exceedingly difficult in civilized countries to escape artificial disturbances.
TABLE XLI.--Diurnal Distribution of Pulsations.
+---------------+-----+-----+-----+--------+--------+-----+-----+------+ | Hours. | 0-3.| 3-6.| 6-9.| 9-Noon.| Noon-3.| 3-6.| 6-9.| 9-12.| +---------------+-----+-----+-----+--------+--------+-----+-----+------+ | Batavia | 28 | 9 | 2 | 6 | 8 | 6 | 13 | 28 | | Zi-ka-wei (i) | 33 | 5 | 2 | 7 | 4 | 4 | 10 | 35 | | " (ii) | 23 | 6 | 8 | 11 | 7 | 5 | 14 | 26 | | Kew | 4 | 8 | 19 | 14 | 22 | 18 | 11 | 4 | +---------------+-----+-----+-----+--------+--------+-----+-----+------+
Lunar Influence.
§ 40. The fact that the moon exerts a small but sensible effect on the earth's magnetism seems to have been first discovered in 1841 by C. Kreil. Subsequently Sabine[55] investigated the nature of the lunar diurnal variation in declination at Kew, Toronto, Pekin, St Helena, Cape of Good Hope and Hobart. The data in Table XLII. are mostly due to Sabine. They represent the mean lunar diurnal inequality in declination for the whole year. The unit employed is 0´.001, and as in our previous tables + denotes movement to the _west_. By "mean departure" is meant the arithmetic mean of the 24 hourly departures from the mean value for the lunar day; the range is the difference between the algebraically greatest and least of the hourly values. Not infrequently the mean departure gives the better idea of the importance of an inequality, especially when as in the present case two maxima and minima occur in the day. This double daily period is unusually prominent in the case of the lunar diurnal inequality, and is seen in the other elements as well as in the declination.
TABLE XLII.--Lunar Diurnal Inequality of Declination (unit 0´.001).
+----------+-----------+-----------+-----------+-----------+-----------+-----------+ | Lunar | Kew. | Toronto. | Batavia. | St Helena.| Cape. | Hobart. | | Hour. | 1858-1862.| 1843-1848.| 1883-1899.| 1843-1847.| 1842-1846.| 1841-1848.| +----------+-----------+-----------+-----------+-----------+-----------+-----------+ | 0 | +103 | +315 | -70 | - 43 | -148 | - 98 | | 1 | +160 | +275 | -63 | - 5 | -107 | -138 | | 2 | +140 | +158 | -39 | + 37 | - 35 | -142 | | 3 | + 33 | + 2 | - 8 | + 70 | + 43 | -107 | | 4 | + 10 | -153 | +38 | + 85 | +108 | - 45 | | 5 | - 67 | -265 | +63 | + 77 | +140 | + 27 | | 6 | -150 | -302 | +87 | + 48 | +132 | + 88 | | 7 | -188 | -255 | +77 | + 5 | + 82 | +122 | | 8 | -160 | -137 | +40 | - 43 | + 5 | +120 | | 9 | - 78 | + 7 | - 4 | - 82 | - 78 | + 82 | | 10 | + 2 | +178 | -45 | -102 | -143 | + 17 | | 11 | + 92 | +288 | -80 | - 98 | -177 | - 57 | | 12 | +160 | +323 | -87 | - 73 | -165 | -120 | | 13 | +188 | +272 | -68 | - 32 | -112 | -152 | | 14 | +158 | +148 | -43 | + 13 | - 30 | -147 | | 15 | + 90 | - 17 | - 8 | + 52 | + 58 | -105 | | 16 | + 10 | -180 | +30 | + 73 | +132 | - 35 | | 17 | - 85 | -297 | +62 | + 73 | +172 | + 45 | | 18 | -142 | -337 | +72 | + 52 | +168 | +112 | | 19 | -163 | -290 | +68 | + 17 | +122 | +152 | | 20 | -147 | -170 | +52 | - 25 | + 45 | +152 | | 21 | -123 | - 7 | + 8 | - 58 | - 40 | +113 | | 22 | - 40 | +155 | -28 | - 73 | -112 | + 47 | | 23 | + 27 | +265 | -56 | - 68 | -153 | - 30 | +----------+-----------+-----------+-----------+-----------+-----------+-----------+ | Mean De-\| | | | | | | | parture /| 105 | 200 | 50 | 54 | 104 | 93 | +----------+-----------+-----------+-----------+-----------+-----------+-----------+ | Range | 376 | 660 | 174 | 187 | 349 | 304 | +----------+-----------+-----------+-----------+-----------+-----------+-----------+
Lunar action has been specially studied in connexion with observations from India and Java. Broun[56] at Trivandrum and C. Chambers[57] at Kolaba investigated lunar action from a variety of aspects. At Batavia van der Stok[58] and more recently S. Figee[59] have carried out investigations involving an enormous amount of computation. Table XLIII. gives a summary of Figee's results for the mean lunar diurnal inequality at Batavia, for the two half-yearly periods April to September (Winter or W.), and October to March (S.). The + sign denotes movement to the west in the case of declination, but numerical increase in the case of the other elements. In the case of H and T (total force) the results for the two seasons present comparatively small differences, but in the case of D, I and V the amplitude and phase both differ widely. Consequently a mean lunar diurnal variation derived from all the months of the year gives at Batavia, and presumably at other tropical stations, an inadequate idea of the importance of the lunar influence. In January Figee finds for the range of the lunar diurnal inequality 0´.62 in D, 3.1[gamma] in H and 3.5[gamma] in V, whereas the corresponding ranges in June are only 0´.13, 1.1[gamma] and 2.2[gamma] respectively. The difference between summer and winter is essentially due to solar action, thus the lunar influence on terrestrial magnetism is clearly a somewhat complex phenomenon. From a study of Trivandrum data, Broun concluded that the action of the moon is largely dependent on the solar hour at the time, being on the average about twice as great for a day hour as for a night hour. Figee's investigations at Batavia point to a similar conclusion. Following a method suggested by Van der Stok, Figee arrives at a numerical estimate of the "lunar activity" for each hour of the solar day, expressed in terms of that at noon taken as 100. In summer, for instance, in the case of D he finds the "activity" varying from 114 at 10 a.m. to only 8 at 9 p.m.; the corresponding extremes in the case of H are 139 at 10 a.m. and 54 at 6 a.m.
TABLE XLIII.--Lunar Diurnal Inequality at Batavia in Winter and Summer.
+----------+---------------+----------------+----------------+----------------+----------------+ | | Declination | Inclination, S.| H. (unit | V. (unit | T. (unit | | | (unit 0´.001).| (unit 0´.001). | 0.01[gamma]). | 0.01[gamma]). | 0.01[gamma]). | +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+ | Lunar | | | | | | | | | | | | Hour. | W. | S. | W. | S. | W. | S. | W. | S. | W. | S. | +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+ | 0 | +30 | -170 | - 1 | +25 | -15 | - 56 | - 9 | + 4 | - 17 | -47 | | 1 | +21 | -147 | -23 | +49 | -40 | - 87 | -54 | +20 | - 61 | -67 | | 2 | + 5 | - 83 | -49 | +69 | -25 | -107 | -82 | +37 | - 62 | -76 | | 3 | - 5 | - 12 | -51 | +47 | -21 | - 76 | -83 | +24 | - 59 | -55 | | 4 | + 1 | + 76 | -37 | +43 | -13 | - 59 | -58 | +18 | - 39 | -38 | | 5 | - 8 | +134 | -23 | +12 | +10 | - 9 | -27 | +11 | - 4 | - 3 | | 6 | - 7 | +181 | - 2 | -21 | +21 | + 43 | + 9 | - 6 | + 23 | +35 | | 7 | -10 | +164 | +30 | -12 | +23 | + 45 | +55 | + 8 | + 47 | +43 | | 8 | - 7 | + 86 | +36 | -21 | +38 | + 52 | +71 | - 1 | + 68 | +45 | | 9 | - 8 | 0 | +28 | -23 | +46 | + 30 | +64 | -16 | + 71 | +19 | | 10 | - 5 | - 85 | +34 | -20 | +13 | + 13 | +54 | -21 | + 38 | + 1 | | 11 | -15 | -144 | +27 | -11 | -12 | - 6 | +31 | -19 | + 5 | -15 | | 12 | - 9 | -164 | +19 | - 5 | -47 | - 23 | 0 | -19 | - 41 | -29 | | 13 | + 1 | -136 | - 3 | +17 | -59 | - 46 | -36 | - 2 | - 69 | -41 | | 14 | - 7 | - 79 | -13 | +27 | -66 | - 44 | -55 | +14 | - 84 | -32 | | 15 | - 8 | - 8 | -32 | +25 | -53 | - 37 | -74 | +14 | - 82 | -26 | | 16 | -12 | + 72 | -37 | +25 | -34 | - 17 | -70 | +26 | - 64 | - 2 | | 17 | -13 | +137 | -33 | + 4 | - 1 | + 28 | -47 | +21 | - 24 | +35 | | 18 | -21 | +165 | - 2 | -10 | +20 | + 47 | + 8 | +12 | + 21 | +47 | | 19 | -12 | +147 | +21 | -42 | +44 | + 81 | +53 | -14 | + 64 | +64 | | 20 | +10 | + 95 | +21 | -62 | +75 | +107 | +71 | -28 | +100 | +80 | | 21 | +13 | + 4 | +26 | -70 | +65 | + 98 | +72 | -44 | + 92 | +65 | | 22 | +25 | - 82 | +35 | -41 | +35 | + 35 | +68 | -38 | + 64 | +12 | | 23 | +36 | -147 | +34 | - 4 | - 7 | - 14 | +44 | -13 | + 15 | -19 | +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+ | Mean De-\| | | | | | | | | | | | parture /| 12 | 150 | 26 | 29 | 33 | 48 | 50 | 18 | 51 | 37 | +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+ | Range | 57 | 351 | 87 | 139 | 141 | 214 | 155 | 81 | 184 | 156 | +----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+
The question whether lunar influence increases with sun-spot frequency is obviously of considerable theoretical interest. Balfour Stewart in the 9th edition of this encyclopaedia gave some data indicating an appreciably enhanced lunar influence at Trivandrum during years of sun-spot maximum, but he hesitated to accept the result as finally proved. Figee recently investigated this point at Batavia, but with inconclusive results. Attempts have also been made to ascertain how lunar influence depends on the moon's declination and phase, and on her distance from the earth. The difficulty in these investigations is that we are dealing with a small effect, and a very long series of data would be required satisfactorily to eliminate other periodic influences.
Planetary Influence.
§ 41. From an analysis of seventeen years data at St Petersburg and Pavlovsk, Leyst[60] concluded that all the principal planets sensibly influence the earth's magnetism. According to his figures, all the planets except Mercury--whose influence he found opposite to that of the others--when nearest the earth tended to deflect the declination magnet at St Petersburg to the west, and also increased the range of the diurnal inequality of declination, the latter effect being the more conspicuous. Schuster,[61] who has considered the evidence advanced by Leyst from the mathematical standpoint, considers it to be inconclusive.
Magnetic Surveys.
§ 42. The best way of carrying out a magnetic survey depends on where it has to be made and on the object in view. The object that probably still comes first in importance is a knowledge of the declination, of sufficient accuracy for navigation in all navigable waters. One might thus infer that magnetic surveys consist mainly of observations at sea. This cannot however be said to be true of the past, whatever it may be of the future, and this for several reasons. Observations at sea entail the use of a ship, specially constructed so as to be free from disturbing influence, and so are inherently costly; they are also apt to be of inferior accuracy. It might be possible in quiet weather, in a large vessel free from vibration, to observe with instruments of the highest precision such as a unifilar magnetometer, but in the ordinary surveying ship apparatus of less sensitiveness has to be employed. The declination is usually determined with some form of compass. The other elements most usually found directly at sea are the inclination and the total force, the instrument employed being a special form of inclinometer, such as the Fox circle, which was largely used by Ross in the Antarctic, or in recent years the Lloyd-Creak. This latter instrument differs from the ordinary dip-circle fitted for total force observations after H. Lloyd's method mainly in that the needles rest in pivots instead of on agate edges. To overcome friction a projecting pin on the framework is scratched with a roughened ivory plate.
The most notable recent example of observations at sea is afforded by the cruises of the surveying ships "Galilee" and "Carnegie" under the auspices of the Carnegie Institution of Washington, which includes in its magnetic programme a general survey. To see where the ordinary land survey assists navigation, let us take the case of a country with a long seaboard. If observations were taken every few miles along the coast results might be obtained adequate for the ordinary wants of coasting steamers, but it would be difficult to infer what the declination would be 50 or even 20 miles off shore at any particular place. If, however, the land area itself is carefully surveyed, one knows the trend of the lines of equal declination, and can usually extend them with considerable accuracy many miles out to sea. One also can tell what places if any on the coast suffer from local disturbances, and thus decide on the necessity of special observations. This is by no means the only immediately useful purpose which is or may be served by magnetic surveys on land. In Scandinavia use has been made of magnetic observations in prospecting for iron ore. There are also various geological and geodetic problems to whose solution magnetic surveys may afford valuable guidance. Among the most important recent surveys may be mentioned those of the British Isles by A. Rücker and T. E. Thorpe,[62] of France and Algeria by Moureaux,[63] of Italy by Chistoni and Palazzo,[64] of the Netherlands by Van Ryckevorsel,[65] of South Sweden by Carlheim Gyllenskiöld,[66] of Austria-Hungary by Liznar,[67] of Japan by Tanakadate,[68] of the East Indies by Van Bemmelen, and South Africa by J. C. Beattie. A survey of the United States has been proceeding for a good many years, and many results have appeared in the publications of the U.S. Coast and Geodetic Survey, especially Bauer's _Magnetic Tables and Magnetic Charts_, 1908. Additions to our knowledge may also be expected from surveys of India, Egypt and New Zealand.
For the satisfactory execution of a land survey, the observers must have absolute instruments such as the unifilar magnetometer and dip circle, suitable for the accurate determination of the magnetic elements, and they must be able to fix the exact positions of the spots where observations are taken. If, as usual, the survey occupies several years, what is wanted is the value of the elements not at the actual time of observation, but at some fixed epoch, possibly some years earlier or later. At a magnetic observatory, with standardized records, the difference between the values of a magnetic element at any two specified instants can be derived from the magnetic curves. But at an ordinary survey station, at a distance from an observatory, the information is not immediately available. Ordinarily the reduction to a fixed epoch is done in at least two stages, a correction being applied for secular change, and a second for the departure from the mean value for the day due to the regular diurnal inequality and to disturbance.
The reduction to a fixed epoch is at once more easy and more accurate if the area surveyed contains, or has close to its borders, a well distributed series of magnetic observatories, whose records are comparable and trustworthy. Throughout an area of the size of France or Germany, the secular change between any two specified dates can ordinarily be expressed with sufficient accuracy by a formula of the type
[delta] = [delta]0 + a(l - l0) + b([lambda] - [lambda]0) (i),
where [delta] denotes secular change, l latitude and [lambda] longitude, the letters with suffix _0_ relating to some convenient central position. The constants [delta]0, a, b are to be determined from the observed secular changes at the fixed observatories whose geographical co-ordinates are accurately known. Unfortunately, as a rule, fixed observatories are few in number and not well distributed for survey purposes; thus the secular change over part at least of the area has usually to be found by repeating the observations after some years at several of the field stations. The success attending this depends on the exactitude with which the sites can be recovered, on the accuracy of the observations, and on the success with which allowance is made for diurnal changes, regular and irregular. It is thus desirable that the observations at repeat stations should be taken at hours when the regular diurnal changes are slow, and that they should not be accepted unless taken on days that prove to be magnetically quiet. Unless the secular change is exceptionally rapid, it will usually be most convenient in practice to calculate it from or to the middle of the month, and then to allow for the difference between the mean value for the month and the value at the actual hour of observation. There is here a difficulty, inasmuch as the latter part of the correction depends on the diurnal inequality, and so on the local time of the station. No altogether satisfactory method of surmounting this difficulty has yet been proposed. Rücker and Thorpe in their British survey assumed that the divergence from the mean value at any hour at any station might be regarded as made up of a regular diurnal inequality, identical with that at Kew when both were referred to _local_ time, and of a disturbance element identical with that existing at the same absolute time at Kew. Suppose, for instance, that at hour h G.M.T. the departure at Kew from the mean value for the month is d, then the corresponding departure from the mean at a station [lambda] degrees west of Kew is d - e, where e is the increase in the element at Kew due to the regular diurnal inequality between hour h - [lambda]/15 and hour h. This procedure is simple, but is exposed to various criticisms. If we define a diurnal inequality as the result obtained by combining hourly readings from all the days of a month, we can assign a definite meaning to the diurnal inequality for a particular month of a particular year, and after the curves have been measured we can give exact numerical figures answering to this definition. But the diurnal inequality thus obtained differs, as has been pointed out, from that derived from a limited number of the quietest days of the month, not merely in amplitude but in phase, and the view that the diurnal changes on any individual day can be regarded as made up of a regular diurnal inequality of definite character and of a disturbance element is an hypothesis which is likely at times to be considerably wide of the mark. The extent of the error involved in assuming the regular diurnal inequality the same in the north of Scotland, or the west of Ireland, as in the south-east of England remains to be ascertained. As to the disturbance element, even if the disturbing force were of given magnitude and direction all over the British Isles--which we now know is often very far from the case--its effects would necessarily vary very sensibly owing to the considerable variation in the direction and intensity of the local undisturbed force. If observations were confined to hours at which the regular diurnal changes are slow, and only those taken on days of little or no disturbance were utilized, corrections combining the effects of regular and irregular diurnal changes could be derived from the records of fixed observations, supposed suitably situated, combined in formulae of the same type as (i).
§ 43. The field results having been reduced to a fixed epoch, it remains to combine them in ways likely to be useful. In most cases the results are embodied in charts, usually of at least two kinds, one set showing only general features, the other the chief local peculiarities. Charts of the first kind resemble the world charts (figs. 1 to 4) in being free from sharp twistings and convolutions. In these the declination for instance at a fixed geographical position on a particular isogonal is to be regarded as really a mean from a considerable surrounding area.
Various ways have been utilized for arriving at these _terrestrial isomagnetics_--as Rücker and Thorpe call them--of which an elaborate discussion has been made by E. Mathias.[69] From a theoretical standpoint the simplest method is perhaps that employed by Liznar for Austria-Hungary. Let l and [lambda] represent latitude and longitude relative to a certain central station in the area. Then assume that throughout the area the value E of any particular magnetic element is given by a formula
E = E0 + al + b[lambda] + cl² + d[lambda]² + el[lambda],
where E0, a, b, c, d, e are absolute constants to be determined from the observations. When determining the constants, we write for E in the equation the observed value of the element (corrected for secular change, &c.) at each station, and for l and [lambda] the latitude and longitude of the station relative to the central station. Thus each station contributes an equation to assist in determining the six constants. They can thus be found by least squares or some simpler method. In Liznar's case there were 195 stations, so that the labour of applying least squares would be considerable. This is one objection to the method. A second is that it may allow undesirably large weight to a few highly disturbed stations. In the case of the British Isles, Rücker and Thorpe employed a different method. The area was split up into _districts_. For each district a mean was formed of the observed values of each element, and the mean was assigned to an imaginary central station, whose geographical co-ordinates represented the mean of the geographical co-ordinates of the actual stations. Want of uniformity in the distribution of the stations may be allowed for by weighting the results. Supposing E0 the value of the element found for the central station of a district, it was assumed that the value E at any actual station whose latitude and longitude exceeded those of the central station by l and [lambda] was given by E = E0 + al + b[lambda], with a and b constants throughout the district. Having found E0, a and b, Rücker and Thorpe calculated values of the element for points defined by whole degrees of longitude (from Greenwich) and half degrees of latitude. Near the common border of two districts there would be two calculated values, of which the arithmetic mean was accepted.
The next step was to determine by interpolation where isogonals--or other isomagnetic lines--cut successive lines of latitude. The curves formed by joining these successive points of intersection were called _district_ lines or curves. Rücker and Thorpe's next step was to obtain formulae by trial, giving smooth curves of continuous curvature--terrestrial isomagnetics--approximating as closely as possible to the district lines. The curves thus obtained had somewhat complicated formulae. For instance, the isogonals south of 54°.5 latitude were given for the epoch Jan. 1, 1891 by
D = 18° 37´ + 18´.5(l - 49.5) - 3´.5 cos {45°(l - 49.5)} + {26´.3 + 1´.5(l - 49.5)} ([lambda] - 4) + 0´.01([lambda] - 4)² (l - 54.5)²,
where D denotes the westerly declination. Supposing, what is at least approximately true, that the secular change in Great Britain since 1891 has been uniform south of lat. 54°.5, corresponding formulae for the epochs Jan. 1, 1901, and Jan. 1, 1906, could be obtained by substituting for 18° 37´ the values 17° 44´ and 17° 24´ respectively. In their very laborious and important memoir E. Mathias and B. Baillaud[69] have applied to Rücker and Thorpe's observations a method which is a combination of Rücker and Thorpe's and of Liznar's. Taking Rücker and Thorpe's nine districts, and the magnetic data found for the nine imaginary central stations, they employed these to determine the six constants of Liznar's formula. This is an immense simplification in arithmetic. The declination formula thus obtained for the epoch Jan. 1, 1891, was
D = 20° 45´.89 + .53474[lambda] + .34716l + .000021[lambda]² + .000343l[lambda] - .000239l²,
where l + (53° 30´.5) represents the latitude, and ([lambda] + 5° 35´.2) the west longitude of the station. From this and the corresponding formulae for the other elements, values were calculated for each of Rücker and Thorpe's 882 stations, and these were compared with the observed values. A complete record is given of the differences between the observed and calculated values, and of the corresponding differences obtained by Rücker and Thorpe from their own formulae. The mean numerical (calculated ~ observed) differences from the two different methods are almost exactly the same--being approximately 10´ for declination, 5´½ for inclination, and 70[gamma] for horizontal force. The applications by Mathias[69] of his method to the survey data of France obtained by Moureaux, and those of the Netherlands obtained by van Rïjckevorsel, appear equally successful. The method dispenses entirely with district curves, and the parabolic formulae are perfectly straightforward both to calculate and to apply; they thus appear to possess marked advantages. Whether the method could be applied equally satisfactorily to an area of the size of India or the United States actual trial alone would show.
Local Disturbances.
§ 44. Rücker and Thorpe regarded their terrestrial isomagnetics and the corresponding formulae as representing the normal field that would exist in the absence of disturbances peculiar to the neighbourhood. Subtracting the forces derived from the formulae from those observed, we obtain forces which may be ascribed to regional disturbance.
When the vertical disturbing force is downwards, or the observed vertical component larger than the calculated, Rücker and Thorpe regard it as positive, and the loci where the largest positive values occur they termed _ridge lines_. The corresponding loci where the largest negative values occur were called _valley lines_. In the British Isles Rücker and Thorpe found that almost without exception, in the neighbourhood of a ridge line, the horizontal component of the disturbing force pointed towards it, throughout a considerable area on both sides. The phenomena are similar to what would occur if ridge lines indicated the position of the summits of underground masses of magnetic material, magnetized so as to attract the north-seeking pole of a magnet. Rücker and Thorpe were inclined to believe in the real existence of these subterranean magnetic mountains, and inferred that they must be of considerable extent, as theory and observation alike indicate that thin basaltic sheets or dykes, or limited masses of trap rock, produce no measurable magnetic effect except in their immediate vicinity. In support of their conclusions, Rücker and Thorpe dwell on the fact that in the United Kingdom large masses of basalt such as occur in Skye, Mull, Antrim, North Wales or the Scottish coalfield, are according to their survey invariably centres of attraction for the north-seeking pole of a magnet. Various cases of repulsion have, however, been described by other observers in the northern hemisphere.
§ 45. Rücker and Thorpe did not make a very minute examination of disturbed areas, so that purely local disturbances larger than any noticed by them may exist in the United Kingdom. But any that exist are unlikely to rival some that have been observed elsewhere, notably those in the province of Kursk in Russia described by Moureaux[70] and by E. Leyst.[71] In Kursk Leyst observed declinations varying from 0° to 360°, inclinations varying from 39°.1 to 90°; he obtained values of the horizontal force varying from 0 to 0.856 C.G.S., and values of the vertical force varying from 0.371 to 1.836. Another highly disturbed Russian district Krivoi Rog (48° N. lat. 33° E. long.) was elaborately surveyed by Paul Passalsky.[72] The extreme values observed by him differed, the declination by 282° 40´, the inclination by 41° 53´, horizontal force by 0.658, and vertical force by 1.358. At one spot a difference of 116°½ was observed between the declinations at two positions only 42 metres apart. In cases such as the last mentioned, the source of disturbance comes presumably very near the surface. It is improbable that any such enormously rapid changes of declination can be experienced anywhere at the surface of a deep ocean. But in shallow water disturbances of a not very inferior order of magnitude have been met with. Possibly the most outstanding case known is that of an area, about 3 m. long by 1¼ m. at its widest, near Port Walcott, off the N.W. Australian coast. The results of a minute survey made here by H.M.S. "Penguin" have been discussed by Captain E. W. Creak.[73] Within the narrow area specified, declination varied from 26° W. to 56° E., and inclination from 50° to nearly 80°, the observations being taken some 80 ft. above sea bottom. Another noteworthy case, though hardly comparable with the above, is that of East Loch Roag at Lewis in the Hebrides. A survey by H.M.S. "Research" in water about 100 ft. deep--discussed by Admiral A. M. Field[74]--showed a range of 11° in declination. The largest observed disturbances in horizontal and vertical force were of the order 0.02 and 0.05 C.G.S. respectively. An interesting feature in this case was that vertical force was reduced, there being a well-marked valley line.
In some instances regional magnetic disturbances have been found to be associated with geodetic anomalies. This is true of an elongated area including Moscow, where observations were taken by Fritsche.[75] Again, Eschenhagen[76] detected magnetic anomalies in an area including the Harz Mountains in Germany, where deflections of the plumb line from the normal had been observed. He found a magnetic ridge line running approximately parallel to the line of no deflection of the plumb line.
§ 46. A question of interest, about which however not very much is known, is the effect of local disturbance on secular change and on the diurnal inequality. The determination of secular change in a highly disturbed locality is difficult, because an unintentional slight change in the spot where the observations are made may wholly falsify the conclusions drawn. When the disturbed area is very limited in extent, the magnetic field may reasonably be regarded as composed of the normal field that would have existed in the absence of local disturbance, plus a disturbance field arising from magnetic material which approaches nearly if not quite to the surface. Even if no sensible change takes place in the disturbance field, one would hardly expect the secular change to be wholly normal. The changes in the rectangular components of the force may possibly be the same as at a neighbouring undisturbed station, but this will not give the same change in declination and inclination. In the case of the diurnal inequality, the presumption is that at least the declination and inclination changes will be influenced by local disturbance. If, for example, we suppose the diurnal inequality to be due to the direct influence of electric currents in the upper atmosphere, the declination change will represent the action of the component of a force of given magnitude which is perpendicular to the position of the compass needle. But when local disturbance exists, the direction of the needle and the intensity of the controlling field are both altered by the local disturbance, so it would appear natural for the declination changes to be influenced also. This conclusion seems borne out by observations made by Passalsky[72] at Krivoi Rog, which showed diurnal inequalities differing notably from those experienced at the same time at Odessa, the nearest magnetic observatory. One station where the horizontal force was abnormally low gave a diurnal range of declination four times that at Odessa; on the other hand, the range of the horizontal force was apparently reduced. It would be unsafe to draw general conclusions from observations at two or three stations, and much completer information is wanted, but it is obviously desirable to avoid local disturbance when selecting a site for a magnetic observatory, assuming one's object is to obtain data reasonably applicable to a large area. In the case of the older observatories this consideration seems sometimes to have been lost sight of. At Mauritius, for instance, inside of a circle of only 56 ft. radius, having for centre the declination pillar of the absolute magnetic hut of the Royal Alfred Observatory, T. F. Claxton[77] found that the declination varied from 4° 56´ to 13° 45´ W., the inclination from 50° 21´ to 58° 34´ S., and the horizontal force from 0.197 to 0.244 C.G.S. At one spot he found an alteration of 1°1/3 in the declination when the magnet was lowered from 4 ft. above the ground to 2. Disturbances of this order could hardly escape even a rough investigation of the site.
Gaussian Potential and Constants.
§ 47. If we assume the magnetic force on the earth's surface derivable from a potential V, we can express V as the sum of two series of solid spherical harmonics, one containing negative, the other positive integral powers of the radius vector r from the earth's centre. Let [lambda] denote east longitude from Greenwich, and let µ = cos(½[pi] - l), where l is latitude; and also let _ _ | (n - m)(n - m - 1) | H_n^m = (1 - µ²)^(½m) |µ^(n-m) - ------------------ µ^(n-m-2) + ...|, |_ 2(2n - 1) _|
where n and m denote any positive integers, m being not greater than n. Then denoting the earth's radius by R, we have
V/R = [Sigma](R/r)^(n+1) [H_n^m (g_n^m cos m[lambda] + h_n^m sin m[lambda])] + [Sigma](r/R)^n [H_n^m (g_(-n)^m cos m[lambda] + h_(-n)^m sin m[lambda])],
where [Sigma] denotes summation of m from 0 to n, followed by summation of n from 0 to [infinity]. In this equation g_n^m, &c. are constants, those with positive suffixes being what are generally termed _Gaussian constants_. The series with negative powers of r answers to forces with a source internal to the earth, the series with positive powers to forces with an external source. Gauss found that forces of the latter class, if existent, were very small, and they are usually left out of account. There are three Gaussian constants of the first order, g1^0, g1¹, h1¹, five of the second order, seven of the third, and so on. The coefficient of a Gaussian constant of the n^th order is a spherical harmonic of the n^th degree. If R be taken as unit length, as is not infrequent, the first order terms are given by
V1 = r^(-2) [g1^0 sin l + (g1¹ cos [lambda] + h1¹ sin [lambda]) cos l].
The earth is in reality a spheroid, and in his elaborate work on the subject J. C. Adams[78] develops the treatment appropriate to this case. Here we shall as usual treat it as spherical. We then have for the components of the force at the surface
X = -R^(-1)(1 - µ²)^½ (dV/dµ) towards the astronomical north, Y = -R^(-1)(1 - µ²)^-½ (dV/d[lambda]) " " " west, Z = -dV/dr vertically downwards.
Supposing the Gaussian constants known, the above formulae would give the force all over the earth's surface. To determine the Gaussian constants we proceed of course in the reverse direction, equating the observed values of the force components to the theoretical values involving g_n^m, &c. If we knew the values of the component forces at regularly distributed stations all over the earth's surface, we could determine each Gaussian constant independently of the others. Our knowledge however of large regions, especially in the Arctic and Antarctic, is very scanty, and in practice recourse is had to methods in which the constants are not determined independently. The consequence is unfortunately that the values found for some of the constants, even amongst the lower orders, depend very sensibly on how large a portion of the polar regions is omitted from the calculations, and on the number of the constants of the higher orders which are retained.
TABLE XLIV.--Gaussian Constants of the First Order.
+------+---------+---------+---------+---------+---------+---------+---------+ | | 1829 | | | | | | | | | Erman- | 1830 | 1845 | 1880 | 1885 | 1885 | 1885 | | |Petersen.| Gauss. | Adams. | Adams. |Neumayer.| Schmidt.|Fritsche.| +------+---------+---------+---------+---------+---------+---------+---------+ | g1^0 | +.32007 | +.32348 | +.32187 | +.31684 | +.31572 | +.31735 | +.31635 | | g1^1 | +.02835 | +.03111 | +.02778 | +.02427 | +.02481 | +.02356 | +.02414 | | h1^1 | -.06011 | -.06246 | -.05783 | -.06030 | -.06026 | -.05984 | -.05914 | +------+---------+---------+---------+---------+---------+---------+---------+
Table XLIV. gives the values obtained for the Gaussian constants of the first order in some of the best-known computations, as collected by W. G. Adams.[79]
§ 48. Allowance must be made for the difference in the epochs, and for the fact that the number of constants assumed to be worth retaining was different in each case. Gauss, for instance, assumed 24 constants sufficient, whilst in obtaining the results given in the table J. C. Adams retained 48. Some idea of the uncertainty thus arising may be derived from the fact that when Adams assumed 24 constants sufficient, he got instead of the values in the table the following:--
g1^0 g1¹ h1¹
1842-1845 +.32173 +.02833 -.05820 1880 +.31611 +.02470 -.06071
Some of the higher constants were relatively much more affected. Thus, on the hypotheses of 48 and of 24 constants respectively, the values obtained for g2^0 in 1842-1845 were -.00127 and -.00057, and those obtained for h3¹ in 1880 were +.00748 and +.00573. It must also be remembered that these values assume that the series in positive powers of r, with coefficients having negative suffixes, is absolutely non-existent. If this be not assumed, then in any equation determing X or Y, g_n^m must be replaced by g_n^m + g_(-n)^m, and in any equation determining Z by g_n^m - n/(n + 1) g_n^m; similar remarks apply to h_n^m and h_(-n)^m. It is thus theoretically possible to check the truth of the assumption that the positive power series is non-existent by comparing the values obtained for g_n^m and h_n^m from the X and Y or from the Z equations, when g_(-n)^m and h_(-n)^m are assumed zero. If the values so found differ, values can be found for g_(-n)^m and h_(-n)^m which will harmonize the two sets of equations. Adams gives the values obtained from the X, Y and the Z equations separately for the Gaussian constants. The following are examples of the values thence deducible for the coefficients of the positive power series:--
g_(-1)^0 g_(-1)^1 h_(-1)^1 g_(-4)^0 g_(-5)^0 g_(-6)^0
1842-1845 +.0018 -.0002 -.0014 +.0064 +.0072 +.0124 1880 -.0002 -.0012 +.0015 -.0043 -.0021 -.0013
Compared to g4^0, g5^0 and g6^0 the values here found for g_(-4)^0, g_(-5)^0 and g_(-6)^0 are far from insignificant, and there would be no excuse for neglecting them if the observational data were sufficient and reliable. But two outstanding features claim attention, first the smallness of g_(-1)^0, g_(-1)^1 and h_(-1)^1, the coefficients least likely to be affected by observational deficiencies, and secondly the striking dissimilarity between the values obtained for the two epochs. The conclusion to which these and other facts point is that observational deficiencies, even up to the present date, are such that no certain conclusion can be drawn as to the existence or non-existence of the positive power series. It is also to be feared that considerable uncertainties enter into the values of most of the Gaussian constants, at least those of the higher orders. The introduction of the positive power series necessarily improves the agreement between observed and calculated values of the force, but it is more likely than not to be disadvantageous physically, if the differences between observed values and those calculated from the negative power series alone arise in large measure from observational deficiencies.
TABLE XLV.--Axis and Moment of First Order Gaussian Coefficients.
+-------+-------------------+-----------+------------+--------------+ | Epoch.| Authority for | North | West | M/R³ in | | | Constants. | Latitude. | Longitude. | G.C.S. units.| +-------+-------------------+-----------+------------+--------------+ | | | ° ´ | ° ´ | | | 1650 | H. Fritsche | 82 50 | 42 55 | .3260 | | 1836 | " | 78 27 | 63 35 | .3262 | | 1845 | J. C. Adams | 78 44 | 64 20 | .3282 | | 1880 | " | 78 24 | 68 4 | .3234 | | 1885 | Neumayer-Petersen | | | | | | and Bauer | 78 3 | 67 3 | .3224 | | 1885 | Neumayer, Schmidt | 78 34 | 68 31 | .3230 | +-------+-------------------+-----------+------------+--------------+
§ 49. The first order Gaussian constants have a simple physical meaning. The terms containing them represent the potential arising from the uniform magnetization of a sphere parallel to a fixed axis, the moment M of the spherical magnet being given by
M = R³{(g1^0)² + (g1^1)² + (h1^1)²}^½,
where R is the earth's radius. The position of the north end of the axis of this uniform magnetization and the values of M/R^3, derived from the more important determinations of the Gaussian constants, are given in Table XLV. The data for 1650 are of somewhat doubtful value. If they were as reliable as the others, one would feel greater confidence in the reality of the apparent movement of the north end of the axis from east to west. The table also suggests a slight diminution in M since 1845, but it is open to doubt whether the apparent change exceeds the probable error in the calculated values. It should be carefully noticed that the data in the table apply only to the first order Gaussian terms, and so only to a portion of the earth's magnetization, and that the Gaussian constants have been calculated on the assumption that the negative power series alone exists. The field answering to the first order terms--or what Bauer has called the _normal_ field--constitutes much the most important part of the whole magnetization. Still what remains is very far from negligible, save for rough calculations. It is in fact one of the weak points in the Gaussian analysis that when one wishes to represent the observed facts with high accuracy one is obliged to retain so many terms that calculation becomes burdensome.
Earth-air Currents.
§ 50. The possible existence of a positive power series is not the only theoretical uncertainty in the Gaussian analysis. There is the further possibility that part of the earth's magnetic field may not answer to a potential at all. Schmidt[80] in his calculation of Gaussian constants regarded this as a possible contingency, and the results he reached implied that as much as 2 or 3% of the entire field had no potential. If the magnetic force F on the earth's surface comes from a potential, then the line integral [int]F ds taken round any closed circuit s should vanish. If the integral does not vanish, it equals 4[pi]I, where I is the total electric current traversing the area bounded by s. A + sign in the result of the integration means that the current is downwards (i.e. from air to earth) or upwards, according as the direction of integration round the circuit, as viewed by an observer above ground, has been clockwise or anti-clockwise. In applications of the formula by W. von Bezold[81] and Bauer[82] the integral has been taken along parallels of latitude in the direction west to east. In this case a + sign indicates a resultant upward current over the area between the parallel of latitude traversed and the north geographical pole. The difference between the results of integration round two parallels of latitude gives the total vertical current over the zone between them. Schmidt's final estimate of the average intensity of the earth-air current, irrespective of sign, for the epoch 1885 was 0.17 ampere per square kilometre. Bauer employing the same observational data as Schmidt, reached somewhat similar conclusions from the differences between integrals taken round parallels of latitude at 5° intervals from 60° N. to 60° S. H. Fritsche[83] treating the problem similarly, but for two epochs, 1842 and 1885, got conspicuously different results for the two epochs, Bauer[84] has more recently repeated his calculations, and for three epochs, 1842-1845 (Sabine's charts), 1880 (Creak's charts), and 1885 (Neumayer's charts), obtaining the mean value of the current per sq. km. for 5° zones. Table XLVI. is based on Bauer's figures, the unit being 0.001 ampere, and + denoting an _upwardly_ directed current.
TABLE XLVI.--Earth-air Currents, after Bauer.
+-------------+----------------------+---------------------+ | | Northern Hemisphere. | Southern Hemisphere.| | Latitude. +--------+------+------+-------+------+------+ | | 1842-5.| 1880.| 1885.|1842-5.| 1880.| 1885.| +-------------+--------+------+------+-------+------+------+ | 0° to 15° | - 1 | -32 | -34 | +66 | + 30 | + 36 | | 15° " 30° | -70 | -59 | -68 | + 2 | - 62 | - 63 | | 30° " 45° | + 3 | +14 | -22 | +26 | - 11 | - 14 | | 45° " 60° | -31 | -21 | +78 | + 5 | +276 | +213 | +-------------+--------+------+------+-------+------+------+
In considering the significance of the data in Table XLVI., it should be remembered that the currents must be regarded as mean values derived from all hours of the day, and all months of the year. Currents which were upwards during certain hours of the day, and downwards during others, would affect the diurnal inequality; while currents which were upwards during certain months, and downwards during others, would cause an annual inequality in the absolute values. Thus, if the figures be accepted as real, we must suppose that between 15° N. and 30° N. there are preponderatingly downward currents, and between 0° S. and 15° S. preponderatingly upward currents. Such currents might arise from meteorological conditions characteristic of particular latitudes, or be due to the relative distribution of land and sea; but, whatever their cause, any considerable real change in their values between 1842 and 1885 seems very improbable. The most natural cause to which to attribute the difference between the results for different epochs in Table XLVI. is unquestionably observational deficiencies. Bauer himself regards the results for latitudes higher than 45° as very uncertain, but he seems inclined to accept the reality of currents of the average intensity of 1/30 ampere per sq. km. between 45° N. and 45° S.
Currents of the size originally deduced by Schmidt, or even those of Bauer's latest calculations, seem difficult to reconcile with the results of atmospheric electricity (q.v.).
§ 51. There is no single parallel of latitude along the whole of which magnetic elements are known with high precision. Thus results of greater certainty might be hoped for from the application of the line integral to well surveyed countries. Such applications have been made, e.g. to Great Britain by Rücker,[85] and to Austria by Liznar,[86] but with negative results. The question has also been considered in detail by Tanakadate[68] in discussing the magnetic survey of Japan. He makes the criticism that the taking of a line integral round the _boundary_ of a surveyed area amounts to utilizing the values of the magnetic elements where least accurately known, and he thus considers it preferable to replace the line integral by the surface integral.
4[pi]I = [int][int] (dY/dx - dX/dy) dx dy.
He applied this formula not merely to his own data for Japan, but also to British and Austrian data of Rücker and Thorpe and of Liznar. The values he ascribes to X and Y are those given by the formulae calculated to fit the observations. The result reached was "a line of no current through the middle of the country; in Japan the current is upward on the Pacific side and downward on the Siberian side; in Austria it is upward in the north and downward in the south; in Great Britain upward in the east and downward in the west." The results obtained for Great Britain differed considerably according as use was made of Rücker and Thorpe's own district equations or of a series of general equations of the type subsequently utilized by Mathias. Tanakadate points out that the fact that his investigations give in each case a line of no current passing through the middle of the surveyed area, is calculated to throw doubt on the reality of the supposed earth-air currents, and he recommends a suspension of judgment.
§ 52. A question of interest, and bearing a relationship to the Gaussian analysis, is the law of variation of the magnetic elements with height above sea-level. If F represent the value at sea-level, and F + [delta]F that at height h, of any component of force answering to Gaussian constants of the n^th order, then 1 + [delta]F/F = (1 + h/R)^(-n-2), where R is the earth's radius. Thus at heights of only a few miles we have very approximately [delta]F/F = -(n + 2)h/R. As we have seen, the constants of the first order are much the most important, thus we should expect as a first approximation [delta]X/X = [delta]Y/Y = [delta]Z/Z = -3h/R. This equation gives the same rate of decrease in all three components, and so no change in declination or inclination. Liznar[86a] compared this equation with the observed results of his Austrian survey, subdividing his stations into three groups according to altitude. He considered the agreement not satisfactory. It must be remembered that the Gaussian analysis, especially when only lower order terms are retained, applies only to the earth's field freed from local disturbances. Now observations at individual high level stations may be seriously influenced not merely by regional disturbances common to low level stations, but by magnetic material in the mountain itself. A method of arriving at the vertical change in the elements, which theoretically seems less open to criticism, has been employed by A. Tanakadate.[68] If we assume that a potential exists, or if admitting the possibility of earth-air currents we assume their effort negligible, we have dX/dz = dZ/dx, dY/dz = dZ/dy. Thus from the observed rates of change of the vertical component of force along the parallels of latitude and longitude, we can deduce the rate of change in the vertical direction of the two rectangular components of horizontal force, and thence the rates of change of the horizontal force and the declination. Also we have dZ/dz = 4[pi][rho] - (dX/dx + dY/dy), where [rho] represents the density of free magnetism at the spot. The spot being above ground we may neglect [rho], and thus deduce the variation in the vertical direction of the vertical component from the observed variations of the two horizontal components in their own directions. Tanakadate makes a comparison of the vertical variations of the magnetic elements calculated in the two ways, not merely for Japan, but also for Austria-Hungary and Great Britain. In each country he took five representative points, those for Great Britain being the central stations of five of Rücker and Thorpe's districts. Table XLVII. gives the mean of the five values obtained. By method (i.) is meant the formula involving 3h/R, by method (ii.) Tanakadate's method as explained above. H, V, D, and I are used as defined in § 5. In the case of H and V unity represents 1[gamma].
TABLE XLVII.--Change per Kilometre of Height.
+---------+-----------------+-----------------+-----------------+ | | Great Britain. | Austria-Hungary.| Japan. | +---------+-------+---------+-------+---------+-------+---------+ | Method. | (i.) | (ii.) | (i.) | (ii.) | (i.) | (ii.) | +---------+-------+---------+-------+---------+-------+---------+ | H | - 8.1 | - 6.7 | -10.1 | - 8.7 | -13.9 | -14.0 | | V | -21.2 | -19.4 | -19.0 | -18.1 | -17.1 | -17.4 | | D (west)| .. | - 0´.04 | .. | + 0´.10 | .. | - 0´.27 | | I | .. | - 0´.05 | .. | - 0´.06 | .. | - 0´.01 | +---------+-------+---------+-------+---------+-------+---------+
The - sign in Table XLVII. denotes a decrease in the numerical values of H, V and I, and a diminution in westerly declination. If we except the case of the westerly component of force--not shown in the table--the accordance between the results from the two methods in the case of Japan is extraordinarily close, and there is no very marked tendency for the one method to give larger values than the other. In the case of Great Britain and Austria the differences between the two sets of calculated values though not large are systematic, the 3h/R formula invariably showing the larger reduction with altitude in both H and V. Tanakadate was so satisfied with the accordance of the two methods in Japan, that he employed his method to reduce all observed Japanese values to sea-level. At a few of the highest Japanese stations the correction thus introduced into the value of H was of some importance, but at the great majority of the stations the corrections were all insignificant.
Schuster's Diurnal Variation Potential.
§ 53. Schuster[87] has calculated a potential analogous to the Gaussian potential, from which the regular diurnal changes of the magnetic elements all over the earth may be derived. From the mean summer and winter diurnal variations of the northerly and easterly components of force during 1870 at St Petersburg, Greenwich, Lisbon and Bombay, he found the values of 8 constants analogous to Gaussian constants; and from considerations as to the hours of occurrence of the maxima and minima of vertical force, he concluded that the potential, unlike the Gaussian, must proceed in positive powers of r, and so answer to forces external to the earth. Schuster found, however, that the calculated amplitudes of the diurnal vertical force inequality did not accord well with observation; and his conclusion was that while the original cause of the diurnal variation is external, and consists probably of electric currents in the atmosphere, there are induced currents inside the earth, which increase the horizontal components of the diurnal inequality while diminishing the vertical. The problem has also been dealt with by H. Fritsche,[88] who concludes, in opposition to Schuster, that the forces are partly internal and partly external, the two sets being of fairly similar magnitude. Fritsche repeats the criticism (already made in the last edition of this encyclopaedia) that Schuster's four stations were too few, and contrasts their number with the 27 from which his own data were derived. On the other hand, Schuster's data referred to one and the same year, whereas Fritsche's are from epochs varying from 1841 to 1896, and represent in some cases a single year's observations, in other cases means from several years. It is clearly desirable that a fresh calculation should be made, using synchronous data from a considerable number of well distributed stations; and it should be done for at least two epochs, one representing large, the other small sun-spot frequency. The year 1870 selected by Schuster had, as it happened, a sun-spot frequency which has been exceeded only once since 1750; so that the magnetic data which he employed were far from representative of average conditions.
Magnetization of Vases, &c.
§ 54. It was discovered by Folgheraiter[89] that old vases from Etruscan and other sources are magnetic, and from combined observation and experiment he concluded that they acquired their magnetization when cooling after being baked, and retained it unaltered. From experiments, he derived formulae connecting the magnetization shown by new clay vases with their orientation when cooling in a magnetic field, and applying these formulae to the phenomena observed in the old vases he calculated the magnetic dip at the time and place of manufacture. His observations led him to infer that in Central Italy inclination was actually southerly for some centuries prior to 600 B.C., when it changed sign. In 400 B.C. it was about 20°N.; since 100 B.C. the change has been relatively small. L. Mercanton[90] similarly investigated the magnetization of baked clay vases from the lake dwellings of Neuchatel, whose epoch is supposed to be from 600 to 800 B.C. The results he obtained were, however, closely similar to those observed in recent vases made where the inclination was about 63°N., and he concluded in direct opposition to Folgheraiter that inclination in southern Europe has not undergone any very large change during the last 2500 years. Folgheraiter's methods have been extended to natural rocks. Thus B. Brunhes[91] found several cases of clay metamorphosed by adjacent lava flows and transformed into a species of natural brick. In these cases the clay has a determinate direction of magnetization agreeing with that of the volcanic rock, so it is natural to assume that this direction coincided with that of the dip when the lava flow occurred. In drawing inferences, allowance must of course be made for any tilting of the strata since the volcanic outburst. From one case in France in the district of St Flour, where the volcanic action is assigned to the Miocene Age, Brunhes inferred a southerly dip of some 75°. Until a variety of cases have been critically dealt with, a suspension of judgment is advisable, but if the method should establish its claims to reliability it obviously may prove of importance to geology as well as to terrestrial magnetism.
Polar Phenomena.
§ 55. Magnetic phenomena in the polar regions have received considerable attention of late years, and the observed results are of so exceptional a character as to merit separate consideration. One feature, the large amplitude of the regular diurnal inequality, is already illustrated by the data for Jan Mayen and South Victoria Land in Tables VIII. to XI. In the case, however, of declination allowance must be made for the small size of H. If a force F perpendicular to the magnetic meridian causes a change [Delta]D in D then [Delta]D = F/H. Thus at the "Discovery's" winter quarters in South Victoria Land, where the value of H is only about 0.36 of that at Kew, a change of 45´ in D would be produced by a force which at Kew would produce a change of only 16´. Another feature, which, however, may not be equally general, is illustrated by the data for Fort Rae and South Victoria Land in Table XVII. It will be noticed that it is the 24-hour term in the Fourier analysis of the regular diurnal inequality which is specially enhanced. The station in South Victoria Land--the winter quarters of the "Discovery" in 1902-1904--was at 77° 51´ S. lat.; thus the sun did not set from November to February (midsummer), nor rise from May to July (midwinter). It might not thus have been surprising if there had been an outstandingly large seasonal variation in the type of the diurnal inequality. As a matter of fact, however, the type of the inequality showed exceptionally small variation with the season, and the amplitude remained large throughout the whole year. Thus, forming diurnal inequalities for the three midsummer months and for the three midwinter months, we obtain the following amplitudes for the range of the several elements[92]:--
D. H. V. I.
Midsummer 64´.1 57[gamma] 58[gamma] 2´.87 Midwinter 26´.8 25[gamma] 18[gamma] 1´.23
The most outstanding phenomenon in high latitudes is the frequency and large size of the disturbances. At Kew, as we saw in § 25, the absolute range in D exceeds 20´ on only 12% of the total number of days. But at the "Discovery's" winter quarters, about sun-spot minimum, the range exceeded 1° on 70%, 2° on 37%, and 3° on fully 15% of the total number of days. One day in 25 had a range exceeding 4°. During the three midsummer months, only one day out of 111 had a range under 1°, and even at midwinter only one day in eight had a range as small as 30´. The H range at the "Discovery's" station exceeded 100[gamma] on 40% of the days, and the V range exceeded 100[gamma] on 32% of the days.
The special tendency to disturbance seen in equinoctial months in temperate latitudes did not appear in the "Discovery's" records in the Antarctic. D ranges exceeding 3° occurred on 11% of equinoctial days, but on 40% of midsummer days. The preponderance of large movements at midsummer was equally apparent in the other elements. Thus the percentage of days having a V range over 200[gamma] was 21 at midsummer, as against 3 in the four equinoctial months.
At the "Discovery's" station small oscillations of a few minutes' duration were hardly ever absent, but the character of the larger disturbances showed a marked variation throughout the 24 hours. Those of a very rapid oscillatory character were especially numerous in the morning between 4 and 9 a.m. In the late afternoon and evening disturbances of a more regular type became prominent, especially in the winter months. In particular there were numerous occurrences of a remarkably regular type of disturbance, half the total number of cases taking place between 7 and 9 p.m. This "special type of disturbance" was divisible into two phases, each lasting on the average about 20 minutes. During the first phase all the elements diminished in value, during the second phase they increased. In the case of D and H the rise and fall were about equal, but the rise in V was about 3½ times the preceding fall. The disturbing force--on the north pole--to which the first phase might be attributed was inclined on the average about 5°½ below the horizon, the horizontal projection of its line of action being inclined about 41°½ to the north of east. The amplitude and duration of the disturbances of the "special type" varied a good deal; in several cases the disturbing force considerably exceeded 200[gamma]. A somewhat similar type of disturbance was observed by Kr. Birkeland[93] at Arctic stations also in 1902-1903, and was called by him the "polar elementary" storm. Birkeland's record of disturbances extends only from October 1902 to March 1903, so it is uncertain whether "polar elementary" storms occur during the Arctic summer. Their usual time of occurrence seems to be the evening. During their occurrence Birkeland found that there was often a great difference in amplitude and character between the disturbances observed at places so comparatively near together as Iceland, Nova Zembla and Spitzbergen. This led him to assign the cause to electric currents in the Arctic, at heights not exceeding a few hundred kilometres, and he inferred from the way in which the phenomena developed that the seat of the disturbances often moved westward, as if related in some way to the sun's position. Contemporaneously with the "elementary polar" storms in the Arctic Birkeland found smaller but distinct movements at stations all over Europe; these could generally be traced as far as Bombay and Batavia, and sometimes as far as Christchurch, New Zealand. Chree,[92] on the other hand, working up the 1902-1904 Antarctic records, discovered that during the larger disturbances of the "special type" corresponding but much smaller movements were visible at Christchurch, Mauritius, Kolaba, and even at Kew. He also found that in the great majority of cases the Antarctic curves were specially disturbed during the times of Birkeland's "elementary polar" storms, the disturbances in the Arctic and Antarctic being of the same order of magnitude, though apparently of considerably different type.
Examining the more prominent of the sudden commencements of magnetic disturbances in 1902-1903 visible simultaneously in the curves from Kew, Kolaba, Mauritius and Christchurch, Chree found that these were all represented in the Antarctic curves by movements of a considerably larger size and of an oscillatory character. In a number of cases Birkeland observed small simultaneous movements in the curves of his co-operating stations, which appeared to be at least sometimes decidedly larger in the equatorial than the northern temperate stations. These he described as "equatorial" perturbations, ascribing them to electric currents in or near the plane of the earth's magnetic equator, at heights of the order of the earth's radius. It was found, however, by Chree that in many, if not all, of these cases there were synchronous movements in the Antarctic, similar in type to those which occurred simultaneously with the sudden commencements of magnetic storms, and that these Antarctic movements were considerably larger than those described by Birkeland at the equatorial stations. This result tends of course to suggest a somewhat different explanation from Birkeland's. But until our knowledge of facts has received considerable additions all explanations must be of a somewhat hypothetical character.
Magnetic Poles.
In 1831 Sir James Ross[94] observed a dip of 89° 59´ at 70° 5´ N., 96° 46´ W., and this has been accepted as practically the position of the north magnetic pole at the time. The position of the south magnetic pole in 1840 as deduced from the Antarctic observations made by the "Erebus" and "Terror" expedition is shown in Sabine's chart as about 73° 30´ S., 147° 30´ E. In the more recent chart in J. C. Adams's _Collected Papers_, vol. 2, the position is shown as about 73° 40´ S., 147° 7´ E. Of late years positions have been obtained for the south magnetic pole by the "Southern Cross" expedition of 1898-1900 (A), by the "Discovery" in 1902-1904 (B), and by Sir E. Shackleton's expedition 1908-1909 (C). These are as follow:
(A) 72° 40´ S., 152° 30´ E. (B) 72° 51´ S., 156° 25´ E. (C) 72° 25´ S., 155° 16´ E.
Unless the diurnal inequality vanishes in its neighbourhood, a somewhat improbable contingency considering the large range at the "Discovery's" winter quarters, the position of the south magnetic pole has probably a diurnal oscillation, with an average amplitude of several miles, and there is not unlikely a larger annual oscillation. Thus even apart from secular change, no single spot of the earth's surface can probably claim to be a magnetic pole in the sense popularly ascribed to the term. If the diurnal motion were absolutely regular, and carried the point where the needle is vertical round a closed curve, the centroid of that curve--though a spot where the needle is never absolutely vertical--would seem to have the best claim to the title. It should also be remembered that when the dip is nearly 90° there are special observational difficulties. There are thus various reasons for allowing a considerable uncertainty in positions assigned to the magnetic poles. Conclusions as to change of position of the south magnetic pole during the last ten years based on the more recent results (A), (B) and (C) would, for instance, possess a very doubtful value. The difference, however, between these recent positions and that deduced from the observations of 1840-1841 is more substantial, and there is at least a moderate probability that a considerable movement towards the north-east has taken place during the last seventy years.
See publications of individual magnetic observatories, more especially the Russian (_Annales de l'Observatoire Physique Central_), the French (_Annales du Bureau Central Météorologique de France_), and those of Kew, Greenwich, Falmouth, Stonyhurst, Potsdam, Wilhelmshaven, de Bilt, Uccle, O'Gyalla, Prague, Pola, Coimbra, San Fernando, Capo di Monte, Tiflis, Kolaba, Zi-ka-wei, Hong-Kong, Manila, Batavia, Mauritius, Agincourt (Toronto), the observatories of the U.S. Coast and Geodetic Survey, Rio de Janeiro, Melbourne.
In the references below the following abbreviations are used: B.A. = _British Association Reports_; Batavia = _Observations made at the Royal ... Observatory at Batavia_; M.Z. = _Meteorologische Zeitschrift_, edited by J. Hann and G. Hellman; P.R.S. = _Proceedings of the Royal Society of London_; P.T. = _Philosophical Transactions_; R. = _Repertorium für Meteorologie_, St Petersburg; T.M. = _Terrestrial Magnetism_, edited by L. A. Bauer; R.A.S. Notices = _Monthly Notices of the Royal Astronomical Society_. Treatises are referred to by the numbers attached to them; e.g. (1) p. 100 means p. 100 of Walker's _Terrestrial Magnetism_.
FOOTNOTES:
[A] For explanation of these numbers, see end of article.
[1] E. Walker, _Terrestrial and Cosmical Magnetism_ (Cambridge and London, 1856).
[1a]: H. Lloyd, _A Treatise on Magnetism General and Terrestrial_ (London, 1874). [2] E. Mascart, _Traité de magnétisme terrestre_ (Paris, 1900).
[3] L. A. Bauer, _United States Magnetic Declination Tables and Isogonic Charts, and Principal Facts relating to the Earth's Magnetism_ (Washington, 1902).
[4] Balfour Stewart, "Terrestrial Magnetism" (under "Meteorology"), _Ency. brit._ 9th ed.
[5] C. Chree, "Magnetism, Terrestrial," _Ency. brit._ 10th ed.
[6] _M.Z._ 1906, 23, p. 145.
[7] (3) p. 62.
[8] _K. Akad. van Wetenschappen_ (Amsterdam, 1895; Batavia, 1899, &c.).
[9] _Atlas des Erdmagnetismus_ (Riga, 1903).
[10] (1) p. 16, &c.
[11] _Kolaba (Colaba) Magnetical and Meteorological Observations_, 1896. Appendix Table II.
[12] (1) p. 21.
[13] _Report_ for 1906, App. 4, see also (3) p. 102.
[14] (1) p. 166.
[15] _Ergebnisse der mag. Beobachtungen in Potsdam_, 1901, p. xxxvi.
[16] _U.S. Coast and Geodetic Survey Report_ for 1895, App. 1, &c.
[17] _T.M._ 1, pp. 62, 89, and 2, p. 68.
[18] (3) p. 45.
[19] _Die Elemente des Erdmagnetismus_, pp. 104.108.
[20] _Zur täglichen Variation der mag. Deklination (aus Heft II. des Archivs des Erdmagnetismus)_ (Potsdam, 1906).
[21] _M.Z._ 1888, 5, p. 225.
[22] _M.Z._ 1904, 21, p. 129.
[23] _P.T._ 202 A, p. 335.
[23a] _Comb. Phil. Soc. Trans._ 20, p. 165.
[24] _P.T._ 208 A, p. 205.
[25] _P.T._ 203 A, p. 151.
[26] _P.T._ 171. p. 541; _P.R.S._ 63, p. 64.
[27] _R.A.S. Notices_ 60, p. 142.
[28] _Rendiconti del R. Ist. Lomb._ 1902, Series II. vol. 35.
[29] _R._ 1889, vol. 12, no. 8.
[30] _B.A. Report_, 1898, p. 80.
[31] _P.R.S._ (A) 79, p. 151.
[32] _P.T._ 204 A, p. 373.
[33] _Ann. du Bureau Central Météorologique, année 1897_, 1 Mem. p. B65.
[34] _P.T._ 161, p. 307.
[35] _M.Z._ 1895, 12, p. 321.
[35a] _P.T._ 1851, p. 123; and 1852, p. 103, see also (4) § 38.
[36] _P.T._ 159, p. 363.
[37] (1) p. 92.
[38] _R.A.S. Notices_ 65, p. 666.
[39] _R.A.S. Notices_, 65, pp. 2 and 538.
[40] _K. Akad. van Wetenschappen_ (Amsterdam, 1906) p. 266.
[41] _R.A.S. Notices_ 65, p. 520.
[42] _B.A. Reports_, 1880, p. 201 and 1881, p. 463.
[43] _Anhang Ergebnisse der mag. Beob. in Potsdam_, 1896.
[44] _M.Z._ 1899, 16, p. 385.
[45] _P.T._ 166, p. 387.
[46] _Trans. Can. Inst._ 1898-1899, p. 345, and Proc. Roy. Ast. Soc. of Canada, 1902-1903, p. 74, 1904, p. xiv., &c.
[47] _R.A.S. Notices_ 65, p. 186.
[48] _T.M._ 10, p. 1.
[49] _Expédition norvégienne de 1899-1900_ (Christiania, 1901).
[50] _Thèses présentées à la Faculté des Sciences_ (Paris, 1903).
[51] _Nat. Tijdschrift voor Nederlandsch-Indië_, 1902, p. 71.
[52] _Wied. Ann._ 1882, p. 336.
[53] _Sitz. der k. preuss. Akad. der Wiss._, 24th June 1897, &c.
[54] _T.M._ 12, p. 1.
[55] _P.T._ 143, p. 549; _St Helena Observations_, vol. ii., p. cxlvi., &c., (1) § 62.
[56] _Trans. R.S.E._ 24, p. 669.
[57] _P.T._ 178 A, p. 1.
[58] _Batavia_, vol. 16, &c.
[59] _Batavia_, Appendix to vol. 26.
[60] _R._ vol. 17, no. 1.
[61] _T.M._ 3, p. 1, &c.
[62] _P.T._ 181 A, p. 53 and 188 A.
[63] _Ann. du Bureau Central Mét._ vol. i. for years 1884 and 1887 to 1895.
[64] _Ann. dell' Uff. Centrale Met. e Geod._ vol. 14, pt. i. p. 57.
[65] _A Magnetic Survey of the Netherlands for the Epoch 1st Jan. 1891_ (Rotterdam, 1895).
[66] _Kg. Svenska Vet. Akad. Handlingar_, 1895, vol. 27, no. 7.
[67] _Denkschriften der math. naturwiss. Classe der k. Akad. des Wiss._ (Wien), vols. 62 and 67.
[68] _Journal of the College of Science, Tokyo_, 1904, vol. 14.
[69] _Ann. de l'observatoire ... de Toulouse_, 1907, vol. 7.
[70] _Ann. du Bureau Central Mét._ 1897, I. p. B36.
[71] _T.M._ 7, p. 74.
[72] _Bull. Imp. Univ. Odessa_ 85, p. 1, and _T.M._ 7, p. 67.
[73] _P.T._ 187 A, p. 345.
[74] _P.R.S._ 76 A, p. 181.
[75] _Bull. Soc. Imp. des Naturalistes de Moskau_, 1893, no. 4, p. 381, and _T.M._ 1, p. 50.
[76] _Forsch. zur deut. Landes- u. Volkskunde_, 1898, Bd. xi, 1, and _T.M._ 3, p. 77.
[77] _P.R.S._ 76 A, p. 507.
[78] Adams, _Scientific Papers_, II. p. 446.
[79] _B.A. Report_ for 1898, p. 109.
[80] _Abhand. der bayer, Akad. der Wiss._, 1895, vol. 19.
[81] _Sitz. k. Akad. der Wiss_. (Berlin), 1897, no. xviii., also _T.M._ 3, p. 191.
[82] _T.M._ 2, p. 11.
[83] _Die Elemente des Erdmagnetismus_ (St Petersburg, 1899), p. 103.
[84] _T.M._ 9, p. 113.
[85] _T.M._ 1, p. 77, and Nature, 57, pp. 160 and 180.
[86] _M.Z._ 15, p. 175.
[86a] _Sitz, der k. k. Akad. der Wiss. Wien, math. nat. Classe_, 1898, Bd. cvii., Abth. ii.
[87] _P.T._ (A) 180, p. 467.
[88] _Die Tägliche Periode der erdmagnetischen Elemente_ (St Petersburg, 1902).
[89] _R. Accad. Lincei Atti_, viii. 1899, pp. 69, 121, 176, 269 and previous volumes, see also _Séances de la Soc. Franc. de Physique_, 1899, p. 118.
[90] _Bull. Soc. Vaud., Sc. Nat._ 1906, 42, p. 225.
[91] _Comptes rendus_, 1905, 141, p. 567.
[92] _National Antarctic Expedition 1901-1904_, "Magnetic Observations."
[93] _The Norwegian Aurora Polaris Expedition 1902-1903_, vol. i.
[94] (1) p. 163.
(C. Ch.)