Part 3

Sir John Leslie used to attribute the stability of this tower to the cohesion of the mortar it is built with being sufficient to maintain it erect, in spite of its being out of the condition required by physics--to wit, that “in order that a column shall stand, a perpendicular let fall from the centre of gravity must fall within the base.” Sir John describes the Tower of Pisa to be in violation of this principle; but, according to later authorities, the perpendicular falls within the base.

EARLY PRESENTIMENTS OF CENTRIFUGAL FORCES.

Jacobi, in his researches on the mathematical knowledge of the Greeks, comments on “the profound consideration of nature evinced by Anaxagoras, in whom we read with astonishment a passage asserting that the moon, if the centrifugal force were intermitted, would fall to the earth like a stone from a sling.” Anaxagoras likewise applied the same theory of “falling where the force of rotation had been intermitted” to all the material celestial bodies. In Aristotle and Simplicius may also be traced the idea of “the non-falling of heavenly bodies when the rotatory force predominates over the actual falling force, or downward attraction;” and Simplicius mentions that “water in a phial is not spilt when the movement of rotation is more rapid than the downward movement of the water.” This is illustrated at the present day by rapidly whirling a pail half-filled with water without spilling a drop.

Plato had a clearer idea than Aristotle of the _attractive force_ exercised by the earth’s centre on all heavy bodies removed from it; for he was acquainted with the acceleration of falling bodies, although he did not correctly understand the cause. John Philoponus, the Alexandrian, probably in the sixth century, was the first who ascribed the movement of the heavenly bodies to a primitive impulse, connecting with this idea that of the fall of bodies, or the tendency of all substances, whether heavy or light, to reach the ground. The idea conceived by Copernicus, and more clearly expressed by Kepler, who even applied it to the ebb and flow of the ocean, received in 1666 and 1674 a new impulse from Robert Hooke; and next Newton’s theory of gravitation presented the grand means of converting the whole of physical astronomy into a true _mechanism of the heavens_.

The law of gravitation knows no exception; it accounts accurately for the most complex motions of the members of our own system; nay more, the paths of double stars, far removed from all appreciable effects of our portion of the universe, are in perfect accordance with its theory.[8]

HEIGHT OF FALLS.

The fancy of the Greeks delighted itself in wild visions of the height of falls. In Hesiod’s _Theogony_ it is said, speaking of the fall of the Titans into Tartarus, “if a brazen anvil were to fall from heaven nine days and nine nights long, it would reach the earth on the tenth.” This descent of the anvil in 777,600 seconds of time gives an equivalent in distance of 309,424 geographical miles (allowance being made, according to Galle’s calculation, for the considerable diminution in force of attraction at planetary distances); therefore 1½ times the distance of the moon from the earth. But, according to the _Iliad_, Hephæstus fell down to Lemnos in one day; “when but a little breath was still in him.”--_Note to Humboldt’s Cosmos_, vol. iii.

RATE OF THE FALL OF BODIES.

A body falls in gravity precisely 16-1/16 feet in a second, and the velocity increases according to the squares of the time, viz.:

In ¼ (quarter of a second) a body falls 1 foot. ½ (half a second) 4 feet. 1 second 16 ” 2 ditto 64 ” 3 ditto 144 ”

The power of gravity at two miles distance from the earth is four times less than at one mile; at three miles nine times less, and so on. It goes on lessening, but is never destroyed.--_Notes in various Sciences._

VARIETIES OF SPEED.

A French scientific work states the ordinary rate to be:

per second. Of a man walking 4 feet. Of a good horse in harness 12 ” Of a rein-deer in a sledge on the ice 26 ” Of an English race-horse 43 ” Of a hare 88 ” Of a good sailing ship 19 ” Of the wind 82 ” Of sound 1038 ” Of a 24-pounder cannon-ball 1300 ”

LIFTING HEAVY PERSONS.

One of the most extraordinary pages in Sir David Brewster’s _Letters on Natural Magic_ is the experiment in which a heavy man is raised with the greatest facility when he is lifted up the instant that his own lungs, and those of the persons who raise him, are inflated with air. Thus the heaviest person in the party lies down upon two chairs, his legs being supported by the one and his back by the other. Four persons, one at each leg, and one at each shoulder, then try to raise him--the person to be raised giving two signals, by clapping his hands. At the first signal, he himself and the four lifters begin to draw a long and full breath; and when the inhalation is completed, or the lungs filled, the second signal is given for raising the person from the chair. To his own surprise, and that of his bearers, he rises with the greatest facility, as if he were no heavier than a feather. Sir David Brewster states that he has seen this inexplicable experiment performed more than once; and he appealed for testimony to Sir Walter Scott, who had repeatedly seen the experiment, and performed the part both of the load and of the bearer. It was first shown in England by Major H., who saw it performed in a large party at Venice, under the direction of an officer of the American navy.[9]

Sir David Brewster (in a letter to _Notes and Queries_, No. 143) further remarks, that “the inhalation of the lifters the moment the effort is made is doubtless essential, and for this reason: when we make a great effort, either in pulling or lifting, we always fill the chest with air previous to the effort; and when the inhalation is completed, we close the _rima glottidis_ to keep the air in the lungs. The chest being thus kept expanded, the pulling or lifting muscles have received as it were a fulcrum round which their power is exerted; and we can thus lift the greatest weight which the muscles are capable of doing. When the chest collapses by the escape of the air, the lifters lose their muscular power; reinhalation of air by the liftee can certainly add nothing to the power of the lifters, or diminish his own weight, which is only increased by the weight of the air which he inhales.”

“FORCE CAN NEITHER BE CREATED NOR DESTROYED.”

Professor Faraday, in his able inquiry upon “the Conservation of Force,” maintains that to admit that force may be destructible, or can altogether disappear, would be to admit that matter could be uncreated; for we know matter only by its forces. From his many illustrations we select the following:

The indestructibility of individual matter is a most important case of the Conservation of Chemical Force. A molecule has been endowed with powers which give rise in it to various qualities; and those never change, either in their nature or amount. A particle of oxygen is ever a particle of oxygen; nothing can in the least wear it. If it enters into combination, and disappears as oxygen; if it pass through a thousand combinations--animal, vegetable, mineral; if it lie hid for a thousand years, and then be evolved,--it is oxygen with the first qualities, neither more nor less. It has all its original force, and only that; the amount of force which it disengaged when hiding itself, has again to be employed in a reverse direction when it is set at liberty: and if, hereafter, we should decompose oxygen, and find it compounded of other particles, we should only increase the strength of the proof of the conservation of force; for we should have a right to say of these particles, long as they have been hidden, all that we could say of the oxygen itself.

In conclusion, he adds:

Let us not admit the destruction or creation of force without clear and constant proof. Just as the chemist owes all the perfection of his science to his dependence on the certainty of gravitation applied by the balance, so may the physical philosopher expect to find the greatest security and the utmost aid in the principle of the conservation of force. All that we have that is good and safe--as the steam-engine, the electric telegraph, &c.--witness to that principle; it would require a perpetual motion, a fire without heat, heat without a source, action without reaction, cause without effect, or effect without cause, to displace it from its rank as a law of nature.

NOTHING LOST IN THE MATERIAL WORLD.

“It is remarkable,” says Kobell in his _Mineral Kingdom_, “how a change of place, a circulation as it were, is appointed for the inanimate or naturally immovable things upon the earth; and how new conditions, new creations, are continually developing themselves in this way. I will not enter here into the evaporation of water, for instance from the widely-spreading ocean; how the clouds produced by this pass over into foreign lands and then fall again to the earth as rain, and how this wandering water is, partly at least, carried along new journeys, returning after various voyages to its original home: the mere mechanical phenomena, such as the transfer of seeds by the winds or by birds, or the decomposition of the surface of the earth by the friction of the elements, suffice to illustrate this.”

TIME AN ELEMENT OF FORCE.

Professor Faraday observes that Time is growing up daily into importance as an element in the exercise of Force, which he thus strikingly illustrates:

The earth moves in its orbit of time; the crust of the earth moves in time; light moves in time; an electro-magnet requires time for its charge by an electric current: to inquire, therefore, whether power, acting either at sensible or insensible distances, always acts in _time_, is not to be metaphysical; if it acts in time and across space, it must act by physical lines of force; and our view of the nature of force may be affected to the extremest degree by the conclusions which experiment and observation on time may supply, being perhaps finally determinable only by them. To inquire after the possible time in which gravitating, magnetic, or electric force is exerted, is no more metaphysical than to mark the times of the hands of a clock in their progress; or that of the temple of Serapis, and its ascents and descents; or the periods of the occultation of Jupiter’s satellites; or that in which the light comes from them to the earth. Again, in some of the known cases of the action of time something happens while _the time_ is passing which did not happen before, and does not continue after; it is therefore not metaphysical to expect an effect in _every_ case, or to endeavour to discover its existence and determine its nature.

CALCULATION OF HEIGHTS AND DISTANCES.

By the assistance of a seconds watch the following interesting calculations may be made:

If a traveller, when on a precipice or on the top of a building, wish to ascertain the height, he should drop a stone, or any other substance sufficiently heavy not to be impeded by the resistance of the atmosphere; and the number of seconds which elapse before it reaches the bottom, carefully noted on a seconds watch, will give the height. For the stone will fall through the space of 16-1/8 feet during the first second, and will increase in rapidity as the square of the time employed in the fall: if, therefore, 16-1/8 be multiplied by the number of seconds the stone has taken to fall, this product also multiplied by the same number of seconds will give the height. Suppose the stone takes five seconds to reach the bottom:

16-1/8 × 5 = 80-5/8 × 5 = 403-1/8, height of the precipice.

The Count Xavier de Maistre, in his _Expédition nocturne autour de ma Chambre_, anxious to ascertain the exact height of his room from the ground on which Turin is built, tells us he proceeded as follows: “My heart beat quickly, and I just counted three pulsations from the instant I dropped my slipper until I heard the sound as it fell in the street, which, according to the calculations made of the time taken by bodies in their accelerated fall, and of that employed by the sonorous undulations of the air to arrive from the street to my ear, gave the height of my apartment as 94 feet 3 inches 1 tenth (French measure), supposing that my heart, agitated as it was, beat 120 times in a minute.”

A person travelling may ascertain his rate of walking by the aid of a slight string with a piece of lead at one end, and the use of a seconds watch; the string being knotted at distances of 44 feet, the 120th part of an English mile, and bearing the same proportion to a mile that half a minute bears to an hour. If the traveller, when going at his usual rate, drops the lead, and suffers the string to slip through his hand, the number of knots which pass in half a minute indicate the number of miles he walks in an hour. This contrivance is similar to a _log-line_ for ascertaining a ship’s rate at sea: the lead is enclosed in wood (whence the name _log_), that it may float, and the divisions, which are called _knots_, are measured for nautical miles. Thus, if ten knots are passed in half a minute, they show that the vessel is sailing at the rate of ten knots, or miles, an hour: a seconds watch would here be of great service, but the half-minute sand-glass is in general use.

The rapidity of a river may be ascertained by throwing in a light floating substance, which, if not agitated by the wind, will move with the same celerity as the water: the distance it floats in a certain number of seconds will give the rapidity of the stream; and this indicates the height of its source, the nature of its bottom, &c.--See _Sir Howard Douglas on Bridges_. _Thomson’s Time and Time-keepers._

SAND IN THE HOUR-GLASS.

It is a noteworthy fact, that the flow of Sand in the Hour-glass is perfectly equable, whatever may be the quantity in the glass; that is, the sand runs no faster when the upper half of the glass is quite full than when it is nearly empty. It would, however, be natural enough to conclude, that when full of sand it would be more swiftly urged through the aperture than when the glass was only a quarter full, and near the close of the hour.

The fact of the even flow of sand may be proved by a very simple experiment. Provide some silver sand, dry it over or before the fire, and pass it through a tolerably fine sieve. Then take a tube, of any length or diameter, closed at one end, in which make a small hole, say the eighth of an inch; stop this with a peg, and fill up the tube with the sifted sand. Hold the tube steadily, or fix it to a wall or frame at any height from a table; remove the peg, and permit the sand to flow in any measure for any given time, and note the quantity. Then let the tube be emptied, and only half or a quarter filled with sand; measure again for a like time, and the same quantity of sand will flow: even if you press the sand in the tube with a ruler or stick, the flow of the sand through the hole will not be increased.

The above is explained by the fact, that when the sand is poured into the tube, it fills it with a succession of conical heaps; and that all the weight which the bottom of the tube sustains is only that of the heap which _first_ falls upon it, as the succeeding heaps do not press downward, but only against the sides or walls of the tube.

FIGURE OF THE EARTH.

By means of a purely astronomical determination, based upon the action which the earth exerts on the motion of the moon, or, in other words, on the inequalities in lunar longitudes and latitudes, Laplace has shown in one single result the mean Figure of the Earth.

It is very remarkable that an astronomer, without leaving his observatory, may, merely by comparing his observations with mean analytical results, not only be enabled to determine with exactness the size and degree of ellipticity of the earth, but also its distance from the sun and moon; results that otherwise could only be arrived at by long and arduous expeditions to the most remote parts of both hemispheres. The moon may therefore, by the observation of its movements, render appreciable to the higher departments of astronomy the ellipticity of the earth, as it taught the early astronomers the rotundity of our earth by means of its eclipses.--_Laplace’s Expos. du Syst. du Monde._

HOW TO ASCERTAIN THE EARTH’S MAGNITUDE.

Sir John Herschel gives the following means of approximation. It appears by observation that two points, each ten feet above the surface, cease to be visible from each other over still water, and, in average atmospheric circumstances, at a distance of about eight miles. But 10 feet is the 528th part of a mile; so that half their distance, or four miles, is to the height of each as 4 × 528, or 2112:1, and therefore in the same proportion to four miles is the length of the earth’s diameter. It must, therefore, be equal to 4 × 2112 = 8448, or in round numbers, about 8000 miles, which is not very far from the truth.

The excess is, however, about 100 miles, or 1/80th part. As convenient numbers to remember, the reader may bear in mind, that in our latitude there are just as many thousands of feet in a degree of the meridian as there are days in the year (365); that, speaking loosely, a degree is about seventy British statute miles, and a second about 100 feet; that the equatorial circumference of the earth is a little less than 25,000 miles (24,899), and the ellipticity or polar flattening amounts to 1/300th part of the diameter.--_Outlines of Astronomy._

MASS AND DENSITY OF THE EARTH.

With regard to the determination of the Mass and Density of the Earth by direct experiment, we have, in addition to the deviations of the pendulum produced by mountain masses, the variation of the same instruments when placed in a mine 1200 feet in depth. The most recent experiments were conducted by Professor Airy, in the Harton coal-pit, near South Shields:[10] the oscillations of the pendulum at the bottom of the pit were compared with those of a clock above; the beats of the clock were transferred below for comparison by an electrio wire; and it was thus determined that a pendulum vibrating seconds at the mouth of the pit would gain 2¼ seconds per day at its bottom. The final result of the calculations depending on this experiment, which were published in the _Philosophical Transactions_ of 1856, gives 6·565 for the mean density of the earth. The celebrated Cavendish experiment, by means of which the density of the earth was determined by observing the attraction of leaden balls on each other, has been repeated in a manner exhibiting an astonishing amount of skill and patience by the late Mr. F. Baily.[11] The result of these experiments, combined with those previously made, gives as a mean result 5·441 as the earth’s density, when compared with water; thus confirming one of Newton’s astonishing divinations, that the mean density of the earth would be found to be between five and six times that of water.

Humboldt is, however, of opinion that “we know only the mass of the whole earth and its mean density by comparing it with the open strata, which alone are accessible to us. In the interior of the earth, where all knowledge of its chemical and mineralogical character fails, we are limited to as pure conjecture as in the remotest bodies that revolve round the sun. We can determine nothing with certainty regarding the depth at which the geological strata must be supposed to be in a state of softening or of liquid fusion, of the condition of fluids when heated under an enormous pressure, or of the law of the increase of density from the upper surface to the centre of the earth.”--_Cosmos_, vol. i.

In M. Foucault’s beautiful experiment, by means of the vibration of a long pendulum, consisting of a heavy mass of metal suspended by a long wire from a strong fixed support, is demonstrated to the eye the rotation of the earth. The Gyroscope of the same philosopher is regarded not as a mere philosophical toy; but the principles of dynamics, by means of which it is made to demonstrate the earth’s rotation on its own axis, are explained with the greatest clearness. Thus the ingenuity of M. Foucault, combined with a profound knowledge of mechanics, has obtained proofs of one of the most interesting problems of astronomy from an unsuspected source.

THE EARTH AND MAN COMPARED.

The Earth--speaking roundly--is 8000 miles in diameter; the atmosphere is calculated to be fifty miles in altitude; the loftiest mountain peak is estimated at five miles above the level of the sea, for this height has never been visited by man; the deepest mine that he has formed is 1650 feet; and his own stature does not average six feet. Therefore, if it were possible for him to construct a globe 800 feet--or twice the height of St. Paul’s Cathedral--in diameter, and to place upon any one point of its surface an atom of 1/4380th of an inch in diameter, and 1/720th of an inch in height, it would correctly denote the proportion that man bears to the earth upon which he moves.

When by measurements, in which the evidence of the method advances equally with the precision of the results, the volume of the earth is reduced to the millionth part of the volume of the sun; when the sun himself, transported to the region of the stars, takes up a very modest place among the thousands of millions of those bodies that the telescope has revealed to us; when the 38,000,000 of leagues which separate the earth from the sun have become, by reason of their comparative smallness, a base totally insufficient for ascertaining the dimensions of the visible universe; when even the swiftness of the luminous rays (77,000 leagues per second) barely suffices for the common valuations of science; when, in short, by a chain of irresistible proofs, certain stars have retired to distances that light could not traverse in less than a million of years;--we feel as if annihilated by such immensities. In assigning to man and to the planet that he inhabits so small a position in the material world, astronomy seems really to have made progress only to humble us.--_Arago._

MEAN TEMPERATURE OF THE EARTH’S SURFACE.

Professor Dove has shown, by taking at all seasons the mean of the temperature of points diametrically opposite to each other, that the mean temperature _of the whole earth’s surface_ in June considerably exceeds that in December. This result, which is at variance with the greater proximity of the sun in December, is, however, due to a totally different and very powerful cause,--the greater amount of land in that hemisphere which has its summer solstice in June (_i. e._ the northern); and the fact is so explained by him. The effect of land under sunshine is to throw heat into the general atmosphere, and to distribute it by the carrying power of the latter over the whole earth. Water is much less effective in this respect, the heat penetrating its depths and being there absorbed; so that the surface never acquires a very elevated temperature, even under the equator.--_Sir John Herschel’s Outlines._

TEMPERATURE OF THE EARTH STATIONARY.