mm. The mean result of nearly 100 fairly accordant determinations

was:--

Velocity of light in air 299,828 km. per sec. Reduction to a vacuum +82 Velocity of light in a vacuum 299,910 ± 50

Newcomb.

While this work was in progress Simon Newcomb obtained the official support necessary to make a determination on a yet larger scale. The most important modifications made in the Foucault-Michelson system were the following:--

1. Placing the reflector at the much greater distance of several kilometres.

2. In order that the disturbances of the return image due to the passage of the ray through more than 7 km. of air might be reduced to a minimum, an ordinary telescope of the "broken back" form was used to send the ray to the revolving mirror.

3. The speed of the mirror was, as in Michelson's experiments, completely under control of the observer, so that by drawing one or the other of two cords held in the hand the return image could be kept in any required position. In making each measure the receiving telescope hereafter described was placed in a fixed position and during the "run" the image was kept as nearly as practicable upon a vertical thread passing through its focus. A "run" generally lasted about two minutes, during which time the mirror commonly made between 25,000 and 30,000 revolutions. The speed per second was found by dividing the entire number of revolutions by the number of seconds in the "run." The extreme deviations between the times of transmission of the light, as derived from any two runs, never approached to the thousandth part of its entire amount. The average deviation from the mean was indeed less than {1/5000} part of the whole.

To avoid the injurious effect of the directly reflected flash, as well as to render unnecessary a comparison between the directions of the outgoing and the return ray, a second telescope, turning horizontally on an axis coincident with that of the revolving mirror, was used to receive the return ray after reflection. This required the use of an elongated mirror of which the upper half of the surface reflected the outgoing ray, and the lower other half received and reflected the ray on its return. On this system it was not necessary to incline the mirror in order to avoid the direct reflection of the return ray. The greatest advantage of this system was that the revolving mirror could be turned in either direction without break of continuity, so that the angular measures were made between the directions of the return ray after reflection when the mirror moved in opposite directions. In this way the speed of the mirror was as good as doubled, and the possible constant errors inherent in the reference to a fixed direction for the sending telescope were eliminated. The essentials of the apparatus are shown in fig. 4. The revolving mirror was a rectangular prism M of steel, 3 in. high and 1½ in. on a side in cross section, which was driven by a blast of air acting on two fan-wheels, not shown in the fig., one at the top, the other at the bottom of the mirror. NPO is the object-end of the fixed sending telescope the rays passing through it being reflected to the mirror by a prism P. The receiving telescope ABO is straight, and has its objective under O. It was attached to a frame which could turn around the same axis as the mirror. The angle through which it moved was measured by a divided arc immediately below its eye-piece, which is not shown in the figure. The position AB is that for receiving the ray during a rotation of the mirror in the anti-clockwise direction; the position A´B´ that for a clockwise rotation.

In these measures the observing station was at Fort Myer, on a hill above the west bank of the Potomac river. The distant reflector was first placed in the grounds of the Naval Observatory, at a distance of 2551 metres. But the definitive measures were made with the reflector at the base of the Washington monument, 3721 metres distant. The revolving mirror was of nickel-plated steel, polished on all four vertical sides. Thus four reflections of the ray were received during each turn of the mirror, which would be coincident were the form of the mirror invariable. During the preliminary series of measures it was found that two images of the return ray were sometimes formed, which would result in two different conclusions as to the velocity of light, according as one or the other was observed. The only explanation of this defect which presented itself was a tortional vibration of the revolving mirror, coinciding in period with that of revolution, but it was first thought that the effect was only occasional.

In the summer of 1881 the distant reflector was removed from the Observatory to the Monument station. Six measures made in August and September showed a systematic deviation of +67 km. per second from the result of the Observatory series. This difference led to measures for eliminating the defect from which it was supposed to arise. The pivots of the mirror were reground, and a change made in the arrangement, which would permit of the effect of the vibration being determined and eliminated. This consisted in making the relative position of the sending and receiving telescopes interchangeable. In this way, if the measured deflection was too great in one position of the telescopes, it would be too small by an equal amount in the reverse position. As a matter of fact, when the definitive measures were made, it was found that with the improved pivots the mean result was the same in the two positions. But the new result differed systematically from both the former ones. Thirteen measures were made from the Monument in the summer of 1882, the results of which will first be stated in the form of the time required by the ray to go and come. Expressed in millionths of a second this was:--

Least result of the 13 measures 24.819 Greatest result 24.831 Double distance between mirrors 7.44242 km.

Applying a correction of +12 km. for a slight convexity in the face of the revolving mirror, this gives as the mean result for the speed of light in air, 299,778 km. per second. The mean results for the three series were:--

Observatory, 1880-1881 V in air = 299,627 Monument, 1881 V " = 299,694 Monument, 1882 V " = 299,778

The last result being the only one from which the effect of distortion was completely eliminated, has been adopted as definitive. For reduction to a vacuum it requires a correction of +82 km. Thus the final result was concluded to be

_Velocity of light in vacuo_ = 299,860 km. per second.

This result being less by 50 km. than that of Michelson, the latter made another determination with improved apparatus and arrangements at the Case School of Applied Science in Cleveland. The result was

_Velocity in vacuo_ = 299,853 km. per second.

So far as could be determined from the discordance of the separate measures, the mean error of Newcomb's result would be less than ±10 km. But making allowance for the various sources of systematic error the actual probable error was estimated at ±30 km.

It seems remarkable that since these determinations were made, a period during which great improvements have become possible in every part of the apparatus, no complete redetermination of this fundamental physical constant has been carried out.

The experimental measures thus far cited have been primarily those of the velocity of light in air, the reduction to a vacuum being derived from theory alone. The fundamental constant at the basis of the whole theory is the speed of light in a vacuum, such as the celestial spaces. The question of the relation between the velocity in vacuo, and in a transparent medium of any sort, belongs to the domain of physical optics. Referring to the preceding section for the principles at play we shall in the present part of the article confine ourselves to the experimental results. With the theory of the effect of a transparent medium is associated that of the possible differences in the speed of light of different colours.

Velocity and wave-length.

The question whether the speed of light in vacuo varies with its wave-length seems to be settled with entire certainty by observations of variable stars. These are situated at different distances, some being so far that light must be several centuries in reaching us from them. Were there any difference in the speed of light of various colours it would be shown by a change in the colour of the star as its light waxed and waned. The light of greatest speed preceding that of lesser speed would, when emanated during the rising phase, impress its own colour on that which it overtook. The slower light would predominate during the falling phase. If there were a difference of 10 minutes in the time at which light from the two ends of the visible spectrum arrived, it would be shown by this test. As not the slightest effect of the kind has ever been seen, it seems certain that the difference, if any, cannot approximate to {1/1.000.000} part of the entire speed. The case is different when light passes through a refracting medium. It is a theoretical result of the undulatory theory of light that its velocity in such a medium is inversely proportional to the refractive index of the medium. This being different for different colours, we must expect a corresponding difference in the velocity.

Foucault and Michelson have tested these results of the undulatory theory by comparing the time required for a ray of light to pass through a tube filled with a refracting medium, and through air. Foucault thus found, in a general way, that there actually was a retardation; but his observations took account only of the mean retardation of light of all the wave-lengths, which he found to correspond with the undulatory theory. Michelson went further by determining the retardation of light of various wave-lengths in carbon bisulphide. He made two series of experiments, one with light near the brightest part of the spectrum; the other with red and blue light. Putting V for the speed in a vacuum and V1 for that in the medium, his result was

Yellow light V : V1 = 1.758 Refractive index for yellow 1.64 Difference from theory +0.12

The estimated uncertainty was only 0.02, or 1/6 of the difference between observation and theory.

The comparison of red and blue light was made differentially. The colours selected were of wave-length about 0.62 for red and 0.49 for blue. Putting V_r and V_b for the speeds of red and blue light respectively in bisulphide of carbon, the mean result compares with theory as follows:--

Observed value of the ratio V_r, V_b 1.0245 Theoretical value (Verdet) 1.025

This agreement may be regarded as perfect. It shows that the divergence of the speed of yellow light in the medium from theory, as found above, holds through the entire spectrum.

The excess of the retardation above that resulting from theory is probably due to a difference between "wave-speed" and "group-speed" pointed out by Rayleigh. Let fig. 5 represent a short series of progressive undulations of constant period and wave-length. The wave-speed is that required to carry a wave crest A to the position of the crest B in the wave time. But when a flash of light like that measured passes through a refracting medium, the front waves of the flash are continually dying away, as shown at the end of the figure, and the place of each is taken by the wave following. A familiar case of this sort is seen when a stone is thrown into a pond. The front waves die out one at a time, to be followed by others, each of which goes further than its predecessor, while new waves are formed in the rear. Hence the group, as represented in the figure by the larger waves in the middle, moves as a whole more slowly than do the individual waves. When the speed of light is measured the result is not the wave-speed as above defined, but something less, because the result depends on the time of the group passing through the medium. This lower speed is called the group-velocity of light. In a vacuum there is no dying out of the waves, so that the group-speed and the wave-speed are identical. From Michelson's experiments it would follow that the retardation was about {1/14} of the whole speed. This would indicate that in carbon bisulphide each individual light wave forming the front of a moving ray dies out in a space of about 15 wave-lengths.

AUTHORITIES.--For Foucault's descriptions of his experiments see _Comptes Rendus_ (September 22 and November 24, 1862), and _Recueil de Travaux Scientifiques de Léon Foucault_ (2 vols., 4to, Paris, 1878). Cornu's determination is found in _Annales de l'Observatoire de Paris, Mémoires_, vol. xiii. The works of Michelson and Newcomb are published _in extenso_ in the _Astronomical Papers of the American Ephemeris_, vols. i. and ii. (S. N.)

FOOTNOTES:

[1] The invention of "aethers" is to be carried back, at least, to the Greek philosophers, and with the growth of knowledge they were empirically postulated to explain many diverse phenomena. Only one "aether" has survived in modern science--that associated with light and electricity, and of which Lord Salisbury, in his presidential address to the British Association in 1894, said, "For more than two generations the main, if not the only, function of the word 'aether' has been to furnish a nominative case to the verb 'to undulate.'" (See AETHER.)

[2] With the Greeks the word "Optics" or [Greek: Optika] (from [Greek: optomai], the obsolete present of [Greek: orô], I see) was restricted to questions concerning vision, &c., and the nature of light.

[3] It seems probable that spectacles were in use towards the end of the 13th century. The Italian dictionary of the _Accademici della Crusca_ (1612) mentions a sermon of Jordan de Rivalto, published in 1305, which refers to the invention as "not twenty years since"; and Muschenbroek states that the tomb of Salvinus Armatus, a Florentine nobleman who died in 1317, bears an inscription assigning the invention to him. (See the articles TELESCOPE and CAMERA OBSCURA for the history of these instruments.)

[4] Newton's observation that a second refraction did not change the colours had been anticipated in 1648 by Marci de Kronland (1595-1667), professor of medicine at the university of Prague, in his _Thaumantias_, who studied the spectrum under the name of _Iris trigonia_. There is no evidence that Newton knew of this, although he mentions de Dominic's experiment with the glass globe containing water.

[5] The geometrical determination of the form of the surface which will reflect, or of the surface dividing two media which will refract, rays from one point to another, is very easily effected by using the "characteristic function" of Hamilton, which for the problems under consideration may be stated in the form that "the optical paths of all rays must be the same." In the case of reflection, if A and B be the diverging and converging points, and P a point on the reflecting surface, then the locus of P is such that AP + PB is constant. Therefore the surface is an ellipsoid of revolution having A and B as foci. If the rays be parallel, i.e. if A be at infinity, the surface is a paraboloid of revolution having B as focus and the axis parallel to the direction of the rays. In refraction if A be in the medium of index µ, and B in the medium of index µ´, the characteristic function shows that µAP + µ´PB, where P is a point on the surface, must be constant. Plane sections through A and B of such surfaces were originally investigated by Descartes, and are named Cartesian ovals. If the rays be parallel, i.e. A be at infinity, the surface becomes an ellipsoid of revolution having B for one focus, µ´/µ for eccentricity, and the axis parallel to the direction of the rays.

[6] Young's views of the nature of light, which he formulated as _Propositions_ and _Hypotheses_, are given _in extenso_ in the article INTERFERENCE. See also his article "Chromatics" in the supplementary volumes to the 3rd edition of the _Encyclopaedia Britannica_.

[7] A crucial test of the emission and undulatory theories, which was realized by Descartes, Newton, Fermat and others, consisted in determining the velocity of light in two differently refracting media. This experiment was conducted in 1850 by Foucault, who showed that the velocity was less in water than in air, thereby confirming the undulatory and invalidating the emission theory.

[8] Newton, _Opticks_ (London, 1704).

[9] _Trans. Irish Acad._ 15, p. 69 (1824); 16, part i. "Science," p. 4 (1830), part ii., _ibid._ p. 93 (1830); 17, part i., p. 1 (1832).

[10] This kind of type will always be used in this article to denote vectors.

[11] _Phil. Trans._ (1802), part i. p. 12.

[12] _Oeuvres complètes de Fresnel_ (Paris, 1866). (The researches were published between 1815 and 1827.)

[13] _Ann. Phys. Chem._ (1883), 18, p. 663.

[14] H. A. Lorentz, _Zittingsversl. Akad. v. Wet. Amsterdam, 4_ (1896), p. 176.

[15] H. A. Lorentz, _Abhandlungen über theoretische Physik_, 1 (1907), p. 415.

[16] Clerk Maxwell, _A Treatise on Electricity and Magnetism_ (Oxford, 1st ed., 1873).

[17] H. Abraham, _Rapports présentés au congrès de physique de 1900_ (Paris), 2, p. 247.

[18] Ibid., p. 225.

[19] _Phil. Trans._, 175 (1884), p. 343.

[20] _Ann. d. Phys. u. Chem._ 155 (1875), p. 403.

[21] Ibid. 153 (1874), p. 525.

[22] _Ann. d. Phys_. 11 (1903), p. 873.

[23] _Phys. Review_, 13 (1901), p. 293.

[24] _Hertz, Untersuchungen über die Ausbreitung der elektrischen Kraft_ (Leipzig, 1892).

[25] A. Righi, _L'Ottica delle oscillazioni elettriche_ (Bologna, 1897); P. Lebedew, _Ann. d. Phys. u. Chem._, 56 (1895), p. 1.

[26] "Reflection and Refraction," _Trans. Cambr. Phil. Soc._ 7, p. 1 (1837); "Double Refraction," ibid. p. 121 (1839).

[27] "Double Refraction," _Ann. d. Phys. u. Chem._ 25 (1832), p. 418; "Crystalline Reflection," _Abhandl. Akad. Berlin_ (1835), p. 1.

[28] _Trans. Irish Acad._ 21, "Science," p. 17 (1839).

[29] _Math. and Phys. Papers_ (London, 1890), 3, p. 466.

[30] Helmholtz, _Ann. d. Phys. u. Chem._, 154 (1875), p. 582.

[31] H. A. Lorentz, _Versuch einer Theorie der elektrischen u. optischen Erscheinungen in bewegten Körpern_ (1895) (Leipzig, 1906); J. Larmor, _Aether and Matter_ (Cambridge, 1900).

LIGHTFOOT, JOHN (1602-1675), English divine and rabbinical scholar, was the son of Thomas Lightfoot, vicar of Uttoxeter, Staffordshire, and was born at Stoke-upon-Trent on the 29th of March 1602. His education was received at Morton Green near Congleton, Cheshire, and at Christ's College, Cambridge, where he was reckoned the best orator among the undergraduates. After taking his degree he became assistant master at Repton in Derbyshire; after taking orders he was appointed curate of Norton-under-Hales in Shropshire. There he attracted the notice of Sir Rowland Cotton, an amateur Hebraist of some distinction, who made him his domestic chaplain at Bellaport. Shortly after the removal of Sir Rowland to London, Lightfoot, abandoning an intention to go abroad, accepted a charge at Stone in Staffordshire, where he continued for about two years. From Stone he removed to Hornsey, near London, for the sake of reading in the library of Sion College. His first published work, entitled _Erubhin, or Miscellanies, Christian and Judaical, penned for recreation at vacant hours_, and dedicated to Sir R. Cotton, appeared at London in 1629. In September 1630 he was presented by Sir R. Cotton to the rectory of Ashley in Staffordshire, where he remained until June, 1642, when he went to London, probably to superintend the publication of his next work, _A Few and New Observations upon the Book of Genesis: the most of them certain; the rest, probable; all, harmless, strange and rarely heard of before_, which appeared at London in that year. Soon after his arrival in London he became minister of St Bartholomew's church, near the Exchange; and in 1643 he was appointed to preach the sermon before the House of Commons on occasion of the public fast of the 29th of March. It was published under the title of _Elias Redivivus_, the text being Luke i. 17; in it a parallel is drawn between the Baptist's ministry and the work of reformation which in the preacher's judgment was incumbent on the parliament of his own day.

Lightfoot was also one of the original members of the Westminster Assembly; his "Journal of the Proceedings of the Assembly of Divines from January 1, 1643 to December 31, 1644," now printed in the thirteenth volume of the 8vo edition of his _Works_, is a valuable historical source for the brief period to which it relates. He was assiduous in his attendance, and, though frequently standing almost or quite alone, especially in the Erastian controversy, he exercised a material influence on the result of the discussions of the Assembly. In 1643 Lightfoot published _A Handful of Gleanings out of the Book of Exodus_, and in the same year he was made master of Catharine Hall by the parliamentary visitors of Cambridge, and also, on the recommendation of the Assembly, was promoted to the rectory of Much Munden in Hertfordshire; both appointments he retained until his death. In 1644 was published in London the first instalment of the laborious but never completed work of which the full title runs _The Harmony of the Four Evangelists among themselves, and with the Old Testament, with an explanation of the chiefest difficulties both in Language and Sense: