Chapter XXIII: Act 1871: , the jurisdiction, duties and command exercised by the lord (5)

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: