Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/453

This page has been proofread, but needs to be validated.

Closing Years of the Nineteenth Century.

433

Lorentz, in a communication to the Amsterdam Academy;^[1]after which it won favour in a gradually widening circle, until eventually it came to be generally taken as the basis of all theoretical investigations on the notion of ponderable bodies through the aether.

Let us first see how it explains Michelson's result. On the supposition that the aether is motionless, one of the two portions into which the original beam of light is divided should accomplish its journey in a time less than the other by $w 2 l / c 2$ , where $w$ denotes the velocity of the earth, $c$ the velocity of light, and $l$ the length of each arm. This would be exactly compensated if the arm which is pointed in the direction of the terrestrial motion were shorter than the other by an amount $w 2 l /2 c 2$ ; as would be the case if the linear dimensions of moving bodies were always contracted in the direction of their motion in the ratio of $(1 - w 2 /2 c 2)$ to unity. This is FitzGerald's hypothesis of contraction. Since for the earth the ratio $w / c$ is only

${\frac {30{\text{km./sec.}}}{300,000{\text{km./sec.}}}},$

the fraction $w 2 / c 2$ is only one hundred-millionth.

Several further contributions to the theory of electrons in motionless aether were made in a short treatise^[2] which was published by Lorentz in 1895. One of these related to the explanation of an experimental result obtained some years previously by Th, des Coudres,^[3] of Leipzig. Des Coudres had observed the mutual inductance of coils in different circumstances of inclination of their common axis to the direction of the earth's motion, but had been unable to detect any effect depending on the orientation. Lorentz now showed that this could be explained by considerations similar to those which

↑ Verslagen d. Kon. Ak, van Wetenschappen, 1892-3, p. 74 (November 26th 1892).
↑ Versuch einer Theorie der electrischen und optischen Erscheinungen in beweglen Körpern, von H. A. Lorentz; Leiden, E. J. Brill. It was reprinted by Teubner, of Leipzig, in 1906.
↑ Ann. d. Phys. xxxviii (1889), p. 73.

2 F

[1] Verslagen d. Kon. Ak, van Wetenschappen, 1892-3, p. 74 (November 26th 1892).

[2] Versuch einer Theorie der electrischen und optischen Erscheinungen in beweglen Körpern, von H. A. Lorentz; Leiden, E. J. Brill. It was reprinted by Teubner, of Leipzig, in 1906.

[3] Ann. d. Phys. xxxviii (1889), p. 73.

[1]

[2]

[3]