Closing Years of the Nineteenth Century. 433 



Lorentz, in a communication to the Amsterdam Academy;* 

 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 motion 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 

 ur*l/c?, where w denotes the velocity of the earth, c the velocity 

 of light, and I 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 //2c 3 ; 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' /2c~) to unity. This is 

 Fitz Gerald's hypothesis of contraction. Since for the earth the 

 ratio w/c is only 



30 km. /sec. 

 300,000 km./sec.' 



the fraction w^jc- is only one hundred-millionth. 



Several further contributions to the theory of electrons in a 

 motionless aether were made in a short treatisef 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,J of Leipzig. Des Coudres had 

 observed the mutual inductance of coils in different circum- 

 stances 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). 



t Versuch einer Theorie Jer electrischen und optischen Erscheinungen in bewegten 

 Eorpern, 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 



