DEVELOPMENTS IN ELECTEOMAGNETISM- — BLOCH. 227 



theory shows that the effects should be of the order of ^- or smaller. 

 This theory then received a rude shock from the celebrated experi- 

 ment of Michelson (1881) relative to the interference of two rays 

 propagated at right angles to each other and which should show 

 the terms of the second order of ^. The negative result was irrec- 

 oncilable with the theory, the effect observed being less than one 

 one-hundredth of that calculated.^ We must therefore modify the 

 theory. 



The modification necessary was announced almost at the same time 

 by Lorentz and by Fitzgerald. It consisted in supposing that a 

 moving solid body suffers a contraction in the direction of its motion 

 equal to ^V^- This is the celebrated hypothesis known as the " con- 

 traction of Lorentz." It seems very strange at first sight and insti- 

 gated the experiments by Lord Rayleigh,^ and by Brace,^ who tried 

 to find evidence of this contraction in the double refraction which it 

 should produce. Their results were negative. In order to explain 

 these consequences and place the theory in a more satisfactory form, 

 Lorentz was led to a hypothesis which contained the germ of the 

 theory of relativity.* He showed that the electromagnetic equations 

 for bodies in motion could be put in the same form as for bodies at 

 rest by means of what is called the "transformation of Lorentz." 

 This permits the expression of the coordinates a?, y, s, and the time t 

 for a system in motion as a function of the coordinates a?o) 2/0? ^01 and 

 to for the system at rest, thus establishing a correspondence between 

 the electric and magnetic fields of the two systems. This group of 

 transformations contains, as a particular case, the hypothesis of con- 

 traction, which is found to be of the magnitude (1-^-)^, in agree- 

 ment almost to terms of the fourth order with the magnitude origi- 

 nally admitted. It further explains the negative results of Michel- 

 son, Rayleigh, and Brace. Through it we understand the negative 

 results of Trouton and Noble in their electrostatic experiment which 

 was expected to indicate the terms in ^-.^ 



The experiments explained by the transformation of Lorentz go 

 only to the terms in ^-. We do not loiow any at present which go 

 further, but it is natural to suppose that even taking into account 

 terms of higher orders, we will never be able to get evidence of the 

 motion of translation of the earth with reference to the ether. In 

 other words, we can probably detect only the relative motions of two 

 material systems with reference to each other and not their absolute 



1 The original experiment was made by Michelson and Morley in 1887 and repeated 

 most recently by Morley and Miiller. Phil. Mag., vol. 9, p. 680, 1905. 



2 Rayleigh, Phil. Mag., vol. 4, p. 678, 1902. 



3 Brace, Phil. Mag., vol. 7, p. 317, 1904. 



* See the admirable book by Lorentz, entitled " The Theory of p:iectrons," and published 

 by Teubner in Leipzig, 1909. 



8 Trouton and Noble, Phil. Trans., vol. 202, p. 165, 1903. See also Langevin, Comptes 

 Rendus, vol. 140, p. 1171, 1905. 



