360 BELL SYSTEM TECHXICAL JOURNAL 



tern describes the result of setting in motion the particle which is described 

 by the stationary pattern. Without further knowledge or assumptions re- 

 garding the factors which control the form of the pattern, we can go no 

 farther in this direction by theory alone. Rather than try to guess at these 

 factors, it seems preferable to investigate what properties the wave patterns 

 must have in order to conform to the known results of experiment. 



Let us start with the Michelson-Morley experiment to which the earlier 

 ether theory did not conform. The entire apparatus involved in the experi- 

 ment is now to be considered as made up of particles each of which consists 

 of a wave pattern in the ether. The apparatus as a whole may be regarded 

 as a more complicated wave pattern. The interference pattern formed by 

 the light beams may, if we wish, be included in the over-all pattern. The 

 results to be expected in the experiment do not depend on the oscillatory 

 nature of the wave, nor on its amplitude or phase, but only on its spatial 

 distribution, which is determined by the envelope factors. It is obvious from 

 (8) that, for any uniform velocity — F of the ether relative to the apparatus, 

 the ratios of the dimensions of the envelope along the motion to those across 



it are reduced, relative to their values when V is zero, in the ratio - . That is 



to say the apparatus like the fringes undergo this change in relative dimen- 

 sions. But, as is well known, this is exactly what is required in order that 

 there shall be no apparent motion of the fringes. Hence any one of the 

 stationary patterns in a moving ether, as represented by (8), is consistent 

 with the experiment. This experiment therefore furnishes no basis for select- 

 ing any particular pattern. 



More generally, in any experiment, the distances and time intervals 

 which are available as standards of comparison are associated with the 

 wave i)atterns and change with their motion. Thus we may, following the 

 special theory of relativity, define an auxiliary space and time, the units 

 of which are associated with the dimensions and cyclic interval of a par- 

 ticular periodic wave pattern. This pattern then plays the roles of the 

 "practically rigid body" and the "clock" which determine space and time in 

 relativity theory. An examination of (8) shows that the dimensions of the 

 pattern, its frequency, and its phase change with the velocity of the ether 

 relative to the pattern in just the way that the corresponding quantities 

 associated with the rigid body and clock change with velocity in the rela- 

 tivity theory. But there these changes arc known to be sucli that no experi- 

 ment can detect the velocity involved. Tt follows, therefore, that no experi- 

 ment in which the ai)])aratus consists of wave patterns of small amplitude 

 is capable of detecting the velocity V, in (8), which in tliis case is the velocity 

 of the ether relative to the a])])aratus. Hence any of the above j^at terns are 

 consistent with the taiUirc of all exj)erimciils designed to detect motion 



