ON THE PRINCIPLE OF RELATIVITY. 237 



As far as the time-space co-ordinates are conditioned in tins way 

 by laws of dynamics, (xyzt) and {x' y' z' t') are equally valid if 



x' = x — at, y'=y — ht, z' = z — ct, t'=t, 



where (a, b, c) is any constant velocity. 



Transformations of this type form a group, i.e., the successive appli- 

 cation of two such transformations gives the same result as that given by 

 a certain other transformation of the same type. If we say that two 

 events are simultaneous if they have the same t, it is characteristic of what 

 we may call the Newtonian group that simultaneity persists. 



2. 



The advent of the theory of an electromagnetic medium filling all 

 space seemed to promise in the cether a unique frame of reference relative 

 to which the velocities of points might be specified, and experiments were 

 quickly made to determine the velocity of the earth relative to the aether, 

 with results, as everyone well knows, which failed as completely to give 

 evidence of any such velocity, as dynamical science had failed to give 

 evidence of an absolute velocity of a material body in space. 



In the famous Michelson and Morley experiment ' the only suggestion 

 that could be. made to account for the failure to discover a difference 

 between the velocities of propagation of light in different directions was 

 that, owing to the influence of the motion through the aether, the dimen- 

 sions of the apparatus were reduced in the direction of motion in the 

 ratio «/l — v 2 /c 2 . 



The possibility of such an automatic contraction was, of course, sug- 

 gested by the gradually strengthening belief that the forces which hold 

 the elementary constituents of a material body together are of an electrical 

 nature— that is, are exerted through the medium of the aether filling the 

 spaces between those elements. The search for a systematic theory, 

 whereby a contraction of exactly this amount might be expected, inde- 

 pendently of the nature of the body in question, of the size of its molecules, 

 and of the distance between them, was the means of bringing into pro- 

 minence a remarkable property of the equations of the electromagnetic 

 field,' which is, in fact, the whole foundation of the principle of relativity 

 from a mathematical point of view. 



This property, first noted in another connection by Voigt, was de- 

 veloped and applied by Larmor ' and Lorcntz. ' 



It is assumed that there is a frame of reference for which the funda- 

 mental equations in free space have the form 



= curl h —■-«- = curl c 



c ot c at 



div e = dir h = . . . (a) 



where e, h are the electric and magnetic intensities, and c is the velocity 

 of light. 



v. Phil. Mag., (6) 8, p. 753. 2 v. JEtlier and Matter, p. 173. 



3 v. Amst. Proceedings, 1904. 



