444 The Theory of Aether and Electrons in the 



system of measurement furnished by the transformed axes, 

 with reference to which the particles are at rest. But accord- 

 ing to FitzGerald's hypothesis of contraction, when a material 

 body is in motion relative to the aether, in a direction parallel 

 to the axis of x, its dimensions parallel to this direction 

 contract in precisely this ratio; so that the equation of the 

 body, in terms of the coordinates x }) y^ z ly which move with 

 it, is unaltered. Thus the hypothesis of Fitz Gerald may be 

 expressed by the statement .that the equations of the figures 

 of ponderable bodies are covariant with respect to those trans- 

 formations for which the fundamental equations of the aether 

 are covariant. 



The covariance holds with respect to all linear homogeneous 

 transformations in the variables (x, y, z, t), of determinant 

 unity, which transform the expression (x" 2 + y 2 - + z~ - c 2 f) into 

 itself. This group comprises an infinite number of transforma- 

 tions ; so that there are an infinite number of sets of variables 

 resembling (x }) y lt c,, ,), of which any one set (x r , y r , z r , t r ) can 

 be derived from any other set (.r s , y s , z s , t s ) by a transformation 

 of the group ; among the sets we must of course include the 

 original set of coordinates (x, y, z, t). But hitherto we have 

 proceeded on the assumption that the original set (x, y, z, t) is 

 entitled to a primacy among all the other sets, since the axes 

 (x, y, z) have been supposed to possess the special property of 

 having no motion relative to the aether, and the time repre- 

 sented by the variable t has been understood to be a definite 

 physical quantity. The other sets of variables (.r r , y r , s r , t r ) 

 have been regarded merely as symbols convenient for use in 

 problems relating to moving bodies, but not as corresponding 

 to physical entities in the same degree as (x, y, z, t). "We 

 must now inquire whether this view is justified. 



The question amounts to asking whether absolute position 

 in space, or at any rate absolute fixity relative to the aether, is 

 something which can be brought within the bounds of human 

 knowledge. 



It is well known that the science of dynamics, as founded 



