Non-existence of Density in the Elemental ^Ether. 477 



write everywhere the element of volume instead. It is itself 

 the integral of these elements of volume ; in other words, it 

 is spaee under a new aspect. In the geometrical way of 

 conceiving space, the parts into which it may be conceived 

 to be divided are thought of as they would be if at rest 

 relatively to one another. In the kinematical way of con- 

 ceiving space, which alone is in accordance with ichat ob- 

 jectively exists, we are to recognize that each portion of 

 volume is pervaded by the motions that actually subsist 

 within it, and that it can travel about carrying those motions 

 with it. In fact the volume occupied by a block of iron differs 

 from an equal volume occupied by air, only by the motions 

 that are going on within the one volume being different from 

 those that pervade the other. In every other respect they 

 are as exactly alike as one stationary portion of space is to 

 another. One such portion of space is not another : but it 

 is exactly like it ; and there is no limit to this resemblance 

 however small the portions compared may be. There is no 

 " texture " until there is motion. 



On the other hand, when, in investigating the motions of 

 ponderable matter, we have occasion to conceive the bodies 

 we are dealing with divided into small portions, it is only if 

 we stop short in our division so that the blocks we form do not 

 fall below a certain size, that we are justified in treating them 

 as resembling one another. When we thus stop short, the 

 blocks are in reality accumulations of more minute internal 

 motions ; and if we do not stop short, but carry the division 

 sufficiently far, we shall come down upon the individual 

 motions themselves, between which of course the most marked 

 differences would be found. 



It appears to be the same in regard to the luminiferous 

 aether. It is only when we do not subdivide too far, that we 

 are justified in speaking of the blocks as resembling one 

 another. The luminiferous aether seems to be a textured 

 medium like ponderable matter. But in the elemental aether 

 — in space itself regarded as movable — there are no such 

 limits. Its portions, however small, resemble one another 

 with mathematical exactness * ; except so far as there may be 

 different motions prevailing within those portions. 



* Empty coreless vortices involve the hypothesis of a medium that is 

 discontinuous and has boundaries ; or else (in the case of some coreless 

 vortices) of a medium which obeys two laws of motion, one for the part 

 of the medium that is interned on one side of a closed vortex sheet, and 

 another for the rest of the medium. Now it seems very improbable that 

 the objectively existing elemental tether — space under its kinematical 



