612 APPLIED MATHEMATICS 



at A, for example, will be late, but all will be equally so, and the 

 observer who ascertains them will not perceive it, since his watch is 

 slow; so, as the principle of relativity would have it, he will have no 

 means of knowing whether he is at rest or in absolute motion. 



Unhappily, that does not suffice, and complementary hypotheses 

 are necessary ; it is necessary to admit that bodies in motion undergo 

 a uniform contraction in the sense of the motion. One of the dia- 

 meters of the earth, for example, is shrunk by 200i0 w >000 in conse- 

 quence of the motion of our planet, while the other diameter retains 

 its normal length. Thus, the last little differences find themselves 

 compensated. And then there still is the hypothesis about forces. 

 Forces, whatever be their origin, gravity as well as elasticity, would 

 be reduced in a certain proportion in a world animated by a uniform 

 translation; or, rather, this would happen for the components perpen- 

 dicular to the translation; the components parallel would riot change. 



Resume, then, our example of two electrified bodies; these bodies 

 repel each other, but at the same time if all is carried along in a 

 uniform translation, they are equivalent to two parallel currents of 

 the same sense which attract each other. This electro-dynamic 

 attraction diminishes, therefore, the electro-static repulsion, and the 

 total repulsion is more feeble than if the two bodies were at rest. 

 But since to measure this repulsion we must balance it by another 

 force, and all these other forces are reduced in the same proportion, 

 we perceive nothing. 



Thus, all is arranged, but are all the doubts dissipated? 



What would happen if one could communicate by non-luminous 

 signals whose velocity of propagation differed from that of light? 

 If, after having adjusted the watches by the optical procedure, one 

 wished to verify the adjustment by the aid of these new signals, 

 then would appear divergences which would render evident the com- 

 mon translation of the two stations. And are such signals incon- 

 ceivable, if we admit with Laplace that universal gravitation is 

 transmitted a million times more rapidly than light? 



Thus, the principle of relativity has been valiantly defended in 

 these latter times, but the very energy of the defense proves how 

 serious was the attack. 



Let us speak now of the principle of Newton, on the equality of 

 action and reaction. 



This is intimately bound up with the preceding, and it seems 

 indeed that the fall of the one would involve that of the other. 

 Thus we should not be astonished to find here the same difficulties. 



Electrical phenomena, we think, are due to the displacements of 

 little charged particles, called electrons, immersed in the medium 

 * that we call ether. The movements of these electrons produce per- 

 turbations in the neighboring ether; these perturbations propagate 



