WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 569 



But if we now have two particles with constant accelerations, op- 

 positely directed, we see that the vectors g and h for one of the par- 

 ticles will have nearly opposite directions to the corresponding vectors 

 for the other particle at points very far from the two masses. For 

 such points we may then say the total gravitational force is 



_ _^ mir22ip i + W2?'ia-p2 



The fraction B'p^/^pi will have a meaning only in a case where it is 

 multiplied by a product of a scalar by a^i, or in a case where a^i and 

 2ip2 have the same direction, as in the limit ^i = oc , when it will ap- 

 proach a scalar limit. Unless this limit is — mi/mz, g will be an infini- 

 tesimal of the order of l/n. But if lim apa/a^i = — mjmxt then we 

 readily see that g and h are both infinitesimals of the order of \/rx or 

 of a higher order, and gxh is of the order of Xjrx or higher. But 

 this is possible for all directions only if m-iji.^ = — m^^^, and therefore 

 in this case, and only in this case, 



rLzffs^^-^^ = o 



where S is & sphere of radius r, surrounding the particles. Hence we 

 see that there is no radiation of negative energy from a pair of uni- 

 formly accelerated particles momentarily at rest, if, and only if, 



mi&i = — m-^2. 



Radiation from a Rotating Body. — Since Theory IV, with C ^ c, 

 is inconsistent with the unconditional relativity principle, we must, in 

 assuming the truth of it, assume the existence of an ether and an 

 absolute system of simultaneity. But if now we assume that gravity 

 is transmitted through an ether that is independent of the electro- 

 magnetic ether, and moving through it, we must assume the time 

 to be the same absolute time in both cases, and the lengths to be 

 measured in absolute units of length. 



If, with these assumptions, we consider the motion of a body rotating, 



