AVEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 571 



any energy. But since the inertias of two equal particles would be 

 unequal when they were going in opposite directions not perpendicular 

 to the direction of motion of the electric ether, we see that if the 

 system were brought into the condition assumed above, the accel- 

 erations at opposite points would be unequal and there would be 

 radiation. Hence to avoid radiation we must have the two ethers 

 relatively at rest. 



If we introduce internal forces other than those due to gravity, we 

 make the problem much more complicated, but it is evident that the 

 results would be of the same general nature, and that if the two ethers 

 were relatively at rest there would be absolutely no radiation. 



With this assumption of relative rest, we may now solve the problem 

 of the radiation from such a collection of minute particles rotating 

 about its axis, and at the same time moving through the ethers with a 

 velocity comparable to that of light. From the similarity of the 

 gravitational equations to the electromagnetic, we see that if we intro- 

 duce a gravitational relativity principle, exactly like the electro- 

 magnetic relativity principle with C substituted for c in all formulas, 

 the condition that two equal volume elements opposite to each other in 

 the body shall not radiate negative energy to infinity is that the 

 accelerations of the matter in them measured in the gravitational units 

 of moving distance and local time shall be equal and opposite. 



We may now suppose the particles to be brought into positions and 

 velocities that appear at a certain instant of the gravitational local 

 time of a system moving with the axis to be absolutely symmetrical 

 about the axis. But since the equation " force equals rate of increase 

 of momemtum," holds only when the electromagnetic units of local 

 time and moving distance are used, we see that the accelerations of 

 opposite particles are equal in the gravitational system only if all the 

 corresponding units are equal, or if 



C=c. 



And we see also that if other internal forces are introduced, the problem 

 is again more complicated, but that we have a similar result, that there 

 is absolutely no radiation of negative energy from any body rotating 

 about an axis of symmetry only with Theory V. 



Radiation from two or more Gravitating Bodies. — If, however, we 

 consider the more general case of two or more bodies moving under the 

 action of no forces but those of gravity, we shall find a small amount 

 of radiation even with Theory V. But this unavoidable radiation is 

 very small, being in general for any pair of bodies less than the product 



