WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 565 



less we make such a definition we have no single- valued definition of 

 any of our time derivatives, even though we have a definition of abso- 

 lute time. The physical significance of this statement is that, accord- 

 ing to Theory IV, all gravitational disturbances must be propagated 

 with a velocity C through an ether that is not necessarily at rest relative 

 to the electromagnetic ether. Therefore to define Theory V completely 

 in terms of Theory IV, we must say that the two ethers must be at 

 rest relative to each other, and that the two velocities C and c must 

 be equal. 



Objectio7i against Theories I-III. — If we now examine further the 

 consequences of these theories, we shall see that Theory I, if not im- 

 possible, is highly improbable ; and that Theory V is the only other 

 that does not involve a continual increase of energy of any system of 

 gravitating bodies. 



Assuming the unconditional relativity principle, all but Theory V 

 are, of course, impossible. But assuming the conditional relativity 

 principle, we see that Theory I involves either instantaneous action 

 through a medium that is also capable of propagation of disturbances 

 with a finite velocity, or else it involves true "action at a distance." 

 Also it has been shown by Wilkens ® that the changes of the perihelion 

 of Mercury and other astronomical phenomena, which are consistent 

 with the electromagnetic theory, are inconsistent with Theory I. 



These difficulties make it necessary to look for some other theory, 

 such as II. But if we assume the truth of this theory, we must say 

 that the components of a binary star revolving in circles about their 

 centre of gravity will each be accelerated at time ^ by a force directed 



towards a point where the other was at time ( ^ — 7^ ) ; and this force 



will have a component in the direction of motion which is an infini- 

 tesimal, if C is allowed to become infinite, of the order of | B | for the 

 other body. But no matter how large C may be, this component of 

 the force will never be absolutely zero. Hence the ever increasing 

 kinetic energy would tear any such system apart, even though the 

 components were unequal and the orbits not circular ; and even a 

 rotating planet would increase its energy of rotation until it burst, 

 and would continue increasing its energy forever, even after disrup- 

 tion ; so that, if Theory II held, the earth and the whole solar system 

 would have gone to pieces long ago and left not even the law of the 

 conservation of energy for a vain consolation. 



Theory III might be expected to remove this difficulty, but it does 



« Phys. Zeitsch., 7, No. 23, 846. 



