WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 563 



tion from the element, and h the gravitation constant, 6.480 X 1()~' 



cm 



-„ • This assumption involves the existence of " absolute time " 



gm. sec. 



and instantaneous action at a distance, but is a possible hypothesis if 



these are possible. 



The hypothesis which I shall call " Theory II " is the consequence 



of most of the mechanical explanations of gravitation, such as the 



well known Le Sage theory, and theories of attraction through the 



pressure of invisible radiation or through the pulsations of slightly 



compressible electrons in a less compressible fluid. According to this 



theory the attraction at any time t on any particle is determined by 



the matter that occupied each volume element at a time \i— j,\ 



where C is some very large velocity, and r is, as above, the distance 

 from the element. In this case, if we let [p] equal the value of p in 

 the element at this time, we have 



^-d'sr^^''^ 



For " Theory III " let us suppose any particle moving uniformly to 

 carry a perfectly symmetrical system of lines of force with it, so that 

 at any instant the forces due to it at all equidistant points will have 

 equal intensities and be directed exactly towards it. But if its motion 

 is changed by an infinitesimal amount, let us suppose that the disturb- 

 ance of the force is propagated with a velocity C relative to that of 

 the particle at the time the change of its velocity takes place. 



In this case, 



00 



where / is the distance at which the matter would have been at time 



t, that occupied the element dr with density [p]' at the time ( ^ — 7-, )' 



if it had kept since that time the velocity it then had. We may also 

 say 



„__^. f rr bJriVr 



^~ J J J r\l+B^-2BrTj 



where B is the ratio of the velocity of the matter in the element dr at 

 the time [ t — y^) to the velocity C. 



