564 PROCEEDINGS OF THE AMERICAN ACADEMY 



For " Theory IV " let us assume that there is another vector h re- 

 lated to the vector g in the same way that magnetic force is related to 

 electric, and that these vectors satisfy the set of equations : 



V • g = — 4 irpk 



V -11 = 



ah 



V xg = - 



d{Ct) 



f = g -+- Bxh, 



where f is the force per unit mass due to the gravitational force g and 

 " gravimagnetic " force h. It will be noticed that these equations are 

 very much like the electromagnetic equations : 



V • E = 4 TTC 



V -H^O 



aE 



VxE = — 



d{ct) 



F = E + pxH 



where E and H are electric and magnetic forces, c the charge per unit 

 volume, P the ratio of the velocity of the charge at any point to the 

 velocity, c, of propagation of electromagnetic disturbances, and F the 

 force per unit charge due to electric and magnetic forces. 



If we assume with Einstein that there is no ether, and no universal 

 or absolute time, we readily see that these theories are all inconsistent 

 with this belief, with the single exception of the special case of Theory 

 IV which we may call "Theory V," in which C = c. If, on the other 

 hand, we assume the "conditional relativity principle," of Wiechert ^ 

 and assume the existence of ether and absolute time, we see a wider 

 range for Theory IV than that obtained by merely giving different 

 values to C, in that Theory IV does not define any particular state of 

 motion that may be assumed to be the state of absolute rest, and un- 



Wiechert, Relativitatsprinzip und Ather, Phys. Zeitsch., 12, 18-19. 



