Closing Years of the Nineteenth Century. 425 



encloses a large number of molecules, but which is small com- 

 pared with measurable quantities; and this equation may be 

 written 



Now, if P refers to differentiation at a fixed point of space (as 

 opposed to a differentiation which accompanies the moving body), 



we have 



(/&)*-? + (w.V)P, 



and (d/dt) V = Fdiv w; 

 so that 



/ou = P + (w . V) P + div w . P 



= P + curl [P . w] + div P . w + (P . V) w, 

 and therefore 



pu + pw = P + curl [P . w]. 



This equation determines the part of f>v which arises from the 

 dielectric molecules. 



The general equations of the aether thus become, when the 

 averaging process is performed, 



div d = 4>!r<?pi ~ 4-Trc 2 div P, div h = 0, 

 curl d = - h, 



curl h =- (1/c 2 ) d + 47r , 



( + P + curl [P . w] I 



In order to assimilate these to the ordinary electromagnetic 

 equations, we must evidently write 



d = E, the electric force; 

 (1/4-7TC 2 ) E + P = D, the electric induction ; 



h = H, the magnetic vector. 



The equations then become (writing p for p lt as there is no 

 longer any need to use the subscript), 



div D = p, - curl E = H, 



where div H = ' curl H = 4lrS ' 



S = conduction-current + convection-current + D + curl [P . w]. 



convection-current + conduction-current . 



