1884.] equations of the electromagnetic field. 127 



of P will depend partly on electromagnetic, partly on electro- 

 static forces, and partly on the polarization of the dielectric pro- 

 duced by these. In both theories we write — -=- for the first part, 

 Helmholtz and Lorentz denote the electrostatic part by X, the 

 part depending on polarization by - -v- . Maxwell, assuming that 



the electrostatic forces have a potential, combines the two into one 



dW 

 term — ^— . In cases in which the assumption is true the two 

 ax 



methods should lead to the same result. 



We shall however for the sake of convenience in the future 

 work put O and not <I> for the potential of the forces produced by 

 the polarization and write 



*--*-£+* ^ 



remembering that according to Helmholtz H = <I>, while Maxwell 

 treating only the case in which X, Y, Z are derivable from a 

 potential puts generally, 



d£l dW 



dx dx ' 



Then we may state that the values of P, Q, R in the right-hand 

 sides of the two sets of equations 



£ = eP, etc., 



/ = ^P,etc, 



are the same in form though the equations which connect F, G, H 

 with the components of the current are different. 



And this brings us to another distinct point of difference. 

 According to Maxwell the components of the current in a di- 

 electric are f, g, h, according to Helmholtz they are f, 97, £. 



Hence taking Helmholtz's supposition first, we have from 

 (15), (1) and (18), 



dy d/3 d z ® = *j = * £ dP 



dy dz dxdt dt 



. d fdF , d£l v \ /in , 



etc. 

 and two similar equations. 



