41Ö 



X, = i (d.' - d/ - d.') + h (h.' - h/ - h:«), 

 X^ = dx dy + hx hy, X, = dx dz + hx hr, etc, 



.v.^ , . G= — [d.hl. 



c 



This sliows that the ponderomotive forces can still be expressed 

 by means of Maxwell's stresses and of the electromagnetic momen- 

 tum G. It should be noticed that this is possible because we have 

 the positive sign in (5) and the negative sign in (6). 



The well known expressions for the electric and liie magnetic 

 energj and for the tlow of energy likewise remain unchanged. 

 Indeed, starting from the fundamental equations, one finds for the 

 work, per unit of time and unit of volume, of the forces exerted 

 by the field 



(p f • V) + (ft g . w) = - -^ — ^ï« S , 



^=i(cl' + h'), S = c[d.h]. 



^ 4. If the distribution and the motion of the charges are known, 

 the field can be calculated by means of two scalar potentials q , ■/ 

 and two vector potentials a, b. These functions are given by the 

 formulae 



{f ^= — I -^^^ dS, X = - — I dS, 



4jr^y r 4jr J r 



ncj r A TIG J r 



dS, 



4 JTi 



in which the integrations have to be extended over all space. The 

 distance from the point for which one wants to determine the poten- 

 tials for the time t is denoted by r and the meaning of the square 

 brackets is that the quantities q, etc. have to be taken such as they 



are at the time t . 



c 



In terms of the potentials we have for the field 



1 . 



d = a — grad (f — rot bi 



c 



1 . 



h = b — grad X 4- rot a. 



c 



§ 5. We shall now suppose, following Whittaker, that in the 



atom there is a circular ring R, over which magnetism is uniformly 



distributed. We shall consider it as very thin, so that we may speak 



