Mechanism of Radiation. 431 



where 



and 



Or 



where V 2 is that part of the potential of the whole atom upon 

 a unit mass at r, 0, (j> which arises from the term % 2 M U1 * ne 

 potential-function. 



§ 14. The potential of the whole displacement upon the 

 element initially occupying the volume dx dy dz at x, y, ^has 

 been seen to he 



{p(E! + E 2 ) +«-(E t +iy}<fo<Jy«k. 



Since the distribution of doublets which gives rise to the 

 displacement-potential at a?, y, z is of zero strength at x, y, z, 

 the forces arising from the displacement can be calculated by 

 differentiation. The differential operators must, however, 

 act only upon those parts of the displacement-potential which 

 are directly derived from %i(R) and % 2 (E.), so that the term u 

 which occurs in E 2 and E 4 will be exempt from differentiation. 



If, for the sake of generality, we admit externally applied 

 forces of amounts L, M, N per unit charge in the directions 

 of ?', 0, cf> increasing, the equations of motion of the element 

 initially at r } 0, <\> will be 



a w=- ttVn ^ e \ p ~aV +a -jr) 



-K'^ + ***7 +I * (5) 



dt* rdd 



dhv _ ^^ imTl 

 <2F~~~^ rsin<9 



crrsin^^==-S2 l -^^^(pF? + < rG?)+]Srp. . . (7) 



The Equations of Free Vibrations. 



§ 15. Let us suppose that there is a normal vibration such 

 that the element of which the equilibrium position is at ?-, 0, (p 

 is found at time t at the point 



r+«c**, + ve ( p f , Q + ice'Pt, 



u, v, to being given by scheme (1). 



