490 Mr. W. B. Morton on the 



Also, since each element of charge produces a magnetic 

 field with no e-component, we have 7 = in the general case 

 also. Using these two data, the equations connecting the 

 displacement (f,g,h) and the magnetic force (at, ft,y) become 



d/3 . df 



dz dz 



da . da 



— =_ 4t™_^- 



dz dz 



d/3 da, . dh 



j J- = — 4:7TU r=- 



dx dy dz 



dg dh _ u da 



dz'~dy~""^PTz 



dh__df_ u dfl 

 dx dz ~ 47rV 2 dz 9 



dy dx 

 These equations together with 



df + dg + ^ =0 



dx dy dz 

 are satisfied by 



/=_#, ff =-W h=-t?^, 



dx J dy dz 



dy dx 



where <j) is any function satisfying 



da? dy 2 dz 2 



These results have been obtained by Prof. Thomson and Mr. 

 Heaviside. The particular case of a point charge, e, is got 

 by putting 



9 4Tr\/k\x 2 +y 2 )+z 2 ' 



Evidently in the general case (f> must vanish at infinity. 



5. Mr. Heaviside points out that </> = constant is the con- 

 dition holding at a surface of equilibrium. The matter may 

 be stated thus : — If we suppose the field to terminate at the 

 surface of a conductor, inside which the vectors vanish, we 

 must see that the " curl " relations of the field are not violated 



