1884.] of the electromagnetic field. 143 



and transforming this by partial integration, we get 



and as in the former paper let <I> satisfy the equation 



du dv dw 1 o d<& , . N 

 1 1 = — y* (4). 



dx dy dz 4<7r dt 



Then we have 



F= ^///r dx ' d y' dz ' - frr Ijjfa' r dx ' d y' dz ' ^ 



d\ 

 so that rfF = - 4>7tjjlu + ^r- (G). 



etc 



„ .„ T dF dG dH ._. 



He * ceif Jz= d^c + dv + 2J (7) ' 



, T . (du dv dw\ „. 



^ J =-^\j x + dy + -d Z ) + * X - 



Therefore V 2 J"+^v 2 ^= V 2 ^ (8). 



The solution of this is 



X = J+^ a ~ + V. (9), 



where y 2 V= always. 



Thus V is not a function of the time and we may neglect it 

 for our present purposes. 



Hence v »ir_g=_ ^ M + /i || (10 ), 



and substituting in the usual equations connecting a, /3, y aud 



f, a, h 



^_^L 47m _ £* Hi). 



dy dz dxdt 



If we remember that, according to Helmholtz, fjik ~rr = — J, 



these equations are identical with (10) and (15) of my former 

 paper, which may be written 



2C , yd 2 ® . d*3> 



vF+ * k d^-r-* 7r i J ' u+fJ 'd X Tt' 



