TO THE THEORY OF MAGNETISM. 93 



Moreover 



,, ( X(x'-x}+Y(y'-y}Z(z'-z] 



Y = I ax a y dz - 3 



I A j l ,7 IV 



= (dxd dzi^ * + & _1 + ^ -I) 



J ' ' \dx ' dx dy ' dy dz ' dz I 



the triple integrals extending over the whole volume of A, and 

 that relative to da- over its surface, of which da- is an element ; 



d \ 



the quantities (/> and -* belonging to this element. We have, 



Cf/10 



therefore, by substitution 



Now8'F' = 0, and 



d\ 



.dw 



and consequently S'^>' = ; the symbol S' referring to x, y ', s' 

 the co-ordinates of ^/; or, since a?', y' and a' are arbitrary, by 

 making them equal to x, y, z respectively, there results 



0-fc 



in virtue of which, the value of i^', by Article 3, becomes 



r being the distance p, do; and ( -yH belonging to da. The 



former equation serving to determine 0' gives, by changing 

 x, y', z' into x, y, s, 



const. = (1 - a] 6 + -$- (*b + V] ., ..(<?>: 



