33 



CONSTITUTION OF MAGNETS. 



The action of the point O on the shell will be obtained by ex- 

 tending these expressions to the whole surface. Lastly, the action F 

 of the shell on the point O, passes through this point, and the com- 

 ponents X, Y, and Z of this force, are equal and of opposite sign to 

 those of the action of the point on the shell ; we have then 



(26) 



= <i> j* z z x = 3> f_ d r\ 



J r Jr \J 



__ c|) I *_ = . = ^) I "^_ 



J r a 



d * 



y 



347. RECIPROCAL ACTION OF Two SHELLS. We may now de- 

 termine the reciprocal action of two shells S and S'. The action 

 of S on S' may be considered as the resultant of actions, determined 

 by the previous rule, which the shell S would exert on each of the 

 elements ds' of the contour C' of the second shell. 



Fig. 82. 



Let us suppose that one of these elements ds is at O (Fig. 82) 

 and is directed along the axis of x. The action d$ which is exerted 

 on this, element is equal to &Fds' sin a, and is situated in the plane 

 of zy ; the components of this force are 



^' = <!>' Fds' sin a' . cos /5 = ' 

 ^' = - $>'F<&' sin a' . sin )8 = - 



