398 Mr Murphy on the Inverse Method of 



Using the notation of the last Article, it is evident that the 

 whole quantity of electricity in the sphere, i. e. the difference 

 between the quantities of positive and negative fluids, generally* 

 is equal to f t (p = coefficient of 



I in P' (S • Up + J+iaMl-Zf)}* > fr ° m ' = ° t0 ' =1 - 



Now this integral = ^=| . {_!_ _ _!_} = 1 , 



and therefore the quantity of electricity = coefficient of -5 in 

 the external tension, or of - in the internal ; thus in the example 



before us this quantity = - j , but if it were necessary that there 



should be a given excess E of positive above negative electricity 

 on the surface, we have only to superpose the uniform accu- 



+ h 

 mulation —7 — r to the variable accumulation expressed by 



4ira a " \T+2h(l~2t) + k a \* ' 



To find the position of the transition line we must find t 

 in the equation 



E 1 h 2 -l 



eh \\ +2h.(l-2t) + h 2 }i' 



When the electricity is excited merely by influence, we must 

 put E = 0, the law of accumulation is then as 



1 ¥-1 



h \l+2h.(l-<Zt)+/f)i' 



