TO THE THEORY OF ELECTRICITY. 69 



Now writing <j> for the angle formed by dx and dw\ we have 



1 ds _ I b 1 7/1 + &y 2 2 ) _ V(/3 4 aV*) 



cos (f) dy 2x *Jb \/ ( \l bj j <yx 



ds being an element of the generating ellipsis. Hence, as in 

 the preceding example, we shall have 



1 dV' 



dw cos < ' dx 



On the surface A therefore, in this example, the general value 

 of p is 



_-hdV'_ ah$ 



p ~ 4?r dw ~ 27T7 



and the potential function for any pointy', exterior to A, is 



Making now x and y both infinite, in order that p may be at 

 an infinite distance, there results 



and thus the condition determining A, in Q, * ne quantity of 

 electricity upon the surface, is, since E may be supposed equal 



to vo^+y 1 )* 



Q i, tali Q 



i.e. ri = . 



These results of our analysis agree with what has been long 

 known concerning the law of the distribution of electric fluid on 

 the surface of a spheroid, when in a state of equilibrium. 



(13.) In what has preceded, we have confined ourselves to 

 the consideration of perfect conductors. We will now give an 

 example of the application of our general method, to a body that 



