132 PARTICULAR CASES OF EQUILIBRIUM. 



Let us further take 



^-^ 



The condition of equilibrium on the plane Q is satisfied by a layer 

 my, which acts on each side as if it were at A or at B. 



The mass m at A, and the layer my of the plane Q, produce on 

 the plane Q' a layer m (i + y)y' = m', which will act as if it were con- 

 centrated at A or at B r 



The layer m reacting on the plane Q, will produce there a layer 

 - m'y, the image of which is at B x or at A r 



In like manner the layer - m'y at Q gives on Q' a layer m'yy 

 the image of which is A x or B 2 . . . , etc. 



The determination of these successive layers is nothing but the 

 application of Murphy's method. 



We shall thus have, from layer to layer : 

 on the plane Q, 



Successive layers. Images. 



my A or B 



- m'y A : B! 



+ m'y*y A 2 B 2 



and on the plane Q', 



Successive layers. Images. 



m(i+y)y' = m' A or B x 



-m'yy' A, B 2 



A 2 B 3 



The algebraical sum of all these layers will give the final state of 

 equilibrium. 



The total charges M and M' of the planes Q and Q' will be 



M = my - m'y [i - yy' + (yy') 2 - (yy') 3 + ] = my- m'y ; 



r j " 



1 + 77 1+77 



