48 APPLICATION OF THE PRECEDING RESULTS 



~_ ffn-ffn = _ fin ~ A 



P *~ 47T0 ' Pn ~ 47T0 



Now /3 represents the value of the total potential function, 

 within the prime conductor and interior coating of the first phial, 

 and in consequence of the communications established in this 

 system, we have in regular succession, beginning with the prime 

 conductor, and ending with the exterior surface of the last phial, 

 which communicates with the earth, 



= A+^; o=fr + fr; &c. ...o = ^_ 1 + /3 n . 



But the first system of equations gives = p 8 + p 8 , whatever 

 whole number s may be, and the second line of that just ex- 

 hibited is expressed by = p a-1 + p 8 ; hence by comparing these 

 two last equations, 



which shows that every phial of the system is equally charged. 

 Moreover, if we sum up vertically, each of the columns of the 

 first system, there will arise in virtue of the second 



/Q 



I^' 



_ _ Q 



We therefore see, that the total charge of all the phials is 

 precisely the same, as that which one only would receive, if 

 placed in communication with the same conductor, provided its 

 exterior coating were connected with the earth. Hence this 

 mode of charging, although it may save time, will never produce 

 a greater accumulation of fluid than would take place if one 

 phial only were employed. 



(9.) Conceive now a hollow shell of perfectly conducting 

 matter, of any form and thickness whatever, to be acted upon 

 by any electrified bodies, situate without it ; and suppose them to 



