DISCHARGE OF A BATTERY IN CASCADE. 8 1 



The energy expended in the discharge is then 



2 C, C,+C, 



The proportion of the initial energy which has been expended is 



Wi-W a= C 2 i 



W x ~C 1 + C 2 - Cj' 

 C 2 



Let us suppose that the first battery consists of p l jars of the 

 surface Sj and thickness e v and the second of A J ars f ^ e surface 

 S 2 and the thickness * 2 , we shall have 



&'iA.S.-.4 ; ; 



C 2 A S 2 'i 

 which gives 



l 1+ .l.2 



A S 2 ^1 



95. DISCHARGE OF A BATTERY IN CASCADE. The capacity C x 

 of a battery arranged in cascade is connected with the capacities 

 C, C', C" . . . of the several insulated jars by the expression (85) 



_ 



C C' C" 



The expression for the potential energy of the system only comprises 

 the term relative to the first jar ; for all the other conductors are 

 insulated, or in connection with the earth, while being charged. We 

 have thus 



If the battery consist of p identical jars, 



C =- 



which gives for the energy 



_i M 2 _iCV 2 



~~2 P ~Q,~~2~P~' 



For a given charge, the energy of the cascade would be greater 



G 



