72 ELECTRICAL EQUILIBRIUM. 



Connection may be made in two ways : 



i st. All the inner coatings may be connected with each other, on 

 the one hand, and all the outer coatings on the other ; the battery is 

 then said to be arranged for quantity. The whole forms a condenser 

 whose capacity is equal to that of the capacities of all the jars 

 separately. If the battery contains p identical jars, each with the 

 capacity C, the capacity C x of the battery is 



2nd. All the jars being insulated, the outer coating of one is 

 connected with the inner coating of the following one ; the inner 

 coating of the first jar is charged to potential V p the outer coating 

 of the last jar being at potential V 2 , and all the intermediate coatings 

 being insulated ; this arrangement is said to be in series or cascade. 



85. CHARGE BY CASCADE. The first jar receives a charge m 

 on its inner coating, and assumes the potential V 1 an equal and 

 opposite charge -m is produced on the surface of the dielectric 

 next the outer coating. The conductor formed of this coating and 

 the inner coating of the second jar being insulated, will take a 

 charge + m, which is distributed regularly upon this conductor, as if 

 the internal charges did not exist, and produces there a potential V. 

 The greater part of this charge passes to the inner coating of the 

 second jar, the capacity of which is very great in reference to that 

 of the conductor in question. Continuing this reasoning, it will be 

 seen that the inner coatings have continually decreasing charges, but 

 the diminution is very small, and we may consider all the jars as 

 having the same internal charge +m, the successive potentials 

 being V lf V, V", ..... V 2 . 



If the battery contains p jars, we may put 



m = C (Vj - V) = C'(V - V") = ..... = C<*- x >(VO-'> - V 2 ), 

 whence 



