Application of Ohm's Law to Problems of Electrostatics. 329 



and. we take as unity the quantity that would be accumulated on 

 one set of plates, supposing them at first to constitute the only 

 resistance of the circuit, then, when the two sets are placed in 

 circuit, since the resistance of the whole circuit is doubled, the 

 quantity on each plate would be only 0*5 ; and if now the re- 

 sistance of one set be increased by doubling the distance between 

 them, the quantity would be reduced to 0*33. 



By the same means the quantity that would be accumulated 

 on a series of several pairs of equal plates joined " in cascade" 

 may be found, and compared with the quantity that would be ac- 

 cumulated on a single pair ; and it will be seen that, as the resist- 

 ance of m sets of plates will be m times as great as that of one, 

 the quantity accumulated on each set of plates will be m times 

 smaller than that which it would be with one set of plates. But 

 as there are m sets of plates thus charged, the total quantity 

 generated and accumulated is the same as if one set of plates 

 only were employed. This agrees with the result of Green's in- 

 vestigation of the same problem, and is thus enunciated by 

 Green : — "The total quantity of electricity contained in the in- 

 terior of any number of equal and similar jars"*, when one of 

 them communicates with the prime conductor, and the others 

 are charged by cascade, is precisely equal to that which one only 

 would receive if placed in communication with the same con- 

 ductor, its exterior surface being connected with the common 

 reservoir " (that is to say, in connexion through the surrounding 

 objects or the earth with the other pole of the source of generation). 



When one set of surfaces of two or more Ley den jars or other 

 inductive resistances are connected as parallel branch resistances 

 to one pole of a source, the other pole of which is connected either 

 directly or through the surrounding conductors to the other 

 surfaces of such resistances, the quantity that will be accumulated 

 on the surface of any one resistance is quite independent of the 

 magnitude of the other resistances thus grouped. This case has 

 no parallel in the conductive circuit, at least in a galvanic cir- 

 cuit ; and the difference arises from the fact that in the galvanic 

 circuit we have always the resistance of the battery as a resist- 

 ance common to all the branches, whereas in an inductive cir- 

 cuit the resistance of the battery is a conductive and not an in- 

 ductive circuit. If in an inductive circuit we have a resistance 

 (A) common to both of two or more branch resistances (B and 

 C), as in figs. 5 and 6, then this indifference of the branch 

 resistances to one another disappears, and none of the resistances 

 can be altered without affecting the quantity that will be accu- 

 mulated on each. The formula for these I have already published, 



* This is not strictly correct as regards jars. The reason of this is ex- 

 plained further on. — F. C. W. 



