OP AN ELECTRIC DISCHARGE. 25 



coating of the first and the outer coating of the last are free ; 

 and, in charging, these are treated as if both surfaces formed a 

 single battery. 



The principles according to which the charge of such a com- 

 pound battery must be determined, are for the most part already 

 given by Green*. Let the quantities of electricity distributed 

 over the two coatings of the single batteries, and the correspond- 

 ing potential functions be expressed in order by — 



Qi, Q\ ; Q2, Q'2; Q3, Q'3 &c,l . . 



Vi,V\; V„V',; V3,V'3&c.J • • • ^ ^ 



Now if positive electricity be communicated by a conductor 

 to the inner coating of the first battery, the outer coating of the 

 same can only receive its negative charge from the interior of 

 the second battery, which will thus become positively charged ; 

 we therefore have 



Q',= -Q,; 

 and further, as in two bodies which are connected by a con- 

 ductor the potential functions are equal, we have for the same 

 two coatings 



and two equations exactly similar apply to every other pair of 

 connected coatings, so that the following series of equations is 

 given, 



Q\= -Q„ a',= -Q3, Q'3= ~Q, &C.-1 . 



v\= v„v',= V3,v'3= v,&c.J • ^'^r 



Besides this, the four quantities Q, Q', V and V, stand for 

 each of the batteries in such a relation to each other that from 

 every two of the same the two others may be determined. In 

 accordance with the remark at the conclusion of a former paper 

 of mine, if we denote the said four quantities by q, g', V and V, 

 the equation (15), whieh applies to the case where V'=0, 

 can, if we neglect the members of a higher order in respect 

 to k, be changed into the following more general one, 



V-V=-^£=*:, ...... (30) 



where instead of ^-— ^ we may also write q^ or — tj. 



* An Essay on the Application of Mathematical Analysis to the tbeoriea of 

 Electricity and Magnetism, kx\, 8. 



