OHM ON THE GALVANIC CIRCUIT. 463 



duced from the tensions, we now find, when X, \', x" are respect- 



l I' I" 



ively substituted for — , -p-jj -r, — r»j 



■' X CO x' w' k" ui" 



a + a' + a" J_ 



X w' 



J_ 



x'w" 



1 



^ + x^T>^ ■ '^" «'" 



and by the aid of these values we find further, 

 , a + a' + a" / I I \ , 



A + A' + a" Vxw x'wV 



A + a' + a" \ x' w' x" w" X w/ ^ '^ 



By substituting these values, we obtain for the determination of 

 the electroscopic force of the circuit in the parts P, P', P" re- 

 spectively, the following equations : 



_ a + a' + a" a? 

 ^ -a + a' + a"-^ + ^ 

 , a^d -^d^ (x-l ^ I \ . 

 A + A' + a" V t' w' X o)/ 



A + A + A ' \ x" w" x' 0)' X w/ J 



and it is easy to see, that these equations, with the omission of 

 the letter x or w (both where they are explicit, as well as in the 

 expressions for A, A', A"), are the true ones for the case x = v! , or 



CO = a;' = w". 



18. These few cases suffice to demonstrate the law of progres- 

 sion of the formulas ascertained for the electroscopic force, and 

 to comprise them all in a single general expression. To do this 

 with the requisite brevity, for the sake of a more easy and ge- 

 neral survey, we will call the quotients, formed by dividing the 

 length of any homogeneous part of the circuit by its power of 

 conduction and its section, the reduced length of this part ; and 

 when the entire circuit comes under consideration, or a portion 

 of it, composed of several homogeneous parts, we understand 

 by its reduced length the sum of the reduced lengths of all its 

 parts. Having premised this, all the previously found expres- 

 sions for the clccti'oscopic force, which arc given by the equa- 



>(L')- 



