OHM ON THE GALVANIC CIRCUIT. 461 



_ (a + a') x' iiifx 



and that in the part P' by the equation 



, (a + a') xcoa^ — xu) I + x' co' I 

 u =-^ , ,, , Yi ^ + c. 



X 0) i + X U) I' 



I I' 



If we substitute A and A' for — - and -7 — ;, the following; more 



xco x' w' ° 



simple form may be given to these equations : — 



a + a' X 1 



u = , . — + c 



\ + K' x(v I 



, a + a' /x - I l\ , \ (^)' 



* X + X' \ X' Co' X CO/ J 



From the form of these equations it will be immediately per- 

 ceived, that when the conductibility, or the magnitude of the 

 section, is the same in both parts, the expressions for u and u' 

 undergo no other change than that the letter representing the 

 conductibility or the section entirely disappears. 



17. We will now proceed to the consideration of a galvanic 

 circuit, composed of three distinct parts P, P', and P", which 

 case comprises the hydro-circuit. 



If we represent by u, u', u" respectively the electroscopic 

 forces of the parts P, P', and P", then, according to § 15, the 

 case there mentioned being here thrice repeated, we have, in 

 accordance with the equation (c) there found, with respect to 

 the part P, 



M =f^ + C, 



with respect to the part P', 



and with respect to the part P", 



«"=/'' a? + c", 



where/,/',/", c, c', c" may represent any constant magnitudes 

 remaining to be determined from the nature of the problem, 

 and each equation has only so long any meaning as the ab- 

 scissae refer to that part to which the equations appertain. If 

 we suppose the origin of the abscissae at that extremity of the 

 part P, which is connected with the part P", and choose the 

 direction of the abscissae so that they lead from the part P to 

 that of P', and from thence into P" ; if we further respectively 



