OHM ON THE GALVANIC CIRCUIT. 457 



fx^ + c. 

 If we now call the given tension or difference of the electro- 

 scopic foi'ce c, we have 



« = ±/K — ^2)- 

 But x^ — a?2 evidently represents the entire, positive or negative, 

 length of the prismatic conductor ; if we designate this by /, we 

 obtain accordingly 



a = ±fl, 



whence the constant f may be determined. If we now intro- 

 duce the value of the constant thus found into the equation (c), 

 it is converted into 



M = + y ^ + C, 



so that only the constant c remains to be determined. We may 

 consider the ambiguity of the sign + to be owing to the ten- 

 sion a, by ascribing to it a positive value when the extremity 

 of the conductor, belonging to the greater abscissa, possesses 

 the greatest electroscopic force, and when the contrary a 

 negative. Under tliis supposition is then generally 



M = y a? + c. [d) 



The constant c remains in general wholly undetermined, 

 which admits of our allowing the diffusion of the electricity in 

 the conductor to vary arbitrarily, by external influences, in 

 such manner that it occupies the entire conductor everjsvhere 

 uniformly. 



Among the various considerations respecting this constant, 

 there is one of especial importance to the galvanic circuit, I 

 mean that which supposes the circuit to be connected at some 

 one place with a perfect conductor, so that the electroscopic 

 force has to be regarded as constantly destroyed at this place. 

 If we call the abscissa belonging to this place A, then according 

 to the equation {d) 



a 



By determining from this the constant c, and placing its value 

 in the same equation {d), we obtain 



from which the electroscopic force of a galvanic circuit of the 



