464 OHM ON THE GALVANIC CIRCUIT. 



tions (L) and (L'), may be comprised in the following general 

 statement, which is true when the circuit consists of any num- 

 ber of parts whatever. 



The electroscopic force of any place of a galvanic circuit, 

 composed of any number of parts, is found by dividing the sum 

 of all its tensions by its reduced length, multiplying this quo- 

 tient by the reduced length of the part of the circuit comprised 

 by the abscissa, and subtracting from this product the sum of 

 all the tensions abruptly passed over by the abscissa ; lastly, by 

 varying the value thus obtained by a constant magnitude to be 

 determined elsewhere. 



If, therefore, we designate by A the sum of all the tensions of 

 the circuit, by L its entire reduced length, by y the reduced 

 length of the part which the abscissa passes through, and by O 

 the sum of all the tensions to the points to which the abscissa 

 corresponds, lastly, by u, the electroscopic force of any place in 

 any part of the circuit, then 



A 



w=j-y — O + c, 



where c represents a constant, but yet undetermined mag- 

 nitude. 



Thus transformed, this exceedingly simple expression for the 

 electroscopic force of any circuit will allow us hereafter to com- 

 bine generality with conciseness, for which purpose we will, more- 

 over, indicate by y the reduced abscissa. This form of the equa- 

 tion has besides the peculiar advantage that, without anything 

 further, it is even applicable when in any part of the circuit the 

 tensions and conductibilities constantly vary ; for in this casej 

 we should merely have to take, instead of the sums, the cor- 

 responding integrals, and to define their limits according as the' 

 nature of the expression required. Since O does not change ' 

 its value within the entire extent of the same homogeneous 

 part of the circuit, and y constantly varies to the same amount 

 on like portions of this extent, the following properties, already 

 demonstrated less generally with respect to the simple circuit, 

 evidently apply to every galvanic circuit, and in these is ex- 

 pressed the main character of galvanic circuits : — 



a. The electric force of each homogeneous portion of thej 

 circuit varies throughout its entire length constantly,] 

 and on like extents always to the same amount; but] 

 where it ceases and another commences, it suddenly. 



