OHM ON THE GALVANIC CIRCUIT. 485 



needle, under otherwise similar circumstances, is proportional 

 to the magnitude of the current. But long since direct ex- 

 periments have established the correctness of this supposi- 

 tion. 



28. We will now proceed to the consideration of a multiple 

 conduction existing at the same time. If, for instance, we 

 imagine an open circuit, whose separated extremities are con- 

 nected by several conductors, arranged by the side of each 

 other, it may be asked, according to w-hat law is the current 

 distributed in the adjacent conductors ? In answering this 

 question, w^e might proceed directly from the considerations con- 

 tained in § 11 to 13; but we shall more simply attain the re- 

 quired object from the peculiarity of galvanic circuits ascertained 

 in § 25, in which case we will, for the sake of simplicity, sup- 

 pose that none of the former tensions is destroyed by the open- 

 ing of the circuit, nor a new^ tension produced by the conductor 

 w^hich is introduced. 



For if X, >!, x", &c. represent the reduced lengths of the con- 

 ductors brought into connexion with the extremities of the open 

 circuit, and « the difference of the electroscopic forces at the ex- 

 tremities of the circuit, after the conductors have been intro- 

 duced, the same difference will also occur at the ends of the 

 single adjacent conductors, since, according to the supposition 

 we have made, no new tension is introduced by the conductor. 

 Since now, according to § 13, the magnitude of the current in 

 the circuit must be equal to the sum of all the currents in the 

 adjacent conductors, we may imagine the circuit to be divided 

 into as many parts as there are adjacent conductors ; then, ac- 

 cording to § 25, the magnitude of the current in each adjacent 

 conductor, and in the corresponding part of the circuit, will re- 

 spectively be 



« a a - 

 —, 7^' F' ''•' 



whence, in the first place, it results that the magnitude of the 

 current in each adjacent conductor is in inverse ratio to its re- 

 duced length. If we now imagine a single conductor of such 

 nature, that, being substituted for all the adjacent conductors 

 in the circuit, it does not at all alter its current; then, in 

 the first j)lace, a, according to § 25, must retain the same 

 value, and, if we designate by A the reduced length of this 

 conductor, must moreover be 



VOL. II. PART VIII. 2 K 



