OHM ON THE GALVANIC CIRCUIT. 429 



preceding consideration. For if we denote by A the sum of 

 the tensions, and by L the reduced length of any galvanic 

 circuit, 



A 

 L 

 expresses the magnitude of its current. If we now imagine 

 a multiplier of n similar convolutions each of the reduced 

 length X, 



A 

 h + nK 

 indicates the magnitude of the current when the multiplier is 

 brought into the circuit as an integral part. Moreover, if we 

 grant, for the sake of simplicity, that each of the n convolutions 

 exerts the same action on the magnetic needle, the action of the 

 multiplier on the magnetic needle is evidently 



nA 

 L. + nx' 



when the action of an exactly similar coil of the circuit, without 

 the multiplier on the needle, is taken as 



A 



L* 

 Hence it follows directly that the action on the magnetic needle 

 is augmented or weakened by the multiplier, according as nh 

 is greater or smaller than L + re A., i. e., according as n times the 

 reduced length of the circuit without the multiplier is greater or 

 smaller than the reduced length of the circuit with the multiplier. 

 Further, a mere glance at the expression by which the action 

 of the multiplier on the needle has been determined, will show 

 that the greatest or smallest action occurs as soon as L may 

 be neglected with reference to n A, and is expressed by 



A 

 x' 

 If we compare this extreme action of the multiplier with that 

 which a perfectly similarly constructed convolution of the cir- 

 cuit without the multiplier produces, we perceive that both 

 are in the same ratio to one another as the reduced lengths L 

 and X, which relation may serve to determine one of the values 

 when the others are known. The expression found for the extreme 

 action of the multiplier shows that it is proportional to the ten- 

 sion of the circuit, and independent of its reduced length', conse- 



