OHM ON THE GALVANIC CIRCUIT. 483. 



needle ; if we imagine them, therefore, so arranged near one 

 another, that though they are separated by a non-conducting 

 layer, they are j^et situated so close together that the posi- 

 tion of each one toward the magnetic needle may be regarded 

 as the same, they would produce a greater effect on the magnetic 

 needle in proportion as their number increased. Such an ar- 

 rangement is termed a multiplier. 



Now, let A be the sum of the tensions of any circuit, and L 

 its reduced lei:igth ; let also A be the reduced length of one of 

 the interposed conductors formed into a multiplier of n convolu- 

 tions; then, if we represent the reduced length of one such 

 convolution hj K, A. = nX, the action of the multiplier on the 

 magnet needle w ill be proportional to the value 



?z A 

 L + « x" 



But the action of a similar coil of the circuit, without the multi- 

 plier, is, according to the same standard, 



A 



L' 



and we will suppose the portion of the circuit, whence the coil 

 is takeji, to be of the same nature as in the multiplier ; accord- 

 ingly the difference between the former and the present effect 

 is 



» L — (L -f 7? X) A 

 L -h « A ' L^' 

 which is positive or negative according as m L is greater or less 

 than L + » A. Consequently the action on the magnetic needle 

 will be augmented or diminished by the multiplier formed of n 

 coils, according as the n times reduced length of the circuit, 

 without interposed conductor, is greater or less than the entire 

 reduced length of the circuit with the interposed conductor. 



If 7i X is incomparably greater than L, the action of the mul- 

 tiplier on the needle will be 



A 

 x' 

 To this value, which indicates the extreme limit of the action 

 by means of the multiplier, whether it be strengthening or 

 weakening, belong several remarkable properties, which we will 

 briefly notice. It is constantly supposed that the multipher is 

 formed of so many coils that the magnitude of its action may. 



