Page:Scientific Memoirs, Vol. 1 (1837).djvu/525

6. If the electric current is divided into several branches, the lengths of which, reduced in an inverse ratio to their diameter, may be expressed by $l,\,l',\,l'',$ &c., the total action will be the same as if there were only a single connecting wire whose length is expressed by the equation ${\frac {1}{L}}={\frac {1}{l}}+{\frac {1}{l'}}+{\frac {1}{l''}},$ &c. Therefore having $n$ wires of the same length, the total force of the current will be expressed by

$A={\frac {n'E}{{\frac {rl}{nd}}+{\frac {r'l'n'}{d'}}}}={\frac {nn'dd'E}{rld'+r'l'dnn'}}$.

As we can avail ourselves of the magnetizing power of each unity of length of the connecting wire by coiling it round bars of the same dimension, the total power gained by a connecting wire $l$ will be

$A={\frac {lnn'dd'E}{rld'+r'l'dnn'}}$.

From this formula the limits of the action of the current may be deduced, which cannot be increased by the number or the surface of the voltaic pairs, by the length, the diameter, and the number of the connecting branches. Increasing only the surface of the pairs $d'$, the limit of the total power of the current will be $A={\frac {nn'dE}{r}}$; increasing the number $n'$, this limit is $A={\frac {ld'E}{r'l'}}$.

Again this limit will be, by increasing the length of the wire $l$, $A={\frac {nn'dE}{r}}$; the thickness of the wire $d$, $A={\frac {l'd'E}{r'l'}}$; the number of the connecting branches $n$, $A={\frac {ld'E}{r'l'}}$.

In general, in order to increase the force of the current to any degree, it is necessary to enlarge the surface of the plates, and at the same time the thickness of the connecting wire or the number of the branches. The increase of the number of the pairs requires that of the length of the connecting wire, in order to attain the same end.

The experiments, as accurate as they are numerous, which M. Fechner has made on this subject, and which he has published in his work "Maassbestimmungen über die galvanische Kette (1831)," leave no doubt as to the justness of these laws, which express in a very simple manner all the relations of the different elements which constitute the voltaic pile. These experiments have been made for the most part by employing the method of oscillations, which M. Biot was the first to apply ingeniously to this kind of experiments.

9.

In admitting at first that the chemical effects which take place in the voltaic pile, and which represent the expense attending the magnetic