TO THE MOVEMENT OF MACHINES, 513 
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 /, 7, 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 
- = : + : + x ,&e. Therefore having 2 wires of the same length, 
the total force of the current will be expressed by 
oe n EB iy win nd dE 
rl rtln rldt+rtidnn’ 
ndt a 
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 di- 
mension, the total power gained by a connecting wire Z will be 
aes Inn'dd'E 
rid +rl'dnn" 
From this formula the limits of the action of the current may be de- 
duced, which cannot be increased by the number or the surface of the 
voltaic pairs, by the length, the diameter, and the number of the connect- 
ing branches. Increasing only the surface of the pairs d', the limit of 
nnd E 
the total power of the current will be A oo a ; increasing the 
1 
number n’, this limit is 4 = = 
rt! 
Again this limit will be, by increasing the length of the wire J, 
I 1 qi 
A=" = the thickness of the wire d, A = : a — the number of 
r 
1 
the connecting branches 2, A = i 
rit 
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 “Maass- 
bestimmungen iiber 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 
yoltaic pile, and which represent the expense attending the magnetic 
