TRANSACTIONS OF THE SECTIONS. 23 
accustomed to proceed in a legitimate manner, and feeling great regret 
at the irregular attempts which were being made everywhere, without 
any scientific foundation, this state of things appeared to me so un- 
satisfactory, that I could not but direct all my efforts to ascertain clearly 
the laws of these remarkable machines. I submit the formule relative 
to these laws, which appear to me to recommend themselves as much 
by their simplicity as by the natural manner in which they develope 
themselves. Let R represent all the mechanical resistances acting upon 
the machine, and v the uniform velocity with which it moves: we 
have for the power or mechanical effect, the expression T = R v. 
Let n be the number of the coils of the helix which covers the rods ; 
z, the number of the plates of the battery; B, the total resistance of 
the galvanic circuit ; E, the electromotive force; 2, a coefficient, which 
depends on the arrangement of the bars, the distance of the poles, and 
the quality of the iron; we have then for the maximum of the me- 
chanical effect which will be obtained, the expression— 
aw Z2 ER? 
igo Fe 
For the velocity, which corresponds to this maximum, 
B 
Tl. v= 
~ Rn 
For the resistance acting upon the machine, 
n? 2? Ko 
4B 
Lastly, for the ceconomic effect, 7. e. the duty or the mechanical effect 
divided by the consumption of zinc in a given time, 
E 
IV. O= rk 
These formule may be expressed in the terms :— 
lst, The maximum of mechanical effect which may be obtained 
from a machine, is proportional to the square of the number of voltaic 
elements, multiplied by the square of the electromotive force, and 
divided by the total resistance of the voltaic circuit. There enters, 
moreover, into the formula, a factor, which I have designated &, and 
which depends upon the quality of the iron, the form and disposition 
of the rods, and the distance between their extremities. The result is, 
that with reference to some other investigations, which I have made 
of voltaic combinations, and under similar conditions, the use of plati- 
num, zine, the resistance being the same, will produce an effect two or 
three times greater than the use of copper, zinc. 
9nd, Neither the number of the coils of the helix which covers the 
rods, nor the diameter or the length of the rods themselves, has any 
influence upon the maximum of the power. It results, therefore, that 
neither by adding to the iength or diameter of the rods, nor by employ- 
ing a greater quantity of wire, can the power be increased. There is, 
Ts 
Ill. R = 
