Experiments with Girove’s Battery. 393 
long wires, could not be carried into effect, and even the galvanic 
multiplier, which consists essentially of a wire making several 
convolutions round a needle, could have no existence. 
This last objection was first brought forward by Prof. Ritchie, 
of the University of London, as an absolute proof that the law 
referred to is incorrect. 'There is, however, an exceedingly sim- 
ple method of proving that signals may be despatched through 
very long wires, and that the galvanic multiplier, so far from 
controverting the law in question, depends for its very existence 
upon it. 
Assuming the truth of the law of Lenz, the quandzties of elec- 
tricity which can be urged by a constant electromotoric source 
through a series of wires, the lengths of which constitute an 
arithmetical ratio, will always be in a geometrical ratio. Now 
the curve whose ordinates and abscissas bear this relation to each 
other is the logarithmic curve whose equation is a¥=w. 
Ist. If we suppose the base of the system which the curve 
under discussion represents be greater than unity, the values of 
y taken between «=O and «= 1, must be all negative. 
2nd. By taking y=O we find that the curve will intersect the 
axis of the z’s at a distance from the origin equal to unity. 
ord. By making c=0 we find y to be infinite and negative. 
Now these are the properties of the logarithmic curve which 
furnish an explanation of the case in hand. Assuming that the 
a’s represent the quantities of electricity, and the y’s the lengths 
of the wires, we perceive at once that those parts of the curve 
which we have to consider lie wholly in the fourth quadrant, 
where the abscissas are positive and the ordinates negative. 
When, therefore, the battery current passes without the inter- 
vention of any obstructing wire, its value is equal to unity. 
But as successive lengths of wire are continually added, the 
quantities of electricity passing, undergo a diminution at first 
rapid and then more and more slow. And it is not until the wire 
becomes infinitely long that it ceases to conduct at all; for the 
ordinate —y, when z=0, is an asymptote to the curve. 
In point of practice, therefore, when a certain limit is reached 
the diminution of the intensity of the forces becomes very small, 
whilst the increase in the lengths of the wire is vastly great. It 
is, therefore, possible to conceive a wire to be a million times as 
long as another, and yet the two shall transmit quantities of elec- 
Vol. xv, No. 2,—July-Sept. 1843. 50 
