47 
a voltaic battery, the formula becomes F = ^^p r ? that is, 
the force equals the product of the number of elements 
divided by the number of battery resistances, plus the 
circuit resistance. We, therefore, deduce that if the r, 
the circuit resistance, be comparatively small, we obtain little 
more effect from a number of elements combined together in 
a battery than from a single pair of elements; and that if the 
length of the exterior resistance of the circuit be increased 
proportionally with the number of plates, we shall have the 
like effect from the battery as from the single pair. But, 
on the other hand, if the r or exterior resistance be large, 
comparatively, with the R, or resistance of the liquid element 
in a single cell, we shall obtain a considerable increase of 
effect by increasing the number of elements in combination. 
We, therefore, see that the law strictly agrees with the 
practice ; that when considerable resistances are to be over- 
come, for instance, the decomposition of water, the passing 
a shock through the human body, or the transmitting the 
current to a distance, as in the electric telegraph, a con- 
siderable number of elements must be used in combination ; 
but where a considerable quantity of electricity through a 
short circuit, as for many experiments in electro-magnetism, 
or for heating a short length of thick wire, is required, plates 
of considerable size and few in number, and having only a 
slight resistance, are sufficient. But when we require to pro- 
duce powerful galvanic effects at a distance, requiring cur- 
rent in great quantity, and passing through long or imperfect 
conductors, a combination of considerable extent, both as 
regards the size and also the number of the elements, is 
required. 
Although the foregoing equations enable us to ascertain 
the amount of force or effect derivable from any voltaic com- 
bination, they do not assist us in the more important investi- 
gation of the cost of working such a combination ; that is, 
