PROFESSOR DANIELL ON VOLTAIC COMBINATIONS. 
147 
To determine the value of r in the formula, we might compare, in a similar 
manner, as pointed out by Professor Wheatstone, the results of two arrangements, 
in which the electromotive forces being equal, the resistances in the cells alone should 
vary. As, however, from the complicated nature of the arrangements, and the varia- 
bility of different influential circumstances to which I have before alluded, I found 
it impossible to obtain two perfectly unexceptionable results for the comparison, I 
thought it allowable to take the mean of several ; and from this I found that, with a 
voltameter whose platinum plates are three inches in length by one inch in width, 
a quarter of an inch apart, and charged with the standard dilute sulphuric acid, 
(sp. gr. 1T26), r = 0'541 R in a constant battery of the dimensions just described. 
Now if a single cell of such a battery be taken and the circuits closed by a short 
thick wire, and the zinc rod forming the generating plate of the arrangement be 
weighed at intervals of five minutes, it will be found to lose 1T26 grs. for every such 
interval. This is a measure of the effective force of the circuit ; and its equivalent 
in mixed gases is 25 cubic inches. This will be taken as the unit of work in the 
Table that follows, i. e. = l)> and the calculated results for the different com- 
binations will, in the third and fourth columns, be represented in fractions of this 
unit. 
It is evident, that the amount of zinc, dissolved in such a single circuit, furnishes a 
measure of the maximum work that any number of such cells, combined in a single 
series, would be capable of performing ; for = A, and n ^ can never be greater 
E 
than^, however great the value of n may be, so long as r has a positive value. In 
other words, however great the numbeF of cells in a series, it is impossible, so long 
as any external resistance is interposed, that the result should be greater than that of 
a single cell in which no exterior resistance is opposed ; although when r is very small 
when compared with n R, the results may be virtually equal. 
If unity be taken to represent the maximum work that any single circuit can pro- 
duce, then E will be represented by 1, and R also by 1, and 
It is evident that in an effective circuit R can never equal E, but for the convenience 
of calculation it may be assumed to be so ; and as all the quantities in the nume- 
rator are compared with E, and all in the denominator with R, the relative propor- 
tions will be exact. Taking the formula 
n E — e . 
If E = 1 and R = 1, then e = 2‘49, r = 0‘541. 
values for n, we obtain for 
u 2 
Substituting different numerical 
