146 
PROFESSOR DANIELL ON VOLTAIC COMBINATIONS. 
The value of r in the formula, i. e. the resistance which the voltameter and connecting 
wires add to the circuit, will be ascertained in the following manner. The comparison 
was made with two batteries, one single and the other double, of ten cells each ; the 
sum of the electromotive forces, therefore, remained the same, while the resistances 
only varied : 
10E - e 10E - e 
10 R + r : 10 R 
—x f- r 
12’5 : 20 , whence r = 3'333 R. . . . (|3.) 
Substituting the values thus found in the general formula 
n E — e 
(jR + r’ 
he obtained the 
following results : — 
Number of cells .... 3 
4 
5 
10 
15 
20 
Quantity of gas calculated . f 
Q3 
°5 
6 
10A8. 
lz 2 5 
1 5— 
10 2 5 
17 H cubic inches. 
Quantity of gas observed . . 1 |- 
q! 
6 
12 i 
15f 
I 7 i cubic inches. 
The existence of such a contrary electromotive force, and its great energy, are 
amply attested by connecting the platinum plates of a voltameter, which has been 
some time in action, with a galvanometer ; but I purpose to show the general agree- 
ment of the amended formula with the results of various and most trying combina- 
tions of different batteries, many of which were obtained without the slightest suspi- 
cion of the conclusions which might be derived from them. I say general agree- 
ment, for the extremely complicated nature of the actions to be measured, subjected 
as they were to the necessarily variable influence of circumstances affecting them, the 
large scale upon which the experiments were carried on, and the roughness and im- 
perfection of the modes of measurement, would necessarily preclude the expectation 
of absolute accuracy. The remainder of the experiments, already published in my 
fifth letter, made with circuits which contained an equal number in series, but in 
which they were combined as double, treble, quadruple cells, &c., do not furnish re- 
sults according with theory so well as might have been expected ; they were therefore 
repeated with great care, and combined in various ways. The details of these ex- 
periments will presently appear. The first series was made with a constant battery 
composed of copper cylinders, six inches high, 3| inches in diameter, charged in the 
usual way with dilute sulphuric acid and sulphate of copper. 
The first thing to be done was to determine the value of e in these combinations in 
the modified formula, by comparing the results of two arrangements in which the sums 
of the electromotive forces might vary, while the resistance remained the same. Thus 
Cubic inches. 
5 E — £ 
in five single cells, 5 r + r — 11 '25 by experiment ; 
10 E — e 
in ten double cells, p ( — ■ = 337 by experiment ; 
therefore 5 E — e : 10 E — e : : 11*25 : 33*7, or e = 2'49 E. 
