PROFESSOR DANIELL ON VOLTAIC COMBINATIONS. 
145 
grains ; a rod of half the length lost 6 - 6 grains in the same time. The results, there- 
fore, of each cylinder may be taken as directly proportioned to the lengths of the rods 
immersed in them. 
Let us now turn from the consideration of simple circuits, and examine the law of 
a series, or of compound circuits. Ohm’s formula for these is 
wE . 
n R + r ’ 
in which n represents the number of the series. 
Now so long as the external resistance (r) interposed in the circuit is merely me- 
tallic, the expression accords strictly with the results of experiment ; and by doubling 
the number of cells at the same time that we double the efficient surface in each cell, 
we obtain an effect exactly double : thus by the formula 
/ »E \ 2?zE 2raE 
\ftR-f-7V 2 ra R rcR + r’ 
— +r 
since in doubling the surface in each cell, cceteris jparibus, we halve the resistance. 
When, however, a voltameter or other chemical resistance is interposed in a cir- 
cuit, Ohm’s formula will not hold, unless the opposite electromotive force which 
arises from the decomposition of the electrolyte, and consequent accumulation of 
ions upon the electrodes of the decomposing cell, be taken into consideration. This 
is of the same nature as the contrary electromotive force in the cell which we have 
already pointed out and designated by e' in the formula E = (B — b — e'). Professor 
Wheatstone, from a series of experiments made conjointly with myself, with my 
battery, and published in my fifth letter to you, inferred that, if this contrary elec- 
tromotive force be assumed to be constant and be represented by e and introduced 
into the formula, thus 
tables might be calculated which would represent, approximatively, the quantity of 
decomposition for any number of cells of a given battery, while the results obtained 
by regarding the voltameter merely as a resistance, are, it is evident, widely at variance 
with the truth. Professor Wheatstone devised the following simple means to deter- 
mine, on this supposition, the values of this contrary electromotive force, and of 
the added resistance, including that of the voltameter, without having recourse to 
any other measuring instrument than the voltameter itself. To obtain the value of 
the contrary electromotive force, he compared two experiments in which the resist- 
ances remained the same, while the sum of the electromotive forces alone varied. It 
is obvious that, if there existed no contrary electromotive force, the measured effect 
in the two cases should be simply as the number of elements in the series employed. 
A battery of five single cells should have half the power of a battery of ten double 
cells ; but instead of this the effects measured by the voltameter were as 6 : 20 . 
1 0 E — 6 5 E g 
To : 5 TT+ r : : : whence e = 2‘857 E (a.) 
-j-K + r 
MDCCCXLII. 
U 
