262 
THEORY OF GALVANISM. 
The plates are 
electrified in 
each succes- 
sive pair, in 
geometrical 
progression; 
bnt scarcely 
differing from 
an arithmeti- 
cal one. 
Explanation 
of the neutral 
middle pair. 
then by hypothesis, m x = that of the contiguous or first zinc 
plate j also tu x = the quantity in the second copper plate (by 
reason of the conducting fluid 3) but 1 : m : : mx : rn^x = the 
quantity in th£ second zinc plate. In like manner the quantities 
in the successive copper and zinc plates may be found, and will 
constitute ibis series ; 
12 3 4 n 
Copper plates, x, mx, m^x, m 3 x, he mx n ~ l 
Zinc plates, mx, m^x, m 3 x, m*x, he mx n 
Hence it appears that the quantities of electricity in the 
successive plates of copper or of zinc form a geometrical pro- 
gression, the ratio of which is m. Also the total quantities of 
electricity in the successive pairs of plates form a series in 
geometrical progression, as under. 
Pairs of pi. 1 
Quant, of El. 1 -\-m:x 
2 ! 3 I 
m‘ 1 -\-nvx vi 2, 1 -f m'x m 3 1 -f-m x 
he. 
From the above theory of Galvanic action it necessarily 
follows, that if the effect of a pile be in proportion to the 
difference in the electricities of the first and last plates of the 
series, a pile of 50 pairs will not be exactly half so energetic as 
one of 100 pairs, but somewhat less 3 because the differences in 
j 
the terms of a geometrical series increase as the terms increase. 
But, in the present instance, there is great reason to apprehend 
that the ratio of 1 to m is very nearly that of equality. If sq, 
the geometrical series for a moderate number of terms, will 
scarcely differ from an arithmetical one. This accords very 
nearly with experience ; for it has been determined by 
Volta, that if a combination of 20 pairs of plates “produce 
a given effect on the electrometer, a series of 40 will 
produce double the effect j one of 60 triple, and so on. At 
the same time it is probable that the electric intensity of the 
plates, composing each pair, relatively to one another, continues 
unaltered, notwithstanding the change in their absolute 
quantities of electricity. 
When a connection is established between the two extremities 
of a series like the above, for example between the third zinc 
plate, or its contiguous cell, and the first copper plate, the 
opposite 
