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DR. RITCHIE’S EXPERIMENTAL RESEARCHES 
For in that case we should have had 
F : f : : N : n 
and n : N : : n : N 
Hence kF : "Nf : : n N : n N : : 1 : 1. 
That is, the effects of batteries of any number of plates would always have 
been to each other in a ratio of equality. 
15. Had the law of diminution followed the square of the distance instead 
of the square root, there would obviously have been a loss of power by an 
increase in the number of plates. It is obvious, then, that any theory which 
does not take in the law of conduction must be founded on very imperfect 
data. 
16. I was now anxious to ascertain whether the preceding x’easoning was 
borne out by direct experiment, which must always be considered as the cri- 
terion of the truth of any theory in physical science. By the following expe- 
riments this theory of the battery must either stand or fall. 
Exp. V. Having fixed two pieces of copper, an inch broad and two inches 
high, in the bottom of a box separated into two compartments by a diaphragm 
of bladder, and inverted a funnel-mouthed tube over one of them, (the box 
being previously filled with water slightly acidulated,) I connected the plates 
with the ends of a battery of thirty pair of plates. The hydrogen disengaged 
in three minutes was found to occupy about two inches and a half of the tube. 
The plates were now connected with one hundred and twenty plates of the 
same battery, and the decomposition allowed to go on for the same time; when 
it was found that the hydrogen collected was scarcely double that in the 
first experiment. Now the number of plates being as one to four, and the 
quantity of hydrogen nearly as one to two, we have the effects nearly as the 
square roots of the number of plates. By increasing the number of plates to 
a great extent, we should find, agreeably to a remark in § 10 of Part First, 
that the increase of effect would not go on so rapidly as the square root of the 
number of plates. This fact, which follows from theory, is strikingly confirmed 
by direct experiment. 
17 . The theoretical views now unfolded are strikingly confirmed by the 
application of the torsion galvanometer in the following experiment. 
Exp. VI. Two copper plates four inches square, having copper wires soldered 
