IN VOLTAIC ELECTRICITY AND ELECTRO-MAGNETISM. 
289 
effects of two batteries of the same length, and having the same size of plates, 
will be directly proportional to the number of plates. Hence it follows that 
each pair of plates produces an equal effect in whatever part of the battery it 
is placed. This is one of the fundamental principles on which the true theory 
of the battery is founded. 
13. Since each pair of plates, then, produces an equal effect, let us now ex¬ 
amine what will take place with regard to batteries of unequal lengths, when 
the plates are of the same size, and placed at the same distance from one 
another. 
Let A, B be two batteries, having the same size of plates, and placed at the 
same distance from one another, and let n be the number of plates in A, and 
N the number in B. Let the voltaic effect of the extreme pair of plates in 
the first battery be denoted by F, and that of the extreme pair in the second 
by f 
Two equal plates of copper c, c are placed at the ends of each, and the ex¬ 
treme cells filled with the same diluted acid as that used in the other cells. 
The extreme pair in the battery A which produce the effect F, are z' c' ; and 
those in the second battery which produce the effect f, are z' c'. 
Now, since the effects of the extreme plates are inversely as the square roots 
of their distances, they will be inversely as the square roots of the number of 
plates. Hence F :f : : -r : —r. Multiplying the terms of this proportion by 
?Z JN 
those of the identical proportion 
n : N : : n : N, 
we have wF:N/::4:p 
or n F : N f : : : N* 
But n F being the accumulated energy of the battery A, and N f that of the 
battery B, we have, within certain limits, the voltaic energies of two batteries, 
very nearly proportional to the square roots of the number of plates. 
14. Had the conducting power of acid solutions in an elementary combina¬ 
tion been in the simple inverse ratio of the distance, there could have been no 
accumulation of voltaic effect; or, in other words, the battery could never have 
existed. 
