ON THE CONTACT THEORY OF VOLTAIC ACTION. 
19 
This is the most general case, it only assumes the electrometer quadrants to be 
symmetrical with reference to the needle, but allows any amount of unsymmetry in our 
induction apparatus. In practice, the motion of the electrometer needle is usually in 
these experiments so small that we may neglect the change in the capacity of the 
quadrants, and in the coefficient of induction of the needle on them produced by this 
motion ; consequently since the charge in the plate 3 and the attached pair of quadrants 
is not altered by the reversal 
AK 1 +BC3+NK,+BC,= (A+a)K' 2 +(D+^)C , 3 +NK, l +(D+^)C ? , 
similarly 
AK / 1 +DC / 4 +NK,+D0,= (A+a)K a +BC 4 +NK 1I +BC, 
. \ aK 2 =A(K / 1 -K 2 ) +D(C' 4 +0,)- B(C 4 + C 9 ) 
d( C' 3 - C ? ) = A (Kj - Kb) +B(C 3 +C ? ) - D(C' 3 +C ? ) 
In order therefore that a, which is the difference of potentials we desire to measure, 
shall be proportional to d, the observed difference of potentials, it is necessary that 
either C 3 = C 4 or B = 0 
and either C' 3 = C' 4 or D = 0 
fK A =K' 2 
and either < or A = 0 
U'^K* 
Now the conditions on the left hand side mean perfect symmetry of our induction 
apparatus before and after reversal. But as this, at any rate in Japan, is practically 
unattainable, it is desirable to make B, D, and A each nought. B can be made nought 
and also D very small by not merely connecting plates 3 and 4 together at the com¬ 
mencement of each experiment, but also with the outside of the electrometer or the 
earth, and we can also make A small by connecting either substance 1 or 2 also with 
the earth. Such connexions were always made in the following experiments. 
In order to rotate the lower substances 1 and 2, it is necessary, if one or both of 
them be a liquid, to first increase the distance between 1 and 2 and between 3 and 4, 
in order that 3 and 4 may not strike against the sides of the vessels containing the 
liquids. In our former apparatus this was done by the table carrying 1 and 2 being- 
supported and capable of revolution on a central leg, which itself was movable up and 
down (Proc. Roy. Soc., No. 186, vol. xxvii., pi. 7). But when the two substances of 
which it was desired to measure the difference of potentials were, say, a vessel of mer¬ 
cury and a comparatively thin plate of metal, the difference of weight on the two sides 
made it almost impossible with this method to obtain sufficient parallelism of the 
surfaces 1, 2, and 3, 4 ; so that our former experiments were necessarily confined to 
pairs of substances not having a great difference in weight. But, as it was obviously 
d 2 
