Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

DISCHARGE OF AN AIR CONDENSER, WITH A DETERMINATION OF "v." 167
Thus so far as the term in SI/S is concerned the correction is one-fourth of that
to be applied in the first case, and this, when the values of S1 and S are 16 and
58'53 respectively, comes to - 022.
If we assume the coefficient of the term in (81/S)2 to be also divided by 4 we
have to add to this + 001. Thus to about one part in 1000 we have
2LS = l — 021 = '978.
If however in the case represented in Fig. 4, we suppose that the lower coil is
uninsulated, the equations can readily be shewn to be those of the first section of this
Part, and the formula for the frequency will be
X2S = 9169..........................................(G ).
There is however another possible arrangement to notice.
-VI D
VI V, 2__2 ---'v \Q~JJ2 V3 û_Qj2L2^ jLOJ^ V.-1 2^2J^'lFIG. 5.
Case iii.
If in Fig. 5, AB, CD represent the two coils, we have supposed above in Fig. 3
that B was connected to C, while A and D are connected to the main condenser. In
some of the experiments however it appears possible that B was connected to D, and
A and C to the external condenser. The distribution of potential would then be as shewn
in the figure, and the solution differs from that of the first case. We can write down
the equations and solve this case, but it can be shewn thus that it reduces to the
second case.
For compare Fig. 5 with Fig. 6, which is obtained by putting the coil DC alongside
AB, and placing above the two a second similar double coil A'B'D'C' with its ends
insulated; the distance between this and the first coil being the same as for the two
coils in Fig. 5. The distribution of currents is clearly the same. Now if S~ be the
capacity of the two coils AB, DC, or A'B', D'C' in Fig. 6, the correcting term is
--- s/12S.