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." 195
formula LS\ = k. In the case in which the two coils were used there is no difficulty
in deciding on the value of k. The formula for X is that given on p. 159 (D),
LSX2' i 1 -J-l + 4 _ 1
Xt=l-= 1- 2(3 S - + 40...,
and hence k = 916.
If only one coil is used two cases may arise; if the lower coil is completely insulated we have the case dealt with in Figure 4; the corresponding formula as far as
terms in S1/S are concerned is (F) on p. 166, viz.:
LSX2=1- 12 (i ~/ ) 1
and the value of k resulting from this is '978. If on the other hand the lower coil
is not insulated the correction necessary will be that indicated in (G), p. 167, and the
resulting value of k will be the same as that for the two coils, viz. '916.
As far as we know the coil was usually insulated; at any rate it was not intentionally connected to earth except for the two plates H and J.
But there is another complication in this case. We assume in this case that the
value of L is that for either half the coil; now this assumes that there is no current
in the unused coil; but in consequence of the electrostatic induction there is a current
in the unused coil. This current will be of the order x S'S if x is the current from
the main condenser, and its effect will therefore alter the coefficient of self-induction
L of the upper coil by an amount proportional to MS'/S or about 3M/120. Now the
value of L1 is about 1'4, and of M about '91. Hence the value of L1 in the experiments with the single coil is uncertain to one part in one hundred and seventy.
Omitting however this correction we get the following Table of values.
TABLE XIII.
Coil used k Frequency L S v Observations
A + B '916 880 4'636 58-53 3-009 x 1010 Mean from seventy sparks
A ( 978 1611 1 409 58-53 2-939 x 1010 Unused coil assumed insulated
(916 1611 1-409 58-53 3 037 x 100,,,, uninsulated
~916 1583 1 409 58-53 2-984 x 1010 Plate H, coil uninsulated
B -978 1607 1'393 58-53 2'922 x 1010 Unusedcoilassumedinsulated
~916 1607 1'393 58'53 3'020 x 10~,,,,,, uninsulated
~916 1595 1-393 58'53 2'990 x 1010 Plate J, coil uninsulated
25-2