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.

162 MESSRS GLAZEBROOK AND LODGE, EXPERIMENTS ON THE OSCILLATORY
used and the value of S1 therefore was 16 metres, the values of S were approximately
2, 5, 5'5 and 10'5 metres. The values of 9b and X2LS can be found for these cases in
the same manner and we thus get the following Table.
TABLE IV.
S S1 S/S1 0 LS
2 16 -125 2~ 37' 48" -2449
5 16 1 312 2 16 40 *4582
5'5 16 -344 2 12 20 -4741
10-5 16 -656 1 52 12 '6498
58-53 16 3-659 56 30 -9169
0 16 238*
The experiments in which the external capacity is small are of no value as a means
of finding "v." They serve however to test the truth of the formula and of the corrections which we have applied.
We may put the correction another way, and say that instead of employing the
whole capacity S to calculate the frequency from the formula 2LS = 1 we have to use
a capacity S/k, where k has the values given in the last column of Table IV.
Throughout the above we have taken L', the effective coefficient of self-induction
of 1/n of the number of turns, as 1/n of the whole coefficient, and neglected the
mutual induction between the turns; we proceed to justify this.
Now the effect of inductance in any wire is made up of the self-induction of that
wire, and the mutual induction of the other wires; moreover the currents in the various
turns are, owing to the capacity, not the same.
Let il be the coefficient of induction of a wire in which the current is &1 due to
itself, mn2, nz13, etc. the mutual coefficients.
Then the strict equations for any wire joining two of the condensers each of
capacity S' will be
1
Ila + %2,2 +... + (XI - x2) = 0;
put L'X1 = l1 + n+122 +.
and let x2 = xc + y2,
X3 = 2i + y3, etc.,
L'5 = (il + m2 +...) 55i + mm.yo + m,) +....
* For this case S, takes the place of S.