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.

160 MEssRs GLAZEBROOK AND LODGE, EXPERIMENTS ON THE OSCILLATORY
The equations to be solved are
X 2 (1- cos )
L'S'
tan (2S - 1)= cot no;
S'= 1 n, -1=30, =-2733,
n-' -
for S= 5853 metres, 1= 16 metres.
Hence (i- 1)= 21
Hence 218 x tan = cot 310.
2
An inspection of the Tables and a trial shews that s is nearly 56'.
By plotting on a large scale the values of cot 31o and 218 tan sb/2 at about 56',
we find the curves intersect at 56' 30".
Hence = 56' 30".
LS
Hence 2LS = 2 (1 - cos s) L-S
2(1S
= 2 (1 - cos s) n (n - 1)
= 919,
substituting for s, n and S/Si.
Thus practically the same value is found as by the series. If we take S= 1 metre,
as in the experiments with coil (A) or (B) singly, then
S/S = 58, 2 (n-1) = 60,
and tan s/2 {58 x 60 - 1} = cot 310.
Thus 3479 x tan ( = cot.310.
A similar procedure gives for s the value 14' 45", and substituting in the equation
for X2LS we obtain
X2LS = 9924.
The solution by series already obtained was 9943.
The case in which there is no outside condenser is given by putting S = S' in the