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." 169
Thus comparing this with the result on p. 161 we see that the frequency is the same
whether the connexions be as in Fig. 3 or in Fig. 5.
In order to solve when S1 is not small compared with S we have with the same
notation from the above equations
sin + ) -n (1 -cos = sin cos
Now we may suppose q is small.
Hence cot né = tan f = 2 (S
2 S' n'2
S 2
Now if X2SL =k = 2nX2SL',
since 2X2S'L' = 2,
we have k = ns _-..'. cot 7z> =n S{ S (
Now S' =- = approximately, and when the connexions are as in Fig. 4, k= 25
for S= 2. Hence assuming k is not very different in the present arrangement
cot 300 = - (1 + 12),
3.36
cot 30 = — 1-68s.
The solution of this gives =- 2~ 50' 30" and k = -2873.
If S =5, k is '45 in the first arrangement. Thus
cot 30, = 6q approximately,
whence b = 2 30'30",
and k='558.
For S = 5 =5, = 574,
while if S=10'5, k ='784.
If then we write 2LS = k we have the following values for k according as the
connexions are made.
VOL. XVIII. 22