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.

166 MESSRS GLAZEBROOK AND LODGE, EXPERIMENTS ON THE OSCILLATORY
put x1 =, x2 =x 1-IY2, x = x-2y3,
Y2= -i (x1- 2), y3= (x - ), etc.,
Y3 - Y2 (x2 - X3), etc.
i.. 1 1 (x 1- 2)
(m + 1) L'=-S _ 2 xHence < L'2 = _X1 - 2 2 - x3
2 2S' 2S '
\ L'$ = i S' (xn_ - xn);. putting x = Xe-t,
i2S' {(m + 1)L' - 1 -1 X1+ X2= 0,
X, + {2S'X2L' - 2} X2 + X3 = O,
Xn,_ + {2S'x2L'- 1} Xm = 0.
Solving these equations as previously, putting S'L'X2 l-cos, we find as the
equation for the periods
Sx,2L'..n...=1...................(E).
+ -cos + sin cot mb)
Expanding as far as b2 and assuming that 02 may be neglected, compared with;,"2)2, we have
S2L' +m + 1,
2S2NowLL, {1 =, 22 = 1'.
N{Now 2mL' = L, 52= 2S'X2L', S = (2m-1))S'.
Heiice LxS {1+ (2N -L) = 1'
or neglecting the terms in (8/8)2,
1- (1......................