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.

156 MESSRS GLAZEBROOK AND LODGE, EXPERIMENTS ON THE OSCILLATORY
Whence to find the periods we have the determinant
P 1 0.... =0
1 Q 10...
o QI O...
0 1 Q 1. (to n columns).
1 R
Now the determinant
=P Q 1... +(- 1 i
Q Q 1 (n- 1) columns Q (n-) columns
i1 l? Q1 0
I1 R 1 0 O
=P R 1... +(-1)2-3 R 1
Q.. (n - 1) columns Q (n- 2) columns.. Q Q 1... 1 Q I Q
Now
R 1 =1R Q 1 0 +(-1),-l 1 0 0... 1
1 i Q 1
(m) columns Q (m - 1) columns
Q 0 I Q Q 1
iQ
=1R Q 1 0... +(- l)2'-3 Q 1 o
1 Q 1... (m - 1) columns 1 Q I (m - 2) columns
Q............
= R\m_i - Am-2,
if An stands for Q 1 0 0... to m columns.
L Q 1...
Q i 0...
0 1 Q 1i...
Q
Thus the given determinant
= P {Ra2 - a_-3} - {RAn_3 -- a 4} = 0.
Now if Q=2cos 8, then we know that
= sin (m+ 1) O (Rayleigh, Sound.)
Hence we have as the equation for the periods
P {R in (- ) - s in (n - 2) O - {R sin (n- 2) - sin (n- 3) } = 0.