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.

368 PROF. LOVE, THE PROPAGATION OF WAVES
in which ic and w have been adjusted so as to satisfy the equation (2) of inextensibility.
Further, we shall take the forms of G6, G2, H to be
G1 = Ag1 eos (ms - pt), G2 = Ag1 sin (s - pt),. (6)
H = (np)-1 Ag, sin (ms - pt)
in which G1 and H have been adjusted so that the third of the equations of moments (3)
is satisfied identically. We then find by (1)
g=- +_ _p Y(-+) 2
A&=_+ B + — F
-p a2 p o( + C2=2 _ + -) +, 2........................ 2 8,
Ag1 I( V W
= - C yB~+ - +omp p p c /
of which the first and third give
g(l+.+2..............(8)
and the second is
^ = r - V t2.W+ f 2 -1. +.)..................................
mzp paP p c2
If 2 - __ - 2- does not vanish we can solve for V and W and obtain
p2 = 2
v(in21~+M + 1$ =_ __ -
(7- - 2 = g 1 + Cm22) p Cr2 mr( (10) p
p2 - C32) pa- 2 jmp\ p2 -2) )
The first two of the equations of moments (3) now give us
N1 = -A (- g + mg2) cos (mîs - pt),
r.................. (11).
{( =- A {(m- 9 g~ + - 2g, sin (ms -pt)
We eliminate T from the equations of motion (4) and obtain
a S+ 1 - 1 - = po p2 ( + 1O2p2) ( /p) cos (ms -pt),
a -s ( ),
+- - p0oplVcos (ms -pt),
or, on substituting for Ni and.2,
l 2 (m - ) + mg2 -+ = poOP2 (1 + m2p?) W,)
A P, /J? _ l............ (1 2 ).