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.

374 PROF. LOVE, THE PROPAGATION OF WAVES, ETC.
and thus the displacement along the tangent to the circular section of the cylinder is
W sec a cos;
the displacement along the radius vector outwards is -a sec2 a a- cos a Wsin ms, or
W sec a sin 0,
and thus the displacement is W sec a at right angles to the plane from which 0 is
measured. The helix is displaced bodily, and there is no deformation.
10. Again, taking m2= llp2 - 1/o2, where a2 is supposed > p2 or a< 47r, we find that
equations (16) and (19) show that either
_ A (m2 - l/p2- 1/a2) 1 - m2p2
po p1 + A/Cm2p2 1 + m2p2'
or g. =, p=2 (m2 _ 1/p2 - 1/-2)2 Sp
poco m2p2
The motion for which g2= 0 is an example of the slower wave, the speed p of this wave
is given by
2 A 4 p2(o_ p2)
p po o4 (22 _ p2) {(1 + A/C) 2 - p2}'
and the flexural couple G2 in the osculating plane and the displacement v along the
binormal both vanish at all points of the helix.
The motion for which g,= O is an example of the quicker wave, the speed p of
this wave is given by
2 A 4 p
po O 04 o-2 - p2'
and the flexural couple G6 about the principal normal, the torsional couple H, and the
displacements u and w along the principal normal and the tangent all vanish at all
points of the helix.