ON OPTICAL THEORIES. 209 
Lord Rayleigh’s paper concludes with another proof of the formula 
which gives the motion due to a force acting parallel to the axis of z. 
Pat for the force Ze’, then the equations of motion become, when 
expressed in terms of the rotation, 
(b?7? + n?) v0, =0 
(bax? — n*) W) = dy (91) 
(b° 7? — n?) vo, => _ 
dz 
Hence 
] ee fem 
= A | = aa Zz 
* rl ||2a( : ) aad 
Qa ee 
where k= =, 
XN b 
and the integral extends over the space T, through which the force 
acts. 
; —ikr 
Within this space +(—) is sensibly constant; and if w be the re- 
y Ue 
sultant rotation which will take place about an axis perpendicular to the 
plane through z and the radius vector, 
Lal RT Aji ay a 
Anh? Yr 
TF sin a Qr 
== ' j—— SESE — —f e ° bs 2 
Hence g [oa Achy 885 (bt—r) (92) 
In the second paper mentioned above Lord Rayleigh points out that 
the cause of reflexion may be diminished rigidity rather than increased 
density, and that in this case a scattered ray might be composed of 
vibrations perpendicular to those of the incident ray ; he then proceeds 
to describe experiments on the composition of the light of the sky, made 
with a view of showing that it is such as would result, according to the 
above formula, from light scattered by small particles. And in the third 
paper he discusses the motion in an elastic solid in which the density and 
rigidity vary from point to point. 
The problem is solved for two media differing slightly in density and 
rigidity, and it is shown that in a direction normal to the incident ray 
the rotation in the scattered ray, when the incident vibrations are parallel 
to z, is given by 
2 92 An)? 2 of AD)? y? 3 
a) sen \ ep oye ; < chee 
where 
__ BT e-itr 
dur rT 
Hence, if Anand AD are both finite, the scattered light can never 
vanish in a plane normal to the incident ray. 
1885. P 
