208 REPORT—1885. 
vibrations be in the plane of polarisation they will be at right angles to 
those in the incident light, while if the vibrations be at right angles to 
the plane of polarisation, they will come from the component of the 
original vibration, which is at right angles to that plane. If, then, on 
this supposition as to the relation between plane of polarisation and 
direction of vibration the incident light be polarised at right angles to the 
plane of reflection—i.e., in the case before us in a horizontal plane—the 
light scattered in the vertical direction should vanish, and this is found 
to be the case. This general reasoning is substantiated by Lord Ray- 
leigh in the papers before us by mathematical reasoning, and, moreover, 
he shows that the intensity of scattered light in any direction varies 
inversely as the fourth power of the wave length. 
This may be seen from a consideration of the dimensions involved. 
The ratio of the two amplitudes in the scattered and incident vibra- 
tion will be a number. It must also involve the volume of the dust 
particles, being directly proportional to it, and it also will be inversely 
proportional to 7, the distance from the disturbance; it must therefore 
depend on T/A?r. 
The mathematical expression for the disturbance is found as follows :— 
Let D’ be the density of the ether in the dust particles, D in the space 
surrounding them. Let the vibrations in the incident wave, when they 
strike the dust, be given by A cos 2 bt. Then the acceleration is 
Deters Noght Loder 
A (> b) cos —~ bt. 
In order that the wave may pass on undisturbed through the parts where 
the density is D’, force would require to be applied; the amount of the 
force will be 
_A('-D) ali Qn 
a I pan 
per unit volume, and hence a force 
2rb\? 20 
A(D’—D) (—— + OE 
(D ) ( ; ) cos ~ bt, 
conceived to act at O, the position of the particle, gives the same disturb- 
ance as is caused by the particle. Now, we have seen in Professor 
Stokes’s paper that a force F cos — bi per unit of volume produces a 
displacement at any other point given by 
F sina Or 
oe fi cat of AEA 
which is this case comes to 
D’/-DT. Qa 
C= A oa in aleos —— (bt — 7) ; : et 90} 
where a is the angle between the radius vector r and the direction of the 
force F, and the displacement takes place in the plane passing through 
the directions of the force and the radius vector, and is at right angles to 
the latter. 
