ON OPTICAL THEORIES. 207 
the rotations are 
or on 
0,  OC08 5 (bt—z), 0; 
and the elementary rotation to which this gives rise is 
Cc ‘ - Ir 
v= — 778 (1 + cos 6) sin W sin = (bt — r), 
w being the angle between the axis of y and the radius vectorr. This 
elementary rotation takes place about a line perpendicular to the radius 
vector, and lying in a plane containing it and the axis of y. 
On passing from one medium to another the rotation is not neces- 
sarily continuous. The only surface conditions are that the displace- 
ments and the stresses are the same on the two sides of the surface of 
separation, and if the rigidity of the ether be different in the two media 
the rotations will be different also. But Professor Stokes’s solution 
does not apply to this case, and for the case to which it does apply is 
complete. 
Chapter VII.—Tue Scarrerine or Licut sy Smauyi Parricrzs. 
§ 1. In his experiments on the light scattered from precipitated clouds 
of fine matter, Tyndall’ showed that when the particles are sufficiently 
fine the light emitted laterally is blue in colour, and in a direction per- 
pendicular to that of the incident beam it is completely polarised. 
The full explanation of this was given by Lord Rayleigh in 1871 ina 
series of papers ® having an important bearing on our present subject— 
the relation between the plane of polarisation and the direction of vibration 
of plane polarised light. Professor Stokes, in his paper on fluorescence,3 
had indicated the connection between the two questions. 
For consider a beam travelling horizontally, and look at it vertically 
downwards: the scattered light is in great part polarised in the plane of re- 
flection. Ifthe scattering particles be small compared with the wave length 
of the incident light, the vibrations in an incident ray cannot be at right 
angles to those in a scattered ray. For the incident vibrations are 
affected by the dust particles, which in consequence of their very great 
mass relative to the ether remain practically at rest. 
We may treat the problem as if the dust particles moved exactly as 
the ether which they replace would do, and then superpose on this motion 
an equal and opposite motion. The first motion will not affect the 
regular propagation of the waves. In consequence of the second the 
particles become centres of disturbance, and set up other motions in the 
ether. These other motions will depend on the direction of apparent 
motion of the dust particles, and the optical effect in any direction will 
depend on the component of the motion at right angles to that direction. 
Now, the reflected ray is polarised in the plane of reflexion. If, then, the 
? Tyndall, Phil. Mag. (4), vol. xxxvii. 
2 J. W. Strutt, ‘On the Light from the Sky, its Polarisation and Colour,’ Phil. 
Mag. ¥eb. and April, 1871; ‘On the Scattering of Light by Small Particles,’ June, 
1871. 
* Stokes ‘On the Change of Refrangibility of Light,’ Phil. Trans. 1852. 
