210 REPORT—1885. 
Now we know from experiment that it does vanish, and hence either 
An or AD must be zero. If we put AD=0, it can be shown from the 
general expression for the rotation that there are six directions along | 
which the scattered ray vanishes, for the components of the rotation are 
given by— 
An yz ) 
wv, =— — 
3 Pp , Pr 
An vy 
Oe day, «78 ‘ (94) 
An 2—22 
2) oe 
Now, there is nothing in the experimental results which at all leads to 
such a conclusion. If the hypothesis of a variable density be adopted, 
and Av be put zero, then, 
D,) 
ke ay rr ; : : 4 » 2(95) 
gs, AD 2 
2 PD r 
and the light vanishes in one direction only, viz. that of the axis of z. 
This result, of course, agrees with that of the former paper, and we must 
conclude that Fresnel’s explanation of the cause of reflexion is the true 
one, while MacCullagh’s is false, and that in plane polarised light the 
vibrations are perpendicular to, not parallel to, the plane of polarisation. 
The theory as left in this paper does not explain the phenomenon of the 
residual blue discovered also by Tyndall, who found that at a certain 
stage in the growth of the particle causing the scattering some light 
is discharged by the cloud parallel to the direction of vibration of the 
incident light, and that this light is of a very intense blue tint. 
Lord Rayleigh points out that this may be due to the higher powers 
of AD/D, which have been omitted, and in a more recent paper, based on 
the electro-magnetic theory, he develops this point more completely.! 
Chapter VIII.—Gernerat Conciusions. 
§ 1. Space compels us to conclude with this the general account of 
recent work on optical theories based solely on the elastic solid theory. 
Special problems of various kinds have received their solution, but to 
these we can only allude ; indeed, for several of them the general proper- 
ties of wave motion with the principle of interference are all that are 
required. Such, for example, are the papers by Prof. Stokes, ‘On the 
Theory of certain Bands seen in the Spectrum,’ 2 ‘On the Formation of 
the Central Spot in Newton’s Rings beyond the Critical Angle.’3—This is 
shown, as was suggested by Lloyd, to be due to the surface disturbance, 
which takes the place of the refracted wave when the angle of incidence 
1 See p. 253. 
2 Stokes, Phil. Trans. 1848 ; Math. and Phys. Papers, vol. ii. p. 14. 
* Stokes, Camb, Phil. Trans. vol. viii.; Math. and Phys. Papers, vol. ii. p. 56. 
