﻿of Light by small Particles. 451 



which show that there are in all six directions from along 

 which there is no scattered ray — two perpendicular to the plane 

 {zx) of original vibration, and four in that plane inclined at 

 angles of 45° to the original ray and its prolongation. No va- 

 nishing of the dispersed light in these oblique directions is known 

 from experiment ; but before unreservedly discarding the theory 

 which indicates it, we ought to inquire how far our approxima- 

 tion is sufficient to warrant such a step. In neglecting the pro- 

 ducts of £, 7], £ with An, we have in reality omitted terms 

 from the result which involve the square and higher powers of 

 An, and it may be that the light corresponding to them would 

 not vanish in the specified directions. I have not been able to 

 satisfy myself whether this would be so or not ; but I think that, in 

 spite of ignorance on this point, the inference may be safely drawn 

 that the theoryis untenable ; for the terms in question, depending 



All 2 

 on the square of the difference of rigidity, are proportional to — g- 



f 1 

 (where fi is the refractive index), and become of less and less im- 

 portance as the media approach one another in refrangibility. 

 In the case of particles of mastic suspended in water, the indices 

 are 1*5 and 1-33, and terms depending on the square of An 

 must be comparatively small. Yet I could find no indication of 

 a falling off of intensity in the predicted directions in some ex- 

 periments that I made with precipitated mastic and soap, and 

 accordingly conclude that the hypothesis of a constant density 

 and variable rigidity must be rejected. The only alternative is 

 to suppose, as in the February Number, that the aether preserves 

 its statical properties unchanged when associated with matter, 

 whose effect is therefore merely to increase the inertia of the vi- 

 brating parts in greater or less degree. 



It may be worth notice that, according to the theory here 

 combated, there would be two polarizing-angles, of 22 J° and 67^° 

 respectively, when light vibrating in the plane of incidence is re- 

 flected from the boundary of two media which differ but little 

 in refrangibility, as may be seen from the reasoning of this paper 

 by remembering that the square of An may be neglected. I 

 need scarcely say that in such a case the polarizing angle is 

 really 45°, and that the reflected light does not tend to vanish 

 at the two first-mentioned incidences, whichever way the light 

 may be polarized*. 



In equations (5), putting An = 0, we have 



* There is a sense in which 45° is the first approximation to the polari- 

 zing-angle for all substances. The difference between the true value and 

 45° may be looked upon as a correction depending on the square and higher 

 powers of the difference of optical density. 



