of some Brilliant Animal Colours. 107 



question then arises, Is there any loophole for escape ? 

 1 think there may be. The polarizing angle, as given 

 by Brewster's law, depends much upon what we may call 

 the smoothness of the reflecting surface. A moderate 

 curvature is of no significance in this connexion, but when 

 the radius of curvature becomes comparable with the wave- 

 length of the light it is another matter. Thus in the case of 

 smooth glass the polarizing angle is about 57° — that is, 

 light incident at this angle with the normal and vibrating in 

 the plane of incidence is not reflected. In this observation the 

 reflected light (if there were any) would be deviated from 

 its original direction through an angle of 2 (90° — 57°) = 66°, 

 and this is the direction in which light initially unpolarized 

 would appear completely polarized. Now replace the flat 

 glass by a sphere of the same material, whose diameter is 

 small in comparison with the wave-length. Light is now 

 scattered in various directions, but the direction in which 

 light originally unpolarized becomes completely polarized is 

 at 90° with the original direction, instead of ()6°. As the 

 sphere grows, the polarization ceases to be complete, and 

 the direction of best polarization moves oppositely to what 

 would be expected — that is, still further away from 66°. 

 When the circumference of the sphere is equal to twice the 

 wave-length, the polarization, still pretty good, occurs at an 

 angle of 135° with the original direction of the light *. In 

 order to carry out the suggestion, we must - abandon the 

 supposition of uniform plane strata, inapplicable anyhow in 

 its integrit}^ to the case where one of the alternate plates 

 is of air, and substitute a structure in which one of the 

 alternatives takes a form such as the spherical. A layer 

 of equal spheres, with centres disposed upon a plane, would 

 give a specular reflexion and a polarizing angle dependent 

 upon the diameter of the spheres and upon the intervals 

 between them. In certain cases, e. g. when the circum- 

 ference of the sphere (of glass) is equal to 1*75 x wave- 

 length, the polarization is very imperfect. To explain a 

 brilliant and highly-coloured reflexion there would need 

 to be several layers of spheres, and it might be supposed 

 that the diameter varied in different layers. In this way 

 it would seem possible to combine a specular and highly- 

 coloured reflexion with a very imperfectly developed 

 polarization, and thus to evade the difficulty which meets 

 us when we confine ourselves to " thin plates." Spheres 

 have been spoken of for simplicity and because some of 



* Phil. Mag. vol. xii. p. 81 (1881) ; Proc. Roy. Soc. A. vol. lxxxiv. 

 p. 25 (1910) ; Scientific Papers, vol. i. p. 518, vol. v. p. 564. 



