in Transparent Substances. 223 



dent pencil. Let the plane of vision be the plane o as com- 

 prising the pencil of light and the visual ray. 



If the dimensions of the body abed are large as compared 

 with the wave-lengths of the light, according to the ordinary laws 

 of reflection the eye in the position o will only receive the rays 

 reflected by a point a, such that the normal a n to the surface 

 of the body at this point is situated in the plane of vision, and 

 that the angle of incidence s an is equal to the angle of reflec- 

 tion n a o. The reflected light will in general be partially po- 

 larized ; and if the eye is in such a position that the visual 

 angle is double the angle of polarization, the ray a o will be 

 totally polarized, the plane of polarization coinciding with the 

 plane of vision. 



But we know that if the reflecting surfaces are not very great 

 as compared with the wave-lengths of the light, the ordinary 

 laws of reflection are no longer applicable, and each point of the 

 reflecting surface may be considered as a centre of disturbance 

 from which waves are really emitted — or, in other words, that 

 the motion of the gether in all directions other than that of the 

 reflected fay in the ordinary case of reflection is no longer an- 

 nulled by interference. This is what results from the reason- 

 ings and experiments of Fresnel. If, then, the body a b c d is 

 very small and has dimensions comparable to the wave-lengths, 

 the eye will receive more or less intense reflected rays pro- 

 ceeding from all points of the illuminated surface of the body. 

 Thus, for instance, the visual angle being double the angle of 

 polarization, the eye no longer receives merely the light totally 

 polarized in the plane of vision reflected from the point a, but also 

 non-polarized light, or light partially polarized, emitted by the 

 other points of the surface illuminated by the incident pencil. 

 There is no longer any reason why the maximum polarization 

 should be exhibited when the angle of vision is twice the polari- 

 zing angle. 



It is clear that this reasoning applies to all the corpuscles 

 which are illuminated by the luminous pencil ; thus a first source 

 of difficulty is removed, that, namely, which you mentioned in 

 your communication to the Royal Society on the 16th of De- 

 cember 1868. 



IV. Let us now suppose that the pencil of light s a, s' c (fig. 2) 

 is polarized in a horizontal plane perpendicular to the plane of the 

 figure ; it illuminates the very small particles, which first of all we 

 will suppose to be spherical. Let us now examine what takes place 

 in the case of one of these particles, abed. The plane of polar- 

 ization being horizontal, we will assume that the incident 

 vibrations of the aether are rectilinear and vertical, and there- 

 fore parallel to the plane of the figure. The vibrations will be 



