224 M. L. Soret on Illumination and Polarization 



reflected by each point of the illuminated part of the sphere j 

 and as the dimensions of this sphere are very small, each 



Fie?. 2. 



point will become a centre of disturbance or of waves. The 

 reflected vibrations forming the system of waves which proceed 

 from one of the points of the spherical surface will be rectilinear, 

 and their direction will be given by the laws of reflection of po- 

 larized light. (You see that I assume the direction of the reflected 

 rays in these conditions to be the same as that which Fresnel 

 assumes in the case of light reflected from large surfaces. The 

 tenability of this hypothesis might in certain cases be contested ; 

 but I think that even if it ought to be modified, that would 

 make no change in the considerations I am about to develope, 

 except for a part of those laid down in § VIII.) 



Each reflected vibration may be regarded as resulting from 

 three component vibrations — one vertical, the second horizontal 

 and parallel to the luminous pencil, the third horizontal and 

 perpendicular to the pencil. 



Suppose the eye placed in the horizontal plane passing through 

 the centre of the sphere. There is no reason why the vertical 

 components of the various reflected waves should not reach the 

 eye, which thus receives light polarized in a horizontal plane and 

 proceeding in greater or less quantity from all the illuminated 

 points of the reflecting corpuscle. 



Let us pass to the horizontal components parallel to the pencil. 

 Consider, for instance, the point m on the vertical great circle of 

 tbe sphere parallel to the pencil, the normal at this point making 

 an angle of 45° with the direction of the pencil. The incident 

 vertical vibrations give rise at the point a to reflected waves en- 

 tirely formed of vibrations horizontal and parallel to the pencil ; 

 that is to say, the other components are null for this point. 

 These vibrations are propagated in all directions,, and therefore 

 also in the direction of the eye placed in the horizontal plane 



