in Transparent Substances. 227 



Now, as we have already said and as we shall show, these com- 

 ponents are very feeble. 



If the angle of vision is less or more than 90°, then the hori- 

 zontal components perpendicular to the pencil, proceeding from 

 the pencil polarized perpendicularly to the plane, begin to act, 

 and the polarization ceases to be at its maximum. 



VII. Let us still suppose the plane of vision to be horizontal, 

 and that the illuminating pencil is formed of natural light — that is 

 to sa}?, of two pencils polarized at right angles, one in the hori- 

 zontal plane, the other in the vertical plane. Let us inquire 

 why in the reflected light the components parallel to the pencil 

 are very feeble as compared with the vertical components. 



In the first place, even if the sphere had an absolute reflecting 

 power, there would be a considerable predominance of the ver- 

 tical components. In fact, on the vertical great circle a e c, the 

 pencil polarized in a horizontal plane will give rise to reflected 

 vertical components at all points, except the two points at 45° 

 from e. The pencil polarized in the vertical plane, on the con- 

 trary, will not produce at any part of the great circle components 

 parallel to the pencil ; the same is the case with the great circle 

 a be. As regards the horizontal great circle b e, the first pencil 

 will everywhere produce only vertical components, while the 

 second pencil will produce no components parallel to itself at b, 

 nor will it at e ; it is only between these points that it will pro- 

 duce any. 



But, further, this preponderance of the vertical components 

 will be greatly increased by the fact that the reflecting power of 

 the sphere is not perfect. Thus on the horizontal great circle 

 b e (which in the case of perfect reflecting power would pro- 

 duce most components parallel to the pencil), the intensity of 

 the vertical components will be least at b, where its value will 



be proportional to ( -) , n being the refractive index of the 



corpuscles as compared with the transparent medium ; from 

 b this intensity will continually increase, up to e, where its 

 value is proportional to 1. On the other hand, the intensity of 

 the components parallel to the pencil will be zero at b, zero again 

 at the point for which the angle of incidence is equal to the 

 angle of polarization, zero again at the point e. Passing three 

 times through zero, the intensity of these components must 

 nowhere be considerable on the great circle b e } &c. 



The exact calculation of these intensities is very complicated. 

 M. Celierier has been kind enough to do it at my request for 

 several values of the refractive index, and he has found that the 

 vertical components greatly predominate over those parallel to 

 the pencil. 



Q2 



