190 APPENDIX TO MEMOIR OF PELTIER. 



ner analyze it at its emergence witli an acLromatic donLle-refracting prism, we 

 shall see two images always colored and presenting complementary colors which 

 change when the bi-rei'racting prism is made to revolve. The reason of this 

 difference is the following: 



A ray of white light polarized is a ray of which all the constituent colored 

 rays have vibrations which are always executed in the same plane. Now, if 

 such a ray be made to pass through a crystal with a single axis, the planes of 

 polarization of these different rays are not modified. The colored rays issue 

 from it as they had entered, and consequently the bi-refi-acting prism employed 

 to study the white ray at its emergence can produce no other phenomena than 

 those which it produces with all ordinary polarized rays. 



It is not the same when quartz is employed. This mineral, in effect, has the 

 property of deflecting the plane of ])olarization of the different-colored rays 

 constituting the polarized white ray. The lamina of quartz turns these different 

 planes around its axis, so that the planes might be said to follow a spiral situated 

 within the crystal; the plane of polarization of the red ray is the least deflected, 

 being that which makes the smallest angle with the primitive plane of polariza- 

 tion; on the contrary, the plane of polarization of the violet ray is most deflected, 

 l)eing that which makes the greatest angle with the above definitive plane. It 

 is thus seen that in the deflection of their planes of polarization, the rays follow 

 the order of their respective refrangibilities, beginning with the least refrangible. 

 When, therefore, the polarized white ray issues from the lamina of quartz, the 

 colored rays which constitute it have each then- plane of special polarization — 

 have each particular and different planes in which their vibrations are performed. 

 When we proceed, then, to analyze such a ray with an achromatic double-refract- 

 ing prism, the colors are distributed in unequal proportions among the ordinary 

 and extraordinary' pencils, which consequently produce colored and complimentary 

 images. 



The planes of polarization of the colored rays which have traversed the axis 

 of a lamina of quartz deviate from their primitive position by a quantity propor- 

 tional to the thickness of the lamina. They exhibit a double angular deviation 

 for a double thickness, and, at the moment of their emergence they present pre- 

 cisely the position in which they would occur if they had been made to turn 

 uniformly in the same direction around the axis during their transit through the 

 lamina. From this it will be seen, that by giving to the lamina of quartz a 

 sufficient thickness, the primitive plane of polarization of a ray might be made 

 to turn even several semi-circumferences. This shows that there is a fundamental 

 difference between the action of the quartz on a polarized white ray, and that of 

 a prism of glass on a ray of natural light; it is, in effect, that the first is a molec- 

 ular action, while the second is due only to the difference of refractive power of 

 the surfaces. 



By giving a suitable thickness to the lamina of quartz, we may obtain, there- 

 fore, such a tint as is desired for a given position of the principal section of the 

 prism. M. Arago has, with reason, chosen the thickness which gives a pure 

 blue of the second order in the ordinar}' image; this thickness is in general fi'om 

 six to seven millimetres. 



It results from what has been said, that the intensity of the blue color in the 

 ordinary ray de})ends upon the perfection of the polarization of the ray which 

 falls on the lamina of quartz, on the thickness of that lamina, and on the posi- 

 tion of the bi-refracting prism. For a constant thickness of the lamina and an 

 equally constant position of the bi-refracting prism, the intensity of the color 

 can, therefore, only depend on the greater or less perfection in the polarization 

 of the incident ray; in other words, on the relative polarization of that ray. 

 Now, when the pile of glasses in the cyano-polarimeter is perpendicular to the 

 incident ray, the polarization is null, and consequently the coloration is equally 

 mdl. The more the pile is inclined and the incidence of the ray oblique, the 



