141 



de MM. xArago, Biot, Fresnel). Elles servent meme a de- 

 terminer les conditions et les lois de ces phenomenes ; elles 

 niontrent que generalement, dans un rayon de lumiere po- 

 larisee, une molecule d'ether decrit une ellipse. Mais dans 

 certains cas particuliers, cette ellipse se change en une droite, 

 et alors on obtient la polarisation rectiligne." " Enfin le calcul 

 prouve que, dans le cristal de roche, I'huile de terebenthine, 

 &c., la polarisation des rayons transmis parallelement a I'axe 

 (s'il s'agit du cristal de roche) n'est pas rigoureusement cir- 

 culaire, niais qu'alors I'ellipse difFere tres peu du cercle." 



Thus, to say nothing for the present of the questions of 

 dispersion and absorption, it appears that M. Cauchy con- 

 ceived he had completely accounted for the facts of circular 

 and elliptic polarization, and that he hatl deduced the for- 

 mulas " which serve to determine the conditions and laws of 

 these phenomena." But neither in this letter, nor in any 

 subsequent version* of his theory, has he given the formulas 

 themselves. Nor has he told us the nature of the calculations 

 by which he was enabled to coi'rect the received opinion, 

 and to prove that the vibrations in a ray transmitted along 

 the axis of quartz, or through oil of turpentine, are not ri- 

 gorously circular, as Fresnel and others have supposed, but 

 slightly elliptical. Now — to take the case of quartz — if we 

 consider that the vibrations of a ray passing along the axis 

 are in a plane perpendicular to it, and if we admit, as M. 

 Cauchy always does in the case of other uniaxal crystals, that 

 there is a perfect optical symmetry all round the axis, we 

 shall find it hard to conceive on what grounds he could have 



* From some statements that have been made within the last few days by Pro- 

 fessor Powell (Phil. Mag. vol. xix. p. 374), at the request of M. Cauchy himself, 

 it appears that the latter republished his views about circular and elliptic polariza- 

 tion, in alithographed memoir of the date of August, 1836. But I do not find that 

 he published, either then or since, the detailed calculations which he seems to have 

 made. 



n2 



