196 Notes on some Points in the Theory of Light. 



quent version* of his theory, has he given the formulas them- 

 selves. Nor has he told us the nature of the calculations by 

 which he was enabled to correct 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 rigorously 

 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 come to 

 the conclusion that the vibrations of such a ray are performed 

 in an ellipse. For if all planes passing through the axis of 

 the crystal be alike in their optical properties, there will be 

 absolutely nothing to determine the position and ratio of the 

 axes of the ellipse ; there will be no reason why its major axis, 

 for example, should lie in one of these planes, rather than in 

 any other. But, whatever may be thought of this case inde- 

 pendently of observation, it is manifestly absurd to suppose 

 that the vibrations are elliptical in the case of a ray passing 

 through oil of turpentine, or any other liquid possessing the 

 property of rotatory polarization; for, in a liquid, all planes 

 drawn through the ray itself are circumstanced alike. From 

 these simple considerations it is evident that the theory of 

 M. Cauchy is unsound; but a closer examination will show 

 that it is entirely without foundation, and that it is directly 

 opposed to the very phenomena which it professes to explain. 

 To make this appear, however, in the easiest way that the 

 abstruseness of the subject will allow, it will be necessary to 



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

 Professor 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 polarization, in a lithographed memoir of the date of August, 1836; 

 but I do not find that he published, either then or since, the detailed calcula- 

 tions which he seems to have made. 



