238 Laws of Metallic Reflexion, and Mode of 



relations (G) and (i) are independent of the value of //, and may 

 hold good though that value should require to be changed. 



All the preceding formulae are merely mathematical conse- 

 quences of those which I published long ago in the Transactions* 

 of the Academy. The formulas which I had previously given 

 in the Proceedings, f are slightly different, and, I think, less 

 likely to be exact, because they are less simple, and do not lead 

 to any of the remarkable relations which may be deduced from 

 the others. 



Having had occasion, in the course of the few experiments 

 which I made with the instrument before mentioned, to study 

 the nature of Fresnel's rhomb, which constitutes an important 

 part of it, I shall here describe the method which must be fol- 

 lowed in order to obtain true results, when the rhomb is em- 

 ployed in observations on light elliptically polarized. A ray in 

 which the vibrations are supposed to be elliptical is given, and 

 what we want is to determine the ratio of the axes of the 

 elliptic vibration, and their directions with respect to a fixed 

 plane passing through the ray ; in other words, to determine 

 the angles which we have denoted by |3 and in the case of a 

 ray reflected from a metal. For this purpose the ray is ad- 

 mitted perpendicularly to the surface at one end of the rhomb, 

 and after having suffered two total reflexions within, passes out 

 perpendicularly to the surface at the other end. Then causing 

 the rhomb to revolve about the ray, we shall find two positions 

 of it in which the emergent light will be the plane-polarized, 

 these positions being readily indicated by a Nicol's prism inter- 

 posed between the rhomb and the eye ; for such a prism, by 

 being turned round the ray, can make the light totally disap- 

 pear when it is plane-polarized, but not otherwise. These two 

 positions of the rhomb will be exactly 90 from each other ; in 

 one of them the principal plane of the rhomb (the plane of re- 

 flexion within it) will be parallel to the major axis of the elliptic 

 vibration, and the angle which it makes with the plane of inci- 



*VoL. xvni. p. 71 (supra-, p. 133). f VOL. i. p. 2 (supra, p. 58). 



