383 



respectively perpendicular and parallel to the plane of inci- 

 dence ; then we shall have 



tan0 = 7'^ > cos2ff = -7-^; (h) 



v'+ V 



from which we may infer that 



sin^ tan2<T = ^, (0 



or that the product on the left side of the last equation is 

 independent of the angle of incidence. It is to be observed 

 that the relations (g) and (i) are independent of the value of 

 fi, and may hold good though that value should require to be 

 changed. 



All the preceding formulae are merely mathematical con- 

 sequences of those which I published long ago in the Tran- 

 sactions of the Academy (vol. xviii. p. 71). The formula? 

 which I had previously given in the Proceedings (vol. i. p. 2) 

 are slightly ditTerent, 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 experi- 

 ments 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 followed in order to obtain true results, when the 

 rhomb is employed in observations on light elliptically pola- 

 rized. 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 Q in the case of a ray reflected from a metal. For 

 this purpose the ray is admitted perpendicularly to the sur- 

 face at one end of the rhomb, and after having suffered two 

 total reflexions within, passes out perpendicularly to the sur- 



