making Experiments upon Elliptic Polarization. 241 



parating surface of two ordinary media ; for we have only to 

 measure the angle of the rhomb and the refractive index of the 

 glass, and to compute, by FresnePs formula, the alteration 

 which the rhomb ought to produce in the difference between the 

 phases of the resolved vibrations; which alteration of phase 

 we may then compare with that deduced, by means of the for- 

 mulae (K) and (L), from direct experiment. 



If, in each position of the rhomb, we measure the angle 

 which the plane of polarization of the emergent ray makes with 

 the plane of incidence on the metal, and call the two angles re- 

 spectively y', y", we shall have 



y^ff-p, 7 " = r + /3', (M) 



and therefore 



y' + y" = 0' + 0" = 29, 2/3' = y" - y' + 0' - 0" ; (N) 



from which it appears that if the rhomb were perfectly exact, 

 that is, if 0' and 6" were equal to each other, the angle would 

 be half the sum of y', y", and the angle ]3 half their difference. 

 It would then be sufficient to measure the angles y' and y", in 

 order to get 6 and |3 accurately. And if the rhomb were erro- 

 neous, the true value of would still be half the sum of y', 

 y" ; but the true value of ]3 would not be discoverable without 

 measuring the angles 0', 0", by the help of which it can be de- 

 duced from the second of formulae (N), combined with the 

 second of formulae (K). Nor can we discover whether the 

 rhomb is erroneous or not, without measuring the angles 0', 

 0" ; and therefore as these angles must be measured in any case, 

 the former method of determining and |3 is to be preferred. 



In making experiments on elliptically polarized light, a 

 plate of mica, or any other doubly-refracting crystal, placed per- 

 pendicular to the ray, may be used instead of Fresnel's rhomb. 

 If the thickness of the crystalline plate be such that the interval 

 between the two rays which emerge from it is equal to the 

 fourth part of the length of a wave, for light of a given refran- 

 gibility, the plate will, for such light, perform all the functions 



