386 



about 8°. The angle given by Fresnel was calculated for 

 glass of which the refractive index is 1.51 ; and the errors 

 of the rhombs are to be attributed to differences in the re- 

 fractive powers of the glass. I was not at all prepared to 

 expect errors so large as these when I began to work with 

 the rhomb, and they perplexed me a good deal at first, 

 until I found the means of taking them into account, and of 

 making the rhomb itself serve to measure and to eliminate 

 them. The value of the rhomb as an instrument of research 

 is much increased by the circumstance that it can thus de- 

 termine its own effect, and that it is not at all necessary to 

 adapt its angle exactly to the refractive index of the glass. 

 It may also be remarked, that this circumstance affords a 

 method of directly and accurately testing the truth of the 

 formulae which Fresnel has given for the case of total re- 

 flexion at the separating surface of two ordinary media; for we 

 have only to measure the angle of the rhomb and the refrac- 

 tive index of the glass, and to compute, by Fresnel's for- 

 mula, 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 formulee (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 respectively 7', 7", we shall have 



y'=0'- /3', j" = 6" + /3', (M) 



and therefore 



j' + y" = e'-{-d"=2d, 2(5' = y"-y'-\-e'-e"; (n) 



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

 that is, if 6' and 9" were equal to each other, the angle 6 

 would be half the sum of y', y", and the angle /3 half their 

 difference. It would then be sufficient to measui'e the angles 

 y' and 7", in order to get B and j3 accurately. And if the 



