240 Laws of Metallic Reflexion, and Mode of 



thus an equation of condition which must always subsist between 

 the angles 6' - 0" and |3. For any given rhomb the sine of the 

 first of these angles is proportional to the tangent of twice the 

 second, and therefore 0' - 0" constantly increases as )3 increases 

 towards 45, that is, as the axes of the elliptic vibration approach 

 to equality. When j3 is equal to 45 - $ e , we have 0' - 0" = 90 ; 

 and for values of j3 still nearer to 45, the value of sin (8 f - 0") 

 becomes greater than unity, that is to say, it becomes impos- 

 sible, by means of the rhomb, to reduce the light to the state of 

 plane-polarization. This is a case that may easily happen with 

 an ordinary rhomb in making experiments on the light re- 

 flected from metals ; because at a certain incidence, and for a 

 certain azimuth of the plane of primitive polarization, the re- 

 flected light will be circularly polarized. 



The rhomb which I used in the experiments tabulated above 

 was made by Mr. Dollond, and was perhaps as accurate as 

 rhombs usually are ; it was cut at an angle of 54^, as pre- 

 scribed by Fresnel. Its error was about 3, and the value of 

 0' - 0", at the incidence of 75, was about 7. But in another 

 rhomb, also procured from Mr. Dollond, and cut at the same 

 angle, the value of 8' - 8", under the same circumstances, was 

 about 20, and the value of e was therefore 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 refractive 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 ac- 

 count, 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 

 determine 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 reflexion at the se- 



