385 



the vibrations to be resolved in directions parallel and per- 

 pendicular to its principal plane, the rhomb is intended to 

 produce a difference of 90° between the phases of the re- 

 solved vibrations, or to alter by that amount the difference 

 of phase which may already exist ; but the effect really pro- 

 duced is usually different from 90°, and this difference, which 

 I call £, is the error of the rhomb. The value of e is given by 

 the formula 



sin(0'-r) 



tan £ = — —7775 — > (i-) 



tan2j3 ^ ^ 



and as the error of the rhomb is a constant quantity, we 

 have thus an equation of condition which must always sub- 

 sist between the angles 9'— 6" 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 6'— 6" constantly 

 inci'eases as /3 increases towards 45°, that is, as the axes of 

 the elliptic vibration approach to equality. When j3 is equal to 

 45°— ^ £, we have 6'— 6" =90° ; and for values of /3 still nearer 

 to 45°, the value of sin [O' — O") becomes greater than unity, 

 that is to say, it becomes impossible, 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 reflected from metals; 

 because at a certain incidence, and for a certain azimuth of 

 the plane of primitive polarization, the reflected light will be 

 circularly polarized. 



The rhomb which I used in the experiments tabulated 

 above, was made by Mr. Dollond, and was perhaps as accu- 

 rate as rhombs usually are ; it was cut at an angle of 54^°, as 

 prescribed by Fresnel. Its error was about 3°, and the value 

 of 6'— 9", 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 o{6'~9", under the same circum- 

 stances, was about 20°, and the value of a was therefore 



