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 (9' -6 ") . . 



tan £ = — 5 — - ; (l) 



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 6'— 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'—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'- 6I"=90° ; and for values of j3 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 

 o{6'—d", 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(Q'—6", under the same circum- 

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



