making Experiments upon Elliptic Polarization. 239 



dence on the metal will be equal to : while in the same posi- 

 tion the angle which the principal plane makes with the plane 

 of polarization of the emergent ray (as given by the Nicol's 

 prism) will be equal to j3. In the other position, the principal 

 plane will be parallel to the minor axis of the elliptic vibration, 

 and the corresponding angles will be equal to 90 - 9 and 

 90 - /3 respectively. This, however, proceeds on the supposi- 

 tion that the rhomb is exact. When it is not so, which is of 

 course the proper supposition, and a very necessary one in the 

 experiments with which we are concerned, there will still be, 

 generally speaking, two positions of it in which the emergent 

 ray will be plane-polarized, or in which a disappearance of the 

 light may be produced by the Nicol's prism ; but these positions 

 will no longer be 90 from each other, nor will the principal 

 plane, in either of them, coincide with an axis of the elliptic 

 vibration. If we now measure the angles between the different 

 planes as before, and denote them by ft', j3' in the first position, 

 and by 90 - 0", 90 - /3" in the second, we shall find that V 

 and 0" are unequal, but we shall have /3' equal to /3". The va- 

 lues of and )3 will then be given by the formulae 



ff + 0" cos 2/3' 



The error of the rhomb may easily be found. Supposing 

 the vibrations to be resolved in directions parallel and perpen- 

 dicular to its principal plane, the rhomb is intended to produce 

 a difference of 90 between the phases of the resolved vibrations, 

 or to alter by that amount the difference of phase which may 

 already exist ; but the effect really produced is usually different 

 from 90, and this difference, which I call E, is the error of the 

 rhomb. The value of e is given by the formula 



sin (ff - 0") 

 tan2/3 ' 



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



