by Reflection from the Pole of a Magnet. 337 



neither so strong nor so pure as those obtained in the second 

 experiment. The strengthening actions of N in (1) and of S 

 in (2) are evidently what was to be expected ; for in (1) the 

 second Nicol leaves the plane of polarization a little to the left, 

 and N turns that plane a little more to the left. But the whole 

 subject deserves a more particular discussion. 



22. To find the intensity of the light which reaches the ob- 

 server's eye in the sixth experiment. 



Suppose the incident vibration directed along X (figure 

 of art. 15), at right angles to the plane of incidence. When 

 the second Nicol is turned (righthandcdly) through a very 

 small (positive) angle YOD = e, the resolved part of the re- 

 flected vibration (of amplitude 1) in the direction D has an 

 amplitude — sine or — e, and the intensity of the light trans- 

 mitted to the eye is e 2 . 



The effect of an additional operation S is to turn the primi- 

 tive vibration out of the direction X through a very small 

 (positive) angle p, or to add to the primitive vibration in X 

 a very small vibration, of amplitude sin p or p, in a direction 

 perpendicular to X. There are therefore two vibrations 

 presented now to the second Nicol — one in X and sensibly of 

 amplitude 1 as before, the other in Y and of amplitude k'p 

 or p' ', where k' is a positive number less than 1, an unknown 

 function of the angle of incidence. According to the hypo- 

 thesis advanced in the end of art. 20, the difference of phases 

 of these components has the same value (/> as if the component 

 p' in Y were due to an operation H or L. The resolved 

 parts of these components hi the direction OD of transmission 

 have amplitudes — sin e and p' cos e, or — e and p' \ the inten- 

 sity of the transmitted light is therefore equal to 



e 2 + // 2 -2e//cosc/>. 



23. Before discussing this formula, I proceed to apply 

 similar considerations very briefly to the second experiment. 

 Suppose the direction X of the primitive vibration still per- 

 pendicular to the plane of incidence, and that positive angles 

 are still those due to righthanded rotations. If two opera- 

 tions, L and S, be applied simultaneously, the vibration is 

 turned through a small angle a before incidence, and through 

 a small angle p in the process of reflection. The amplitudes 

 of the small reflected vibrations thus generated in the direction 

 Y of transmission may be represented by a.' and p' ', where 

 a! is the ka! of equations (1) of art. 15, and p' is the same as 

 in art. 22. According to the hypothesis stated in art. 20, 

 these vibrations are reflected in the same phase, and the inten- 

 sity of the transmitted light is therefore equal to (a! ' + p f ) 2 



Phil. Mag, S. 5. Vol. 3. No. 19. May 1877. Z 



