1893.] Experiments on the Reflection of Light. 75 



Let the analyser be placed in the position of extinction 0^, 

 and be then turned through a small angle 6 towards the right 

 hand of the observer ; the emergent vibration will be 



- ^ cos ^ - 77 sin ^ = ^ (P cos </> + Q sin (/>) - 236' cos ((/> + e/), 



and consequently 



P = Wff' - 2^q (P cos e,' - Q sin e/) d + q" (P' + Q'). 



Whence iiq is positive, the rotation of the plane of polarization 

 will be in the opposite or in the same direction as the araperean 

 current, according as the coefficient of is positive or negative. 

 We have therefore to examine the sign of 



P cos e/ — Q sin e/, 

 or by (7) of 



R cos'i sin (2a — e/) +Pc^ sin (2a — 2m — e/) + c cosi sin (3a — ^^ — e/) 



+ ii^c cos * sin (a — w — e/). . .(12). 



The value of tan e/ is given by (8), and is positive at normal 

 incidence, and the value of e/ as stated in Case I. is about 22° 48'. 

 But if i is very nearly equal to 90°, tan e/ becomes a very small 

 negative quantity, and therefore when i = 90°, e/ = 7r; and under 

 these circumstances the most important term in the above ex- 

 pression is 



Rg" sin (2a - 2u - e/), 



which is nearly equal to 



— Ec^ sin 2 (a — u), 



that is a negative quantity. We therefore see that if the angle 

 of incidence be supposed to increase from normal incidence to 

 grazing incidence, the rotation of the plane of polarization is 

 at first in the opposite direction to that of the current, but it 

 afterwards diminishes and vanishes, and finally takes place in the 

 same direction as that of the current. 



It would seem that Kerr did not particularly examine the 

 effect produced at nearly grazing incidence; Kundt* however 

 found that in the case of an i^wi electromagnet, the rotation 

 was in the opposite direction to that of the current until the 

 angle of incidence became equal to about 82° when it vanished 

 and changed sign, taking place in the same direction when the 

 angle of incidence lay between 82° and 90°. 



To find the exact value of the angle which makes the ex- 

 pression (12) vanish and change sign would necessitate some rather 

 laborious numerical calculations ; it is however not difficult to 

 shew that it is positive when the angle of incidence is equal to 



* Berlin. Sitzungsberichte, July 10th, 1884; translated Phil. Mag. Oct. 1884, p. 308. 



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