76 Mr Basset, A Provisional Theory of Kerr's [May 1, 



the principal incidence, that is when i = 76" 48'. To do this, 

 we observe that at the principal incidence, 



e/ = ei + i7r, 

 so that the expression to be examined becomes 



- R cos^ i cos (2a - e^) - Rd" cos (2a — 2w - e,) 



— c cos i cos (3a — ii — e^ — R^c cos i cos (oc — u—e^) (13). 



From (6) it follows that at the principal incidence 



_ sin'^ 27 sin (a + u) 

 *^''^' 2~^^(7r^2T) ' 



from which I find that 



e, = 5° 12', 

 whence 



2a - e^ = 103° 20', 2a - 2u -e^ = 100° 20', 

 Sa-u-e^= 156° 6', a-u-e^ = 47° 34', 



from which it follows that all four terms of (13) are positive except 

 the last. By calculation I find that 



- Rc^ cos (2a - 2w - e^) = -75288, 

 R^c cos /cos (a — u— e^) = "26251, 



accordingly the expression (13) is positive, and therefore at the 

 principal incidence the rotation is in the opposite direction of 

 the current, and must vanish and change sign for an incidence 

 greater than 76° 48'. 



All the foregoing results, so far as they are qualitative, agree 

 with experiment, and the quantitative result which has just been 

 obtained appears to indicate that more elaborate calculations 

 would shew that the change in the direction of rotation would 

 occur at an angle which does not differ very much from 82°. 



4. We must now consider the case when the magnetization 

 is parallel to the reflecting surface and also to the plane of in- 

 cidence. 



The equations which give the amplitudes of the reflected light 

 when the medium is transparent are (47) and (48) of my paper in 

 the Phil. Trans, and are as follows : 



_ A (Ucosi — Vcosr) 2tqBV ta.n r cos i 



U cosi+Vcosr U (IT cos i +V cos r)(U' cos r + Fcos*) 



......(14), 



„, _ B (Ucosr — Fcos i) 2iqA V tan r cos i 



" Ucosr + V cos i U (U cost +V cos r){U cos r+Vcosi) 



(15). 



k being put equal to unity as before. 



