78 Mr Basset, A Provisional Theory of Kerrs [May 1, 



Case IV. The last case of all that we have to consider arises 

 when the incident light is polarized perpendicularly to the plane 

 of incidence. Here A —6, B = 1, 



^ = q{P,- tQ,) e"^ - q (P, cos cf> + Q, sin <jE>), " 



consequently as in Case II. 



r = WB' + 233g (P, cos el - Q^ sin <) O + q' {P; + Q;'). 



Accordingly when q is positive, so that the current circulates 

 from the right hand towards the left hand of the observer, the 

 value of 6 will be negative, when 



P, cos e/ - Q, sin e/ > (18). 



From this it follows that for angles of incidence which make 

 the left-hand side of (18) positive, the analyser must be rotated in 

 the same direction as the current in order to pi-oduce extinction ; 

 whilst for angles such that the left-hand side is negative, it must 

 be rotated in the opposite direction. 



When the incidence is very nearly equal to 90°, 



e/ = 180°, u = r 35', 



so that the term Q^ sin e' is negligible ; also the most important 

 term in P^ which is Rc^ sin (a — Su) is positive, so that P^ cos e/ is 

 negative. Under these circumstances the analyser must be ro- 

 tated in the opposite direction to that of the current. 

 The left-hand side of the inequality (18) is equal to 



R cos^ i sin (a - M — e/) -1- Rc^ sin {a—Su — e/) 



+ c cos i sin (2a — 2tt — e/) — R^c cos i sin {2u + e/). . .(19). 



At nearly normal incidence u = 0, and e/ is sensibly equal 

 to e^, so that the above expression becomes sensibly equal to (17), 

 which has been shewn to be positive. In this case the rotation 

 must be in the same direction as that of the current. 



These results are in fair agreement with Kerr's experiments, 

 for he found that the rotation was in the opposite direction to 

 that of the current so long as the angle of incidence lay between 

 90° and 75° and in the same direction when it lay between 75° 

 and 0°. At the same time the agreement as regards numerical 

 results is not quite so close as might be desired, for I find that 

 the value of the expression (19) at the principal incidence is 

 about equal to —7, from which it appears that the direction 

 of rotation ought to change sign at an angle which is somewhat 

 smaller* than 75°. All observers seem to give values of the 

 principal incidence and azimuth which lead to values of the 

 * When e/ = 90°, cos t = c/iJ, from which I find i = 75° 14'. 



