1893.] Ewperiments on the Reflection of Light 77 



We have now to transform these equations. The first terms 

 on the right-hand sides merely lead to Cauchy's expressions ; 

 whilst the coefficient of B in the second term of (14) is 



whence 



Pi = —T^^ — {-ft cos^ i sin (a — u) + Be' sin (a — Su) \ 



.(16). 



+ c cos i sin 2 (a — u) — R^c cos i sin 2u 



Qi = ir.ir)'^ {J^ cos''' i COS (« — u) + Rc^ COS (« — 3%) 



+ c COS i COS 2 (a — ■zt) + ii^c cos i cos 2ti}/ 



Case III. Let the incident light be polarized in the plane 

 of incidence and be of amplitude unity ; then B = 0, and we shall 

 find in exactly the same manner as in Case I. that if q be positive, 

 the rotation of the plane of polarization of the reflected light will 

 be towards the right hand of the observer if 



Pj cos e^ — Q^ sin e^ > 0. 



Omitting extraneous factors, this condition becomes by (16) 



R cos'^i sin {a — u — e,) +Pc^sin (a - 3w — ej + c cos^■ sin (2a-2tt— e^) 



— R^c cos i sin (2ii + e^) > 0. . .(17). 



Since the magnetic terms contain sin 2^ as a factor, it follows 

 that they must vanish at normal incidence which agrees with 

 experiment. They also vanish at grazing incidence, which also 

 agrees with experiment, for Kerr found that at 85" the magnetic 

 effects were very faint, but grew stronger as the incidence 

 diminished to about 60°, when they began to grow weaker. 

 When the incidence is very nearly grazing, the most important 

 term of (17) is the second which is positive, since ei = 0, and 



a-3zt=49°31'. 



Now when q is positive the amperean current circulates to- 

 wards the left hand of the observer, whence the analyser must 

 be rotated towards his right hand ; and this agrees with ex- 

 periment. 



When the incidence is nearly normal, the last term of (17), 

 which is negative, has its greatest value. In this case 

 c = l, u = Q, 6^ = 22° 48' 



and it can be shewn that (17) is satisfied. From this it is easily 

 seen that (17) is satisfied for all angles of incidence, and con- 

 sequently the rotation of the plane of polarization of the reflected 

 light is in the opposite direction to that of the current. This 

 agrees with experiment. 



