1893.] Experiments on the Reflection of Light. 69 



mena observed by Kerr* when polarized light is reflected from 

 a magnetized medium, I have endeavoured to arrive at formulae 

 for the amplitudes of the reflected light which give results in 

 agreement with his experiments, and may therefore be regarded 

 as an empirical representation of the facts, I shall therefore 

 first explain how the formulae may be obtained ; I shall then 

 discuss their application with reference to Kerr's experiments ; 

 and I shall lastly consider the theoretical difficulties which lie 

 in the way of placing them on a satisfactory^ dynamical basis. 



2. Cauchy's formulae for metallic reflection can be obtained 

 from Fresnel's sine and tangent formulae in the manner ex- 

 plained in §§ 372 — 5 of my book on Physical Optics] and since 

 the principal incidence / and the principal azimuth ^ can be 

 determined by experiment, the two constants R and a, where 

 i^e'* is the pseudo-refractive index, can be calculated. 



Adopting the notation of my book, it follows from equations 

 (23) and (24) of § 375, that 



i^c cos J = sin"-/ 1 



2/3 = a + wJ ^^' 



By (7) of § 372 combined with these equations we readily 



obtain 



sin 4/3 ._, 



tan 2a = — ;^ — = (2), 



cos4/8 + cot^/ ^ ^' 



which determines a. 



Eliminating c from (7) of § 372, we get 



_ sin" / sin 4/3 

 sin (4/3 -2a) ^ ^' 



which gives R. The values of c and u, when the angle of incidence 

 is equal to the principal incidence can now be obtained from 

 (1) and (2) ; but for other incidences their values must be found 

 from (7) of § 372. 



There is another angle which is denoted in § 376 of my book 

 by vr — %, which is called by French writers the azimuth at which 

 plane polarization is restored — Vazimiith de polarisation retahlie. — 

 This angle has been determined experimentally by Jamin+ and 

 others, and an account of the results will be found in Mascart's 

 Traite d'Optique, vol. IL, p. 524 &c. He denotes this angle by 9^, 

 and the principal azimuth by G ; and it can readily be proved that 



tan 0^ = tan" G = tan" /3 

 in my notation. 



* PMl. Mag. May 1877, March 1878. 



t Ann. de Chim. et de Flujs. (3), Vol. xxn., p. 311. 



