■in 



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



using tlie notation of §§ 372 — 376 of my book on Physical Optics, 

 and distinguishing the equations referred to by square brackets. 



Bj^ § 372, the first term of (4) becomes 



2t7re 



- ^Ae^, 

 where the value of ^ is given by [9], and 



27re 2i2ccos isin(a +!<.) 



The second term of (4) becomes 



-Bq{P-tQ), 

 where 



P = — :^=^ — [R cos^ i sin 2a + Rc^ sin 2 (a - u) 



+ c cos i sin (3a — w) -|- i^^c cos i sin (a — u)] 



Q = — y^ — {R cos''' i cos 2o£ + i^c^ cos 2 (a — u) 



+ c cos i cos (3a — u) + R^c cos i cos (a — u)]j 

 and 



i) = [E' cos' i + c' + 2Ec cos i cos (a - w)] l^V + cos' i 



+ 2Rc cos I cos (a + u)]. 



By § 374, the first term of (5) is 



2i7re' 



Avliere the value of 33 is given by [15], and 



27re' 2jRc cos i sin (a — ii) .^. 



*'^^^ IT = E-cos^--c- ^ (^> 



Case I. Let the incident light be polarized in the plane of 

 incidence and be of amplitude unity, then B = 0. Also let 



^ = (27r/A.) {x cos i + z sin i — Vt), 



e^ = 27re/\, e/ = 27re7\. 



Then if I", 77 be the two component vibrations of the reflected 

 wave perpendicularly to, and in the plane of incidence 



^=_^e''*+^''=-acos((^ + e^), 



'r] = -q{P- iQ)€"l' -=-q(P COS. (}) + Q sin (f>). 



