MAGNETO-OPTIC PHENOMENA OF IRON, NICKEL, AND COBALT. 
121 
In the air {z > 0 ) 
V = -Qg^i-rnz+pt)^ 
10 = 0. 
In the metal {0 > z > — h) 
u = + k' 
IV — 0 . 
In the air (z + /^ < 0 ) 
u — V = iv = 0 , 
wherein the incident ray is represented by Aq, the reflected ra.y by (A, B), and the 
transmitted ray by (E, F). 
It should be noticed that in these assumptions multiple reflections are not neglected; 
all waves in the film are included in the complex constants A^^, A j, A^, and A 3 . 
For surface conditions we may establish the continuity of 
H {u - Hd/cfe (it - H 773 ^), H {v -h and lldjdz (v + II-- 73 U.) 
respectively ; the second of these is the expression of the continuity of the magnetic 
force h, and is used instead of the continuity of iv to which it is equivalent, as it 
leads to more symmetrical analysis. 
At the surface z = 0 these boundary conditions lead to the equcitions 
H (Ao + A) = H' (Ai -F A\ + A3 -h A'3) - Wh-q, {A, + A'l - A3 - Ah), 
Hm (Ao — A) — H' (m-^A^ — m^A\ + m^A.^ — m.^A\) 
— (m^^A^ — nqA\ — WoAo fi- ni,Ah), 
- HiB = H' (Ai + A'l - Ao - A's) - Why)^ {A, + A\ + Ag + Ah), 
— HwtB — H (— nqAj -fi irqA ^ -f- m^k^^ iiioA 3) 
4- (^WiAj — w^Ah + 'J’toAo — m^A'n)- 
At the surface z = ~ h, (if for brevity we write — lyuJi — 9, and — on.Ji = <^), 
the boundary conditions lead to the equations 
VOL. CXC.-A. 
R 
