MAGNETO-OPTTC PHENOMENA OE IRON, NTC^KEE, AND OOPALT. 
99 
From the second and third of these equations we readily get 
H' (A, - A,) = - H. (B„ + B) + JH'. + M,,) H P (A„ - A), 
and 
H' ^(A. + A,) = H (A„ - A) + iHV + Mn,){- H.) (B„ + B). 
Substituting from these for (Aj — Ag) and (Aj + Ag) in the first and fourth of 
(34), remembering (31), and for brevity denoting by fx, we get 
(A„ + A) = (l - H' ^^ H (A„ - A) + J£ H' ik, - M,,,) (B„ + B), 
m 
(B„ - B) = M (B, + B) - JH'£ (!ri, + M,.,) (A„ - A), 
which may be written 
AI 
:\i 
rn 
+ i M - rb I - H' 4 ’'«)} Ao - i - (^1 - M,,) B„ = 0 j. (35), 
Mm ^’^3^ A + (m + M) B — (/r^i + Mr^g) Ao — {m — M)B,. = 0 
and solving these for A and B, we get 
A 
M 
R^,. _ ^ (1 + , ^ + M) A„ - 2.CX (/,, - M^,) B„ 
B 
R2e2‘“ M 
0 I 
h (36), 
1 
which is the complete mathematical solution of the problem of reflection. 
Relation of rj^, r)^ to the Magnetic Field. 
12. Before going further, we must consider how {rj^, rj^, gf) depend on the imposed 
magnetic field ; and first it should be noticed that, tliough {yj^, rjo) appear as 
o 2 
