498 BARON VON WREDE ON THE ABSORPTION OF LIGHT 
By separating the real magnitudes from the imaginary, we obtain 
‘phe sin g 
sini = T= —reosg FU =F | 
and 
, cosg —(1—r)? 
cose = "V1 —2(1—7r)cosg +(1—r)* 
as well as 
rf a.mre(1—r)" 
~ 71 —2(1 —ryecosg + (1 —7r)* 
If we designate the velocity U, which represents the resultants of all 
the transmitted rays, we have U = uw + U’, or 
= [ea —r)m + A! cosi | sin 2m (== =) 
— A'sinicos27 (« — =). 
If we reduce this expression to the form 
U = Asin [2x (+ =) mLAL 
and A, which must then express the intensity of the whole resultant, 
be determined in the common manner, we have 
Acs VRIES Wa A — 9 en 4 
or, by substituting the value already found of A! and cos 2, 
1 +2(m re—(1 —r)? eos q+ [ m r—(1— ry] (10) 
If we differentiate this expression in relation to q, it is clear that A 
becomes a maximum or minimum as often as sin g =0, 2.e. A becomes 
m 
A=a(1—7) 
a maximum when = equals 0, 1,2, 3, 4...., &c., and a minimum 
when 22 equals 3, 3, 3, 3, $--- &e, te. under quite the same 
circumstances as if only two of the presupposed reflecting surfaces 
were present. Hence it follows, that 
yh +mr?—(1 —r)?) 
A; maximum = a (1 —r) ——~y= G—ry 
