498 BARON VON WREDE ON THE ABSORPTION OF LIGHT 



By separating the real magnitudes from the imaginary, we obtain 

 sin q 



V 1 - 2 (1 - r)2 COS y + (1 - »•)* 



and 



cos y — (1 — r)- 



as well as 



a . »i r^ O — »•) 



A' - ^ ' 



\/ 1 — 2 (1 — tY cosy + (1 — ry 



If we designate the velocity U, which represents the resultants of all 

 the transmitted rays, we have U = ?^ + U', or 



U = l^a (1 — r)m + A' cos i\^ sin 2 tt M - y j 

 — A' sin i cos 2 tt I < — — ) . 



V >•) 



If we reduce this expression to the form 



U = Asin r2 7r(<- ^) -Z?!, 



and A, which must then express the intensity of the whole resultant, 

 be determined in the common manner, we have 



A= '/A'* + 2 A'a(l — r)'"cosi +(1 —rfrnfa. 

 or, by substituting the value already found of A' and cos i. 



^mN/l+2(mr2-(l-r)°-)cosy+r»ir"— (l-r)-l , 



A=a(l-r) ^ ^ * - <-^") 



a/1 — 2 (1 — r)'^ cos y + (1 — ry 



If we differentiate this expression in relation to q, it is clear that A 

 becomes a maximum or minimum as often as sin y = 0, i. e. A becomes 



a maximum when — equals 0, 1, 2, 3, 4 , &c., and a minimum 



when ~ equals i, |, |> |. I • • • &c., i.e. under quite the same 



circumstances as if only two of the presupposed reflecting surfaces 

 were present. Hence it follows, that 



(l +mr^-(l-r)^) 

 A ; maxmium = a ( 1 — r ) j _ / j _ ^\2 



