and the Dispersion of Opaque Bodies. 107 



coefficient of absorption must be introduced. If k denotes the 

 quantity of light passing through a layer whose thickness is 1, 

 then, according to the law of absorption given by Herschel and 

 Brewster, and afterwards confirmed by Bunsen, Koscoe, and 

 others, the quantity of light which emerges from a layer of the 

 thickness e is —t. If in deducing the formula (1) we re- 

 member that the amplitude of light in each passage through a 

 layer is diminished to k*, then we obtain for the intensity of the 

 reflected light the expression 



j _ (r + pk e ) 2 — 4r / s£ 6 sin 2 D 

 r (l+rpk*f—4rpk e sm 2 I>* ' * ' 

 The first differential of this magnitude for e gives as common 

 condition for the maxima and minima of the intensity of light 

 the equation 



= sin 4 D 



W-V 2 (1 -p«#") 2 + r 2 (1 + p*k*<) 2 . X 2 . log 2 k Sm2D 



\r(l +pW*) +p{\ +£«)**}« X 2 . log 2 /: t 

 ' 16r 2 7r 2 (l~ / o 2 ^) 2 + r 2 (J + p 9 W)*Aog i . V 

 out of which, for the minima, 



(2) 



+ i 



W) 



sin 2 D = i f l + a ' X<2 ' lo g 9 * + Sl+P. X 2 . Jog 2 k\ 

 2 V l + y.\ a .log*Jfc / 



(4) 



results, in which the sign of the square root is positive, and the 

 coefficients a, /3, y are as follows : 



13 



(i+P*k**)(i+e-+pr+p*kA "; 



16ir*ll-p*k**)* ' 



l-^- r ype_ i _ p 4 /: 4e 



16tt 2 (1- 



(1 -fp 2 £ 2e ) 2 



p 2 k*y 



(5) 



/ 167T a (l-p a ^) 9 



^ Equations (4) and (5) show that the influence of the absorp- 

 tion is only perceptible when the natural logarithm of the coeffi- 

 cient of absorption k has a value equivalent to the reciprocal value 

 of the wave-length X. For all bodies which, with the thickness 

 of 4X, are still perceptibly transparent to light of the wave- 

 length X, from the smallness of the coefficients a, ft y the terms 

 multiplied by X 2 almost entirely disappear in equation (4), and 



