676 



of thickness I, i„ being the intensity of tlie radiation at the snrface, 

 (X the absorption coefficient of the absorbing medium for tlie 

 incident rays. 



By multiplication by t, the time, and equating Ii i := Qi and 

 l^t= Q, we get; 



Q/=Q„f-/'/ (2) 



a formula for the quantity of radiating energy at a distance of I 

 below the surface. Differentiating 2 gives: 



-~dQi = Q,iis-yidl (3) 



an expression for tiie light absorbed in a stratum of thickness dl 

 at a distance / below the surface. As the quantity of silver reduced 

 by development in this stratum is proportional to — c/Q/ we may put: 



dAg = k Q„ ft f-!'' dl (4) 



which integrated gives: 



Ag = KQ,(l-s-y!) (5J 



as a formula for the total quantity of reduced silver lietween the 

 surface and a layer at a distance / below it. 

 From (5) we deduce: 



dA^ 



^"=^'^1-^-'") ■ ■ ^'^ 



i.e. the increase of silver caused by an increase of exposure depends 

 on the absorptioncoefficient ;i. If u is large the differentialquotient 

 is also large. 



In order to calculate the density of the negative, we suppose 

 that the absorption in an infinitely thin layer is proportional to 

 the amount of silver in it and also with the intensity of the light 

 falling on it. Using (4) for the quantity of silver we get the equation : 



— dli=cli . KQii t-~''i dl (7) 



or after integration 



D=log-^=cKQ{l-e-."') (8) 



in which D is the density, i„ the intensity of the light before, and 



Ii the same after passing through the negative. 



From (8) we find : 



dD 



-- = cA'(l-6-."0 (9) 



dl 



This last equation shows that the increase of density also depends 

 on the absorption coefficient jt of the rays used in producing the 

 negative. 



