178 RADIATION BIOLOCY 



Combining this with the previous expectation, 



— -,- a cl 



is ohtained. This icljilion is known variously as the LainlxTt-Hccr or 

 Bouf2;uer-]ieer law. 



Integratiiifz;, it is t'ouiid that 



(J I 



ell, 



or also 



In -J- *^ c/, 



logiu Y °^ ^^• 



The proportionality constant in this etiuation, which applies at eacii 

 wave length, is, of course, characteristic of the absorbing substance. 

 Numerically, it will depend on the logarithmic base employed and on the 



units for concentration (c) and optical path length [1). X'arious com- 

 binations of base and units have been employed, and the most commonly 

 used symbols for the proportionality constant in the various systems are 

 indicated in Table 5-1. Thus 



^ logiu jh/I) 

 ' cl 



where c is in moles per liter and / is in centimeters. 



The (juantit}' logio (lo/I) = eel is often referred to as the optical den- 

 sity^ (/)) of the solution. Thus e is the optical density that would be 

 measured for a 1-cm path of a solution containing 1 mole/liter.''-^ 



' Also referred to as the extinction or the absorhance (Gibson, 1949; Brode, 1949). 



' Another symbol occasionally used to specify absorption is Ef which signifies the 

 optical density of an /-cm path of a solution containing p per cent of tlie absorbing 

 substance. 



' In some circumstances, l<tgiu * <>r logu, J) may be plotted either to compress a ui(h- 

 pinge of vahies into rea.soiial)U' dimensions or to obtain a curve the shape of whicii is 

 independent of the concentration or path length, wliich may be unknown. Since 

 logio D = logii) t f- logio (• + logiu X, the latter will enter only as additive constants. 



