550 PRINCIPLES OF GENERAL PHYSIOLOGY 



The Laws of Lambert and of Beer. In order to be able to compare the amount 

 of light absorbed by one substance or solution with that absorbed by another, it is 

 necessary to take some standard of nirasuivmrnt. Bunscn and Roscoe (1855-1859) 

 introduced the extinction coefficient for this purpose. Their definition of it will 

 be found on p. 6 of the reprint in Ostwald's " Klassiker," No. 38. 



When light of a particular wave length is absorbed by any substance, it is 

 clear that the intensity of the light issuing from it is less than that which 

 enters it, and that there must be some particular thickness of it which reduces 

 the intensity of the light to one-tenth of the value it had on entering. In 

 order that the numbers, characteristic of different substances, should rise or fall 

 in the same direction as the absorbing power of the substance or solution, 

 Bunsen and Roscoe defined the extinction coefficient as being the reciprocal of 

 the depth of the solution required to reduce the intensity of light of a given 

 wave length to one-tenth of that which it had on entering. It is plain that 

 the greater the absorbing power, the less the depth required ; hence the 

 advantage of the inverse value, the extinction coefficient being directly pro- 

 portional to the absorbing power. 



The symbol e is generally used for the extinction coefficient, so that if d is 

 the depth of solution required to reduce light of a given wave length to one-tenth 

 of its value, then the extinction coefficient for this wave length is 



Now in practice it is the intensity of the issuing light that is measured, 

 and it is more convenient to use a constant thickness of solution, and to measure 

 the intensity of the light that has passed through this, than to vary the thickness 

 of the absorbing layer. It is therefore necessary to know the laws which express 

 the relation of the one to the other. 



We have already seen (page 35) that the relation is a logarithmic one, and it 

 is known as Lambert's law when applied to the case of a pure substance, solid 

 or liquid. Beer showed that the same law applies to solutions. Let us call the 

 original intensity of the light I, and that after passing through a layer d, I'. 



Then, by the definition of the extinction coefficient, I' = I x y~ After passing 

 through a second layer, I' = (Ix )x = Ix -- and after x such layers I' = . 



In general, if light of unit intensity is reduced to -th by a certain thickness of 



n 



solution, after passing through x times this thickness, its value will be In 

 order to get rid of the exponent we take logarithms, thus : 



log I' = - X log n. ( 1 ) 



When x = d, I' = , therefore 



log ( ) = - d log n - 1 or d log n=\. 



t. is = - and is therefore = log n. 







From equation (1), log n= - ^ 



x 



Hence, e = - ^ and, knowing the ratio of the light transmitted to that entering 

 x 



a solution of depth x, we can calculate the extinction coefficient. 



For convenience, x is taken of one centimetre depth, so that c = log I', that 

 is, the negative logarithm of the unabsorbed light. 



For example, suppose the intensity of light of the wave length of the D line is reduced to 



