OPTICAL PROPERTIES OF BLOOD. 24! 



same fraction of the light reaching it, and in the same way each unit of 

 added concentration absorbs the same fraction absorbed by the first unit. 

 Supposing the increased absorption of light to follow through the addi- 

 tion of new layers of absorbing substance, the relation between the orig- 

 inal and residual intensities may be reached in this manner. Calling the 

 original intensity / and the intensity after passing the first layer (or first 

 unit of concentration) /' we have 



the original intensity being reduced to by the first layer. By a second, 

 third and following layers we have 



ii iii i 



/ , /-..-..., / . 

 n n n n n n m 



The last expression shows the intensity after passing m layers. For pur- 

 poses of calculation this can be put in another form, taking the original 

 intensity as unity: 



i log/ 



I' = - gives log /' = m log n. log n = -- 



In comparing the light-absorbing powers of solutions some arbitrary 

 basis must be taken. Practically the thickness of layer which will reduce 

 the original intensity to T V its value is so taken. The light-extinguishing 

 power of a substance or its coefficient of extinction, has been defined as 

 the reciprocal value of the thickness of a layer of the substance necessary to 

 reduce the intensity of the transmitted light to ^its original value. 



Representing the extinction coefficient by E and the reduced intensity by 

 /' we have from the above formulas: 



i " 



S=> log= f-=E. 



E 



Therefore 



_log/' 



m 



In practice m may be given a constant value and called I (the thickness 

 of cell, for example). The formula becomes 



= log/'. 



It was said above that increasing the thickness of a layer of absorbing sub- 

 stance has the same effect as increasing its concentration in the same 

 degree. From this it follows that the extinction coefficient must be directly 

 proportional to the concentration. Let E and E' represent two extinction 

 coefficients and C and C' the corresponding concentrations, then 



E : C : : ' : C. 



