ON THE ABSORPTION-FORMULA IN PHOTOMETRY. 5 



II. Correction of the Formula used in Photometry for Ab- 

 sorption when the medium is not perfectly transparent. 

 By James Bottomley, D.Sc, RC.S. 



Bead October 4th, 1881. 



Suppose we have a column of length I, containing q units 

 of colouring- matter per unit of length, the medium being 

 perfectly transparent ; then the light transmitted will be 

 ak ql . Now suppose the colouring-matter, instead of being 

 uniformly diffused through the whole column, to be con- 

 fined to an extremely small section at the bottom, of length 

 V , so that the length of the column above the section may 

 be still taken as /. The intensity of the transmitted light 

 will be the same in both cases; hence k ql =k q ' 1 '. 



If the medium be not transparent, we may now suppose 

 the column of length I above the section containing the 

 colouring-matter to be occupied by some medium that 

 absorbs light. Let p be its coefficient of transmission. 

 The light incident on the bottom of the column is of inten- 

 sity ak q ' 1 '. After penetrating the column the intensity will 

 be ak q ' l p l . But by what precedes, q'P=ql; so that the in- 

 tensity of the transmitted light corrected for absorption 

 by the medium will be a(k q p) 1 . If, then, we have two 

 cylinders containing q and q' units of colouring- matter per 

 unit of length, and columns of liquid / and I', we shall 

 have the relationship (k q g) l =(k q 'g) 1 '. From this equation 

 we may determine p in terms of k and known quantities 

 thus : — 



q'l'-ql 



>=k l ~ V 



In some experiments on the absorption of light by car- 

 bon diffusions I noticed that when one diffusion was much 



