266 DR. JAMES BOTTOMLEY ON 



■vvill be increased relatively to the quantities of any colour- 

 ing-matter remaining, and may be sufficiently sensible to 

 be estimated. 



When I suggested this method of colorimetry, I had not 

 seen the article on Light by Su' John Herschel in the 

 ' Encyclopaedia Metropolitana.' He there gives a probable 

 formula for the intensity of light which has passed through 

 an absorbing medium. His reasoning is as follows : — Let 

 the intensity of the incident light be unity, and its inten- 

 sity on emerging from a unit thickness of the medium k ; 

 then its intensity at incidence on a second layer will be k, 

 and its intensity at emergence k^ ; hence, if t be the thick- 

 ness of the medium, the intensity will be finally k*, and if 

 the original intensity were a, the final intensity would be 

 ak\ Now, light consists of several species ; hence, if the 

 composition of the incident light be a^ + a^^ + a^^^ + . ., &c., 

 the composition of the emergent light will be ajc\ + «ji^ii 

 + ^111^111+ • • •' ^^- ^^ ^^ ^^^ ^^^ letter I to denote inci- 

 dent light, T to denote transmitted light, and A absorbed 

 light, HerscheFs formulae may be written more briefly, as 

 follows : — 



k will be a function of the quantity of colouring-matter 

 present in a unit thickness, li g be that quantity, we may 

 write k=f{ff), or, if we expand, A;=/(o) —/'(o)^ + higher 

 terms in g. Now g is very small. Let, then, the terms 

 higher than the second be neglected. The first term will 

 be the light transmitted when no colouring-matter is 

 present. If the colouring-matter were dissolved in an ab- 

 solutely transparent medium, the first term would be unity. 

 In practice water or some colourless medium is used ; but 

 the amount of light absorbed by a thin layer of pure water 

 is very small ; so that we shall make only a very small error 



