70 DR. JAMES BOTTOMLEY ON COLORIMETRY. 



->^ ( I ) = (^ ( I ) , J) issolve in A another unit of the colouring- 

 matter, and make the column of the standard solution two 

 units long in B ; the colour will remain the same ; hence 

 we have a/t (2) = ^ (2) , If we dissolved three units in A and 

 made B three units long, we should again find '^{3)=4>{3)} 

 and generally ■\lr{7i) = (f)[n). If, then, we know ^/^(^i), we 

 shall obtain (f> (n) . For the intensity of light transmitted 

 through a column n units long, Sir John Herschel has 

 given an expression (to which I have referred in a previous 

 paper) of the form 



k being the intensity of light passing through a unit thick- 

 ness, a the intensity of the incident light, and the summa- 

 tion having reference to the composite nature of light. 

 This formula is given by Herschel in the ' Encyclopaedia 

 Metropolitana,^ also in an article on the absorption of light 

 by coloured media in the '^Transactions of the Royal 

 Society of Edinburgh.^ In neither of these works do I 

 find the experimental confirmation of the formula. It 

 appears to have been obtained a priori. If we assume its 

 accuracy we shall obtain for <^{n) the expression ak^, if we 

 suppose we are dealing with homogeneous light ; if we 

 substitute q for n we shall obtain ak'^ for the intensity of 

 light which has passed through a unit length containing q 

 units of colouring-matter. We may now suppose the 

 length to vary : for two units of length the expression will 

 be a[kiy for three a(/t')' and for t units a{k'')K Finally, 

 if we suppose that there are various kinds of light, we have 



T=tak'i' 



as a probable expression for the intensity of light passing 

 through a column t units long and containing q units of 

 colouring-matter per unit of length. I think that in many 



