DR. JAMES BOTTOMLEY ON COLORIMETRY. 181 



Remarks on the Formula; for the Intensity of Light that 

 has passed through absorbing media, and on a Method of 

 Experimental Verification. 



In my last paper on colorimetry I pointed out that the 

 function which expresses the cotinexion of the intensity of 

 light with the quantity of colouring-matter is of the same 

 form as the function expressing the relationship of the 

 intensity and the length of the absorbing column; and if we 

 accept Herschel's formula "Zak* for the latter relationship, 

 then an expression of the form 2la«Q must be taken to ex- 

 press the former relationship. The connexion of these two 

 may be shown more dii'ectly than I indicated in my last 

 paper. If we grant one of the laws, the other may be 

 deduced from it as a corollary. Take, for instance, the law 

 as given by Herschel, 



T = a,A:/ + flA'+ &c. 



Now it is manifest that, if q be the quantity of colouring- 

 matter per unit of length, we may write the above formula 



t t 



T = a,k^U + a^k^U-^ &c. 



I I I 

 For A;,9 , k^'q, k^l , &c. substitute new constants /Cj, Kj., k^, &c. 



Then we may write 



T=:S«««^ 



Since q denotes the quantity of colouring-matter per unit 

 of length and t the total length, we shall have 



Q=qt, 



