DR. JAMES BOTTOMLEY OX COLORIMETRY. 69 



Thus the result is very near. 



The solutions of caramel ought not to be kept many days. 

 After the lapse of twelve days some of the solutions were 

 turbid and unfit for comparison, owing to the development 

 of vegetable organisms. It seems very probable that even 

 with large differences between the lengths of the columns 

 and with larger quantities of colouring-matter the relation 

 g^ = constant is valid when the colour is constant. But 

 suppose the colour to vary, what will be the connexion 

 between the quantity of colouring-matter, the length of 

 the column, and the intensity of coloiu' ? If g denote the 

 quantity of colouring-matter per unit of length, and t the 

 total length, we have the relation gt = c if the colour be 

 constant ; but if the colour vary, c will be a function of 

 the transmitted light. Hence 



c=f (T) 



if T denote the transmitted light, therefore qt=f (T), or, as 

 we may write it, T = (^ {qt) , the probable form of this func- 

 tion may be obtained as follows : — Suppose we have two 

 perfectly transparent cylinders of unit area and a fluid of 

 such a nature that, if in any portion of it we dissolve some 

 colouring-matter, on further addition of the fluid no 

 decomposition takes place. Suppose we have a standard 

 solution containing one unit of colouring-matter per unit 

 of volume. If the colouring-matter remain constant in 

 quantity, then the intensity of the light will be a function 

 of the length of the column of fluid only, say '^{t); and if 

 the length of the column of fluid remains constant, the 

 intensity of light will be a function of the quantity of 

 colouring-matter only, say ^ [q) . Suppose now that into 

 the cylinders (which we may distinguish as A and B) we 

 pour a unit length of the standard fluid; then the light trans- 

 mitted will be the same in both ; hence we shall have T= 



