404 • LOUIS J. GILLESPIE 



It is well known that the simple law used in ordinary colorim- 

 etry, namely — the thickness of the solution times the concentra- 

 tion equals a constant when the thickness and concentration are 

 varied in such a way as to match a standard color — does not hold 

 for solutions of potassium dichromate. Indeed, with a color 

 standard of different composition from the solution itself, the 

 colors shown by a solution of potassium dichromate, as it is 

 progressively diluted, can not be matched either by dilution of 

 the color standard or by changing the depth of the layers. On 

 the other hand, the changing colors can be matched in the double 

 colorimeter. For standards (in tubes B and C), may be used a 

 highly acid solution of potassium dichromate, and a solution of 

 potassium (yellow) chromate. As the solution in question is 

 diluted, it becomes necessary to change the ratio of the path 

 lengths through the red and the yellow "forms", as well as to 

 increase the path length through the solution (in tube E). It 

 is generally assumed that a change of ionization occurs when 

 potassium dichromate solution is diluted; and there seems to be 

 no reason to doubt that the usual law of absorption holds for the 

 constituents of the solution. There would appear to be no ground 

 for a suspicion that the " dichromatism " of the sulphone- 

 phthalein indicators may interfere with their use in the double 

 colorimeter. 



In fact, to derive the law upon which ordinary colorimetry is 

 based, we assume that light passing through a solution is affected 

 independently by each particle of colored material, these particles 

 usually being alike in kind. In order to apply the law to double 

 colorimetry, we need only the further assumption that the same 

 is true when the particles are not alike in kind, and it appears 

 difficult to doubt this in the given case. Consideration of the 

 expression for the intensity of the emergent light: la""", where I 

 is the intensity of the entering light, a is the fraction absorbed 

 by each particle, e is the thickness, and c is the concentration of 

 particles, leads to the following conclusions.^ 



• The expression is applied to the different wave-lengths entering, the constant 

 a being assumed different for each wave-length. 



