COLORIMETRICAL EXFERIMEXTS. 51 



let there be two solutions containing q and q' of yellow 

 colouring-matter^ and let t and t^ be the corresponding 

 lengths of columns; then the intensity of the light trans- 

 mitted through one cylinder will be 



[i—mqt)Y-\-{i~m^qt)^+{i—m^qt)B', 



m denoting the amount of yellow light absorbed by a unit- 

 layer^ and m^ the amounts of red and blue absorbed by a 

 unit layer. Also the light transmitted by the other cylin- 

 der will be 



{i-mqH')Y-^{i-m,q't')'R+{i-m,qH^)'B. 



Since both cylinders are of the same colour, these expres- 

 sions will be equal, m will be less than m, because the 

 transmitted light is yellow. Let m = mi—/j,; then we 

 shall have 



1(1 -^,§-0 +i^?«fY = I(i-m,g'/') +fiq'i'Y, (A) 



the expression on the right hand denoting the light trans- 

 mitted through one cylinder, and the expression on the 

 left hand denoting the light transmitted through the other 

 cylinder. Each expression consists of two terms. The term 

 of the form I(i —m^qt) denotes the white light transmitted; 

 the term of the form [xqtY denotes the excess of yellow : 

 this term we may call the effective yellow ; for it is the 

 only portion which produces the sensation of colour. Now 

 suppose the light, before passing through the cylinder, to 

 pass through a yellow screen ; suppose the composition of 

 the incident light, after transmission through the screen, 

 to be 



p being greater than p,, say pz=p^^r, so that the compo- 

 sition of the light may be written 



P.I + »-Y, 



E 2 



