498 Mr. Walter Baily on the 



to one another of E, G, V — that is, only by the differences E Gl- 

 and G V. But if we express the same colours at (say) half 

 the luminosity, we must reduce all these distances to one half, 

 as in fig. 2, and so with any other proportion. It is then not 

 the differences E G and G V, but the ratio of these differences 

 which is constant for all this system of colours. Hence, to 

 determine to what system a colour belongs of which we know 

 r, g } r, the quantities of red, green, and violet sensations 



respectively, we have only to obtain — -• 



• > •/ g — v 



In fig. 4, PI. VIII., the vertical line called " spectrum colours " 

 is that along which the spectrum is thrown ; and the lines 

 called " line of no Bed," " line of no Green/'' and " line of no 

 Violet" are lines to which distances are to be measured hori- 

 zontally from any point to show the quantity of red, green, and 

 violet sensations in the colour represented at that point. When 

 these distances are measured from points on the spectrum line, 

 they give the amount of such sensation for the corresponding 

 spectrum colour. The curves which I have used are not 

 intended to represent the true form of such curves, as it is 

 sufficient for explaining the principles of the map that they 

 should be curves having a maximum and shading off on each 

 side. The numbers marked along the " spectrum fine " give 

 the value of the fraction (v—g)/(g — v) at each point ; and it 

 will be seen that the value is large at the red end of the 

 spectrum, probably beginning with infinity, and diminishes to 

 zero, where the red and green are equal. It then changes 

 sign and remains negative until g and r become equal, when 

 the fraction becomes infinite and again changes sign. For 

 the remainder of the spectrum the fraction continues positive 

 and passes from infinity to zero. The fraction (r—g)/{g — v), 

 which may be called the " Colour Index/' has therefore in 

 the spectrum every value from plus to minus infinity, and 

 has all the positive values twice over. Every positive colour 

 index has two spectrum colours: — one in which the order of 

 magnitude of the sensations is Eed, Green, Violet, and the 

 other in which the order is Violet, Green, Eed. In fig. 1, 

 where the order is that required, let the fines S, S ; give the 

 spectrum colours. Then it is clear that these two spectrum 

 colours are complementary to one another. Also that the 

 colour represented by A is equal to the spectrum colour S 

 plus the colour included between S and A, which is white ; 

 and also that the colour at A plus the spectrum colour at S' 

 form the white between A and S'. 



Now suppose the colour index negative, then E, G, V must 

 be arranged in the order E V G or V E G (see fig. 3) . We 



