Construction of a Colour Map. 501 



The coefficient of the white to be added to the spectrum colour 

 is obtained while the colour lies on the right hand by sub- 

 tracting r from the red coefficient above obtained, or by sub- 

 tracting g and v from the other coefficients respectively. When 

 the colour lies on the left hand, the white is obtained by adding 

 r to the above red coefficient, or g and v to the green and 

 violet coefficients respectively. 



I have applied the formulae given above to obtain the 

 curves showing the results of adding together in any pro- 

 portion two spectrum colours so related to each other that 

 if the first is r | g \ v the second is v | g | r. The index of 



the second colour being - — - is the reciprocal of the index 

 of the first. V~ r 



The curves obtained are shown in fig. 5. Consider the 

 curve numbered 2. This is the locus of mixtures of the blue 

 whose index is 2*0, and the yellow whose index is 0*5. The 

 curve passes through these two points of the spectrum, giving 

 the cases in which a zero quantity of one of the colours is 

 taken ; and every other mixture is indicated by some point 

 on the curve joining these two points and lying to the right 

 of the spectrum-line. In this figure the dotted horizontal 

 lines occupy the positions where the indices are zero and 

 infinity respectively, so that the portion of any curve which 

 lies outside of them must be repeated again on the left side of 

 the complementary spectrum -line. In curve No. 2 two small 

 parts do lie outside the dotted lines, and, accordingly, these two 

 parts are repeated to the left of the complementary spectrum- 

 line. We have then the curve No. 2 in three separate portions, 

 which it is not possible to connect physically, as the missing- 

 part of the curve lies in the imaginary and abnormal regions. 

 But what is not possible for physics is easy for geometry. 

 We cannot subtract one spectrum colour from another, but 

 we can subtract the lines representing the sensations in one 

 spectrum colour from the lines representing the sensations in 

 the other spectrum colour ; and so by subtracting one spectrum 

 colour from the other in any proportions we can complete the 

 curve No. 2 through the imaginary and abnormal regions and 

 so obtain the complete and continuous curve. Curves Nos. 1 

 and have no portion on the complementary side, but curves 

 Nos. 3 and 4 have a considerable portion on that side. A 

 new feature is shown when we take the locus numbered 5. 

 This is got by combining the spectrum indigo, having index 

 l'O, with spectrum orange, having the same index. These 

 are complementary colours. When added together in the 

 proper proportion they produce white, and when added in any 



