502 On the Construction of a Colour Map. 



other proportion they produce white plus whichever spectrum 

 colour predominates. Hence the locus consists of horizontal 

 straight lines through the two points in the spectrum line, 

 going off to infinity, where the colour indicated is white, 

 considered as a spectrum colour infinitely diluted with white 

 light. Next consider curve No. 7. The main portion of the 

 curve lies to the left, and starts from points in the comple- 

 mentary spectrum-line which indicate the spectrum colour 

 chosen. The parts of this portion which lie outside the hori- 

 zontal dotted lines are repeated to the right of the spectrum- 

 line ; the remainder, obtained by subtraction, lies wholly in 

 the imaginary and abnormal regions. All these curves pass 

 through a certain pair of points, as may be easily shown. 

 The first spectrum colour is . . . r \ g \ v. 



The second is v \ g \ r. 



By subtraction of one from the other, we get a colour 



r — v | zero | v — r. 

 The resulting colour has therefore no green, and has the red 

 and violet equal in amount but opposite in sign. These con- 

 ditions are satisfied at the two points shown in the figure. 



In this figure the lines are drawn under the condition that 

 the index of one spectrum colour is the reciprocal of the 

 index of the other ; but any number of other systems of lines 

 might be drawn showing combinations of two spectrum 

 colours, so that it is evident that every colour can be resolved 

 into two spectrum colours in an infinite number of ways. 



There are three regions in fig. 5 which are shaded to show 

 that none of the curves pass through them. These regions 

 might probably be filled up by curves drawn through points 

 in the imaginary part of the complementary spectrum to 

 which I have already alluded. 



Now the complementary spectrum-line and the curves 

 giving mixtures of two spectrum colours have been drawn 

 by strict arithmetical methods from certain curves of hypo- 

 thetical form which indicate the intensity of the sensations 

 for each point of the spectrum ; but they can also be plotted 

 out by direct experiment. 



To plot out the complementary spectrum-line, add to a 

 spectrum colour its complementary until white is produced, 

 measure the quantity of white, and mark off a horizontal line 

 to the left from the point in the spectrum of a length pro- 

 portional to the quantity of white. The end of this line is a 

 point in the complementary spectrum ; other points may be 

 obtained in the same way, and the normal part of the com- 

 plementary spectrum -line be drawn. 



