500 Mr. Walter Baily on the 



called an abnormal region. The colours it represents would 

 be visible to eyes more or less colour-blind. There are two 

 abnormal regions on the left of the figure between the com- 

 plementary spectmm-lines and the red and violet zero-lines 

 respectively. 



The remaining portion of the map, viz. that lying between 

 zero sensation lines, is of a different nature. At any point 

 in this region the distances measured to the zero lines are not 

 all in the same direction ; so that one or two out of the three 

 sensations must be considered to be negative. As no one 

 possesses a negative colour sensation, the colours represented 

 in this region are imaginary. This may be called the 

 imaginary region. Though it has no physical meaning it 

 will be found to have its value in connexion with the 

 geometrical structure of the map. As an example of this, 

 consider the complementary spectrum-lines. They end 

 abruptly, leaving a gap opposite the green ; but they may be 

 continued across the gap in such a way as their general form 

 seems to point, and this has been done in fig. 4, by continuing 

 the complementary spectrum-lines until they meet in a cusp 

 at the point on the right marked —1*0. This extension lies 

 wholly in the imaginary and abnormal region, and may repre- 

 sent the missing complementary spectrum of green. 



The map affords convenient methods for calculating the 

 effect of mixing colours. Let a colour which has the sensation 

 red, green, and violet in the proportion r l9 g^ v 1 be represented 

 by r x | g Y | v x . Then, if we take two colours o\ \ g 1 \ v ± and 

 r 2 | 92 | v 2 I > the mixture of these colours in the proportions 

 l x and l 2 will give the result l^\ + l 2 r 2 \ l\g\ + l 2 g 2 I h v i + h v s» 

 The index of this colour is 



^>l—#l) + ^2— #2) 



Let the spectrum colour having the same index be r \ g \ v. 

 In order to find the quantity of white which must be added 

 to this spectrum colour to produce the required colour, it is 

 necessary that the luminosity of the colour should be altered 

 to that luminosity at which the colour is represented in the 

 map. This can be done by multiplying the coefficient of each 

 sensation by the fraction (r—g)/{li(r l —g ] ) + l 2 {r 2 —g 2 ) } or one 

 of the equivalent fractions. The resulting sensation co- 

 efficients are 



Eed . . . {Iir 1 + l2r 2 ){g—v)/{l 1 (g 1 —v 1 )+l 2 (g2-v 2 )}. 



Green . . (%i + % 2 )(>— r)l{h^\—n) +h( v 2~ ^2)}- 



Violet . . {liV\+ kv 2 ) ( r —9)H h( r \ ~9\) + hirz—g*) }• 



