Colour-Sensation. 375 



and that V, 0, and U, the three standard colours, are known 

 to result from these colour-sensations being effected in certain 

 proportions. 



E. g. Y is known to result from R, the red colour- sensation, 

 being effected to an extent r v , Y to an extent i/ v , G to an 

 extent g v , and B to an extent b v ; and may therefore be repre- 

 sented by the equation 



V=r.B+y.Y+^a+5.B; .... (2) 

 and similarly C and U may be represented by 



C^cR+ycY-tfrG + bcB, .... (3) 



U= ru R^ u Y+ 9u G + b u B (4) 



Then from these four equations we can express R, Y, G, and 

 B as linear functions of V, C, U. But every possible colour 

 X must be produced by exciting all or some of the four colour- 

 sensations, and therefore must be capable of being expressed 

 by an equation 



X = r,R+y,Y+^G + ^B. 



Consequently, if R, Y, G, and B be replaced in this equation 

 by the linear functions of Y, C, and U which represent them, 

 every such colour X can be expressed as a linear function of 

 Y, C, and U; i. e. every such colour will conform to the law, 

 which Maxwell and Helmholtz established, of being capable of 

 being made up of any three standard colours. 



The same reasoning might obviously be applied in like 

 manner to five colour-sensations connected by two linear equa- 

 tions of condition, or to n colour-sensations connected by 

 n — 3 linear equations of condition. 



I have taken up this question and endeavoured to show that 

 what Maxwell and Helmholtz established is not inconsistent 

 with the existence of four or more colour-sensations (provided 

 certain relations exist between them), because a certain recent 

 discovery seems to me to have given a particular hypothesis, 

 involving four colour-sensations, a strong claim to be accepted 

 as, in the main, true. This discovery relates to the colours 

 actually seen by colour-blind persons. Two persons have 

 been discovered who, being each colour-blind of only one eye, 

 can explain how far the colours seen by their colour-blind 

 eyes agree with, or differ from, those seen by their normal eyes. 

 It has been found that each of these persons has two colour- 

 sensations complementary to each other. One sees yellow and 

 blue, and is blind to red and green; while the other sees red 

 and bluish green, and is blind to blue and yellow; and with each 

 of them the combination of his two colour-sensations in proper 

 proportions produces white or grey. Professor Holmgren, of 

 Upsala, has given an account of both these cases in the ' Pro- 

 ceedings of the Royal Society,' vol. xxxi. p. 302; and Pro- 



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