238 COLOUR VISION 



Thus, knowing iv, we can calculate what is the ordinate w of the 

 luminosity curve for the 0-5 BS observer corresponding to the 

 colour A. 



" The following statement may make the above argument clearer. 

 When a colour-deficient observer makes a luminosity setting he matches 

 the brightness of the colour as it appears to him against the brightness 

 of the white as this appears to him. Owing to his deficiency both the 

 colour and the white appear less bright. If there were no reduction 

 in the brightness of the white to him, his luminosity setting would be 

 {\X,. + A,^)/(A,. + A^) of the normal setting. Owing, however, to the 

 comparison white being also reduced in brightness the size of his white 

 unit is reduced in the ratio of \Er + Eg to Er -\- Eg ; and hence, as the 

 size of the unit has decreased, he requires more of these units to match 

 the colour, that is, we must multiply the number given above by 

 {Er + Eg)l{\Er + Eg). This decrease in the value of the white unit 

 is the reason why the luminosity curve for a red-blind observer is 

 higher than the normal in the green, and that for a green-blind observer 

 it is higher than the normal in the red. These high values do not 

 indicate that a red-blind person receives a greater stimulus from a given 

 green light, or a green-blind receives a greater stimulus from a red 

 light, than does a normal, but simply that relatively to the stimulus 

 received from a given white light the stimulus received is greater. 



" Using equation (3) and the luminosity curves for a normal eye 

 given by Abney, the luminosity curves for persons having the following 

 red sensations in terms of the normal, RS, 0-33 RS, 0-7 RS, and 

 the following green sensations GS, 0-33 GS, and 0-6 GS, have been 

 calculated. The results together with the normal luminosity curve are 

 shown in Fig. 68. 



" It will be observed that all the luminositv curves intersect at one 

 point, P, which corresponds to SSN 48-8 or a wave-length 5770 A.U. 

 The condition that the luminosity should be the same for the normal as 

 for, say, the 0-5 RS observer is that [equations (1) and (2)] 



... . Er + Eg . . 

 (2 A. + A,) prr^^^ = A, + A„ 



XrEg X Er A,. Er 



that is at a wave-length such that for both observers the ratio of the 

 ordinates of their red and green sensation curves is the same as the ratio 



