436 



REPORT 1886. 



All colour equations are known to be linear and homogeneous, and 

 since both the elementary and the fundamental sensations are the solutions 

 of these equations it follows that the fundamental sensations of every 

 person must be homogeneous linear functions of his elementary sensations, 

 and vice versa. We know the elementary sensations, and hence we can 

 write the following relations : — 



T c; TT 



IL (1) 2B,=a,' W,+/3,' K, 

 (2) aB2=a2' W,+i3,' K, 



where a/ 



«9 



+ i3.' =1 

 +/3,"=1 

 + /3,' =1 



+/32"=1 



III. (1) 91 =<. R +V- G +cJ.Y where < + V 

 ® =aJ'-R +K''.G +c„" V „ a J' + V' 



'" + K'" 



+ w 



+ K" 



(2) 



9S=«,"'R +hJ"G+cJ"V 

 56' =a/ R' +hj G' + c/ Y' 

 ®'=a,"R' +&a"G-' + Ca"V' 

 gi'=<"R' +fea"'G' + c;"V' 



a„ 



+ c„' =1 

 + <'=! 

 + c„"'=l 



+ ^a' =1 

 + Ca" =1 



+ bj"+cj"=l 



By means of these equations we can construct curves having the same 

 relation to fundamental sensations as the others had to elementary sen- 

 sations. 



The object of this superposition is to examine whether among the 

 infinite number of possible curves of fundamental sensations we can find 

 three such curves that a person of the first class will have some one of 

 them, a person of the second class will have some two of them, and a 

 person of the third class will have all three of them. This of course 

 would be the simplest relation between the three classes. 



Such a relation was found to exist, but only after we disregarded the 

 first class and the second (abnormal) division of the third class. But it 

 is a remarkable circumstance that all persons of the first class so far 

 known were found to have pathologically defective eyes. 



The case of the first (normal) subdivision of the third class we shall 

 presently discuss. 



The result of those superpositions were the curve JR, ®, and 35 in 

 fig. 5. They all belong to the normal (the numerous) division of the 



third class. The curves 

 Sd and 9S are identical 

 with the curves 3Bi 

 and ^1 of the first, and 

 the curves ® and 95 

 with the curves 9B2 

 and ,^2 of the second 

 type of the second 

 class. 



A much deeper in- 

 sight into the nature 

 of colour- sensations is 

 obtained by examining 

 aBC D Etr GH more closely the case 



of the abnormal division of the third class. By the above-mentioned pro- 

 cess of superposition we can get the two curves Si and 93, but instead of 

 the middle curve ® we get a transition form between 91 and ®. 



Could we suppose that the first type of the second class is only a 



