416 A Theory of Colour Vision. 



the base are consequently \/3k, i. e. 22*1 and 25*6. I£ we 

 consider the two rectangles as one system and calculate the 

 square of its radius of gyration about the dotted vertical 

 we obtain 



72 _240(163 + 2*6 2 j + 156(219 + 4 2 ) 



k ~ 240 + 156 ~ iyb * 



The correct result should be 198. The discrepancy is due 

 to the values in Table III. having been determined 

 graphically. The mixture is represented by the dotted 

 rectangle. 



In the lower diagram 268 units of X = 5451, i. e. 5=11*0 

 are added to 160 units of X = 6302, i. e. 5 = 21*7. The area 

 of the rectangle to the right is consequently 268 units and 

 of the rectangle to the left 160 units, and their centroids 

 are respectively at 5 = 11*0 and 5 = 21*7. It will be found 

 that the centroid of the combination lies on the dotted 

 vertical. The values of k 2 corresponding 1o 5 = 11*0 and 

 5 = 21*7 are 140 and 223. The lengths of half the base are 

 consequently 20*5 and 25*8. If we consider the two rect- 

 angles as one system and calculate tlie square of its radius 

 of gyration about the dotted vertical, we obtain 



2 _ 268(14 + 4 2 )+ 16 0(223 + 6*7 2 ) 



268 + 160 ^ 



the required value. The dotted rectangle in this case also 

 represents the mixture. 



At first I thought s would specify the hue of the colour 

 and k 2 its degree of saturation, but this is not the case ; 

 k 2 certainly increases as a spectral colour becomes paler, but 

 purple has a greater value of k 2 than white. As regards 

 the arbitrary scale 5, in drawing energy-curves there is no 

 a priori reason why the abscissa should be X or lj\ or any 

 special function of \. So I allowed the observations to 

 define their own scale ; I tind that the general result is the 

 same as if the curves were plotted against the index of 

 refraction of some substance with a greater dispersion than 

 water. It is not necessary, but it is a great simplification 

 to have the origin for 5 at the vertex of the parabola — taking- 

 it elsewhere involves oblique axes for s and P. 



§ 4. To put the difference between the Young-Helmholtz 

 theory and my view as shortly as possible :— 



The Young-Helmholtz theory represents the R and Gr of 

 fig. 2 as linear functions of three primary sensations, my 

 view as linear functions of 5 and k 2 . Hence there can be 



