A Quantum Theory of Colour Vision. 



223 



height at about this point, and as might be anticipated it is in a region of 

 minirmim change of hue with change of wave-length. Abney's green 

 sensation is at about 515 /a/a its position being based on the colour vision of 

 the green blind. 



The red sensation according to Helmholtz and Konig lies at the very 

 extremity of the visible spectrum, in the purplish red or a little beyond it. 

 That is at 800 fjbjjL or even greater wave-length. The blue sensation is defined 

 by Helmholtz as an ultramarine blue. Abney takes a point in the violet 

 beyond G. This will be, say, at 420 fi^i. 



It will be found, taking Helmholtz's green as at 550 /a/x, that the frequencies 

 at these three points may be represented by the three numbers — 2 : 3 : 4. The 

 blue and the red sensations are thus an octave apart. To this fact the blue 

 tone of the extreme red and the red tone of the extreme blue have been 

 before now ascribed : the octave in auditory sensations being the most perfect 

 of the concords. The physical interpretation of this will be presently 

 shown.* 



(7) According to the present theory, the frequencies just cited as proper 

 to the fundamental colours would bear the interpretation that the "red"" 

 quanta {i.e., quanta stimulating the red sensation) act by stimulating two 

 nerve fibres of the cone. The " green " quanta stimulate three fibres ; and 

 the " blue " quanta stimulate four fibres of the cone, or numbers of fibres 

 proportional to these figures ; although for various reasons the smaller 

 numbers appear to be most probable. 



(8) As we know, the several sensations are stimulated by a considerable 

 range of frequencies, and, in fact, they largely over-lap. This condition 

 necessarily arises. It is certain that every quantum of the visible spectrum 

 is competent to activate two fibres, and may do so even if they carry energy 

 sufficient to activate three or four fibres. On the other hand, we may not 

 assume that those quanta which most actively stimulate a fundamental 

 colour sensation represent the minimal stimulus which will activate the 

 particular number of fibres involved ; but rather that this number of fibres 

 may be supplied not only by superior quanta but also by quanta from 



* It is possible to ttnd the relative values 3 : 4 : 5 in the frequencies of fundamental 

 sensations. The end-stretches permit a choice of frequencies over lengths where there 

 is no change of hue. Supjoose, then, we take for the fundamental green sensation 505 fxfi. 

 This gives a frequency which we represent by the number 20. The other frequencies 

 taken as 15 and 25 give the wave-length 660 iifx and 400 fiii, both of which are within the 

 end-stretches. On these figures, however, the red and violet sensations are not an octave 

 apart. There is evidence that they are, in fact, an octave apart ; see (6). These figures, 

 too, involve a larger minimal number of fibres. Here, again, the simpler ratios commend 

 themselves. 



