38 COLOUR VISION 



light mixture can be comprehensively represented as the function of three 

 variables " (v. Kries). Hence a colour diagram representing varying 

 intensities of colours and colour mixtures must be in three dimensions, 

 as in Lambert's colour pyramid 1 or Runge's sphere 2 . 



Within a certain range, which includes all ordinary conditions of 

 colour vision except those mentioned on p. 36, this law shows that 

 every conceivable light or light mixture gives rise to a sensation which 

 can be accurately matched by the sensation produced by a suitable 

 mixture of only three lights. In other words, from the point of view 

 of stimuli normal colour vision is trichromatic. 



It is to be noted carefully that the colour table does not express 

 the change in physiological valency which corresponds to variation 

 in absolute intensity. The unit of intensity is fixed for the given table, 

 as is also the choice of the three variables. Theoretically the choice 

 of unit intensity of the three variables is arbitrary. The choice of 

 variables merely involves a change in the co-ordinate axes. If the 

 variables are selected too close together the table involves negative 

 stimuli and the stimulus values cannot be reproduced experimentally. 

 This is, however, of no theoretical importance. 



We have here the basis of colour equations. For example, if spectral 

 green-blue (Bg) is mixed with red (R) in certain proportions it matches 

 a mixture of green (Gr) and violet (7), which may be expressed thus : 



aBg \-/3R = yGr + V. 

 Hence we can obtain a value for Bg 



which is strictly accurate though incapable of objective interpretation. 

 As Greenwood well puts it 3 in colour equations " addition is uniform, 

 the same result being always obtained when the same quantities are 

 summed ; it is commutative, the order of operations does not affect 

 the result ; it is associative and homogeneous. . . .If we define subtraction, 

 in terms of arithmetical quantity as uniform, non-commutative and non- 

 associative, similar analogies can be observed ; but this is of little 

 importance, since a justification of the use of the symbol of addition 

 will suffice for our purposes." 



1 Beschreibung einer mil don Galau'schen Wachsc ausgemahlten Farbcnpyramide, Berlin, 

 1772. 



2 Die Farbenkugcl, Hamburg, 1810. Cf. Chevron], Expose (Tun moyen dc definir et 

 de nommer les coulcurs, Paris, 1861 ; HSfler, Zl^ch. f. Psychol. u. Physiol. d. Sinnesorg. 

 LVIII. 356, 1911. 



3 Loc. cit. p. 133. 



