Prof. J. D. Forbes on the Clasiification of Colours. 171 



colours, we shall be sure to have none to match which are 

 not included in our suite. 



The question now arises of the number of intermediate 

 mixed colours which can be interpohited between any two 

 primary or simpler colours, so that each may be distinguish- 

 able by the eye upon a close comparison. The number is 

 much smaller than might be supposed. Lambert states, that 

 from perfect black to perfect tichite he could only trace thirty 

 intermediate shades distinguishable by the eye under themosi 

 favourable circumstances possible*. The number of gradations 

 of even the most positive colours is probably considerably less, 

 and of the more neutral colours much less again; at least if 

 we do not repeat those semi-neutral compounds which are 

 indistinguishable from one another. 



As to the transition from one quality of colour to another 

 without regard to its dilution with light or shade, as, for in- 

 stance, from red to blue, the sensible intermediate stages are 

 also probably much fewer than might be suspected. Mayer 

 affirms t that the distinction of mixed colours is evident so 

 long as the sum of the component parts denoted, as in the dia- 

 gram, fig. 2, does not exceed 12. Thus a bright yellow, 

 such as king's yellow, being denoted by z/jg, yellow ochre is 

 ^10 ^'s' umber is j/g r^ b^ ivory black j/g r^ b^, in all which cases 

 the sum of the parts is equal to 12. Upon this scale it is easy 

 to show that the fundamental triangle, whose side is 13, will 

 contain 91 coloured spaces. These embrace all possible com- 

 binations of colour, of the fundamentally greatest intensity 

 which the imperfection of our pigments enable us to procure. 



Allowing 4 gradations of each colour into blackness and 

 4 into whiteness, Mayer reckoned*819 colours in all; a num- 

 ber which will certainly appear small considering the appa- 

 rent infinity of hues and shades. It is probably sufficient, 

 however, for matching any colour by reference to two others, 

 one above and the other below it, in any of the scales ; and 

 such subdivision may probably be carried by the eye to greater 

 accuracy than one intermediate step. The gradation of nine 

 steps from perfect black to perfect white through any colour 

 is perhaps too small ; but on the other hand, the neutral co- 

 lours, as already observed, some of them at least, lose their 

 distinguishable characters compared with one another, when 

 diluted either with black or with white, but especially the 

 former f. Taking advantage of this consideration, Lambert 

 modified Mayer's triangles by reducing them continually in 



* Lambert, Farbenpyramide, § 10, 11. f Ibid. § 29. 



X I suspect, indeed, that in some instances the dilution of the semi- 

 neutrals with white renders them more easily distinguished, but only down 

 to a certain point. 



