80 Intelligence and Miscellaneous Articles. 



a formula in which c is constant and a the angle formed by the 

 straight line joining the two complementary colours to the corre- 

 sponding median line : a is moreover obtained from the equation 



6 = ctan a. 

 The discussion of this equation shows that, as soon as a exceeds 

 45°, b increases much more rapidly than x. From this it follows 

 that the colours situated in the vicinity of a vertex will occupy in 

 the construction a larger space than their complementaries, which 

 are found all assembled towards the middle of the opposite side. 

 That is to say, the, colours situated on both sides of a primary colour, 

 and which to the eye are equidistant, have their complementaries so close 

 to' one another that it becomes difficult to distinguish those which are 

 consecutive. 



This remarkable character is that which constitutes the funda- 

 mental property of the primary triad. It was this phenomenon 

 that attracted my attention when studying the distribution of the 

 complementary colours in a chromatic circle. It has not, there- 

 fore, to be verified experimentally ; thanks to it, I have been able 

 to fix the position of the primary colours within very narrow 

 limits ; and it only remains for me to prove that within those limits 

 there are three colours possessing the characters of a triad. This 

 I will do soon, by showing that they obey the law of the comple- 

 mentary colours* which I have formulated above. 



The cycle of the demonstrations will then be closed ; all the 

 proofs, synthetic and analytic, will then have been given ; and the 

 accordance between the results of experiment and that of calcula- 

 tion will be such that Young's theory may be regarded as established 

 on solid scientific foundations. — Comptes Hendus de VAcademie des 

 Sciences, May 30, 1881, t. xcii. pp. 1286-1289. 



* Yon Bezold (Poggendorff's Annalen, vol. cl. p. 71, 1873), believes he 

 has given the mathematical law of the complementary colours. He has 

 taken as his experimental starting-point the investigation made by Helm- 

 holtz of the distribution of those complementary colours in the spectrum. 

 Unfortunately he has not been able to avoid a confusion which moreover 

 exists in all the special treatises, and which is rendered so easy by the 

 usual language referring to the colours. 



He introduces into his calculations two absolutely heterogeneous data. 

 One is the number of vibrations representing a colour — a valne of a purely 

 physical order, and independent of the properties of the eye ; the other is 

 the law of the mixture of colours, the hypothesis of Young, the notion of 

 the complementary colours — a notion essentially physiological, since it 

 depends on the structure of the eye, and varies according as the latter is 

 or is not normally constituted. The results, too, obtained by von Bezold 

 present sensible discrepancies with experiment; but he attributes to the 

 perturbations induced by the fluorescence of the media of the eye the 

 want of agreement which he necessarily found. 



The number of vibrations cannot have any meaning in the present case, 

 unless employed simply as a means of nomenclature of the colours and 

 not as a mathematical value to be introduced into the calculations. The 

 colours chosen by von Bezold as primary are also very far from possessing 

 the properties of the fundamental sensations. 



