. M. H. Helmholtz on the Theory of Compound Colours. 519 



of two sums, each of them of sixteen squares, is not a sum of 

 sixteen squares. It is proper to remark, that this demonstration, 

 although I think rendered clearer by the introduction of the idea 

 of the system of triplets furnishing the rule for the formation of 

 the expressions ?<;^„ a^^, b,,, c,,, &c., is not in principle different 

 from that contained in Prof. Young's paper on an Extension of 

 a Theorem of Euler's, &c., Irish Transactions, vol. xxi. 

 2 Stone Buildings, Oct. 8, 1852. 



LXXXI. On the Tlieory of Compound Colours. 

 By H. Helmholtz*. 



LUMINOUS rays of different wave-length and colour di- 

 stinguish themselves in their physiological action from 

 tones of different times of vibration, by the circumstance that 

 eveiy two of the former, acting simultaneously upon the same 

 neiTOus fibres, give rise to a simple sensation in which 

 the most practised organ cannot detect the single composing 

 elements, while two tones, though exciting by their united 

 action the peculiar sensation of harmony or discord, are never- 

 theless always capable of being distinguished singly by the ear. 

 The union of the impressions of two different colours to a single 

 one is evidently a physiological phsenomenon, which depends 

 solely upon the peculiar reaction of the visual nerves. In the 

 pure domain of physics such a union never takes place ob- 

 jectively. Rays of different colours proceed side by side with- 

 out any mutual action, and though to the eye they may appear 

 united, they can always be separated from each other by physical 

 means. 



The investigation of this compound action has led to the 

 theory of primitive colours, from the combination of which all 

 others are, or can be, obtained. This theory, however, has been 

 based from the beginning upon a single mode of experiment ; 

 namely, that in which colouring substances are mixed together, 

 the results being assumed to be the same as would follow from 

 the union of the coloured lights themselves, — an assumption the 

 untruth of which I purpose in the following pages to prove. 



Pliny mentions the fact that the oldest Greek painters were 

 able to represent all things by means of four pigments, while in 

 his time a much greater number was made use of, but without 

 the ability to produce an equal effect. Leonardo da Vinci, 

 equally celebrated as an artist as for his scientific treatment of 

 painting, was not aware of the theory of the three so-called pri- 

 mitive colours ; besides black and white, which however are 



* From Miiller's Archiv and Poggendorff's Annalen, 1852. No. 9. Com- 

 municated by Dr. Tyndall. 



