Intelligence and Miscellaneous Articles. 543 



could be fitted to microscopes, and more convenient than those at 

 present employed. 



NOTE ON THE SENSATION OF COLOUR. BY C. S. PEIRCE. 



It may, perhaps, be worth while to notice a few consequences of 

 three theories concerning colour which are usually regarded with 

 some favour. 



First Hypothesis. — The appearance of every mixture of lights 

 depends solely on the appearances of the constituents, without 

 distinction of their physical constitution. This I believe is estab- 

 lished. 



/Second Hypothesis. — Every sensation of light is compounded of 

 not more than three independent sensations, which do not influence 

 one another. This is Young's theory. It follows that, if we de- 

 note the units of the three elementary sensations by i, j, and Jc, 

 every sensation of light may be represented by an expression of 

 the form 



Xi+Y/+Zfc 



Third hypothesis. — The intensity of a sensation is proportional 

 to the logarithm of the strength of the excitation, the barely per- 

 ceptible excitation being taken as of unit strength. Negative loga- 

 rithms are to be taken as zero. This is Fechners law. It is known 

 to be approximately (and only approximately) true for the sensation 

 of light. From this it follows that, if x, y, z be the relative 

 proportions of a mixture of three lights giving the elementary 

 sensations i, j, Jc, the sensation produced by the mixture is 



I logo? .i + Jlogy ./-j-Klogz. k, 



where I, J, K, are three constants. 



From these principles it follows that, if a light giving any sen- 

 sation such as that just written have its intensity increased in any 

 ratio r, the resulting sensation will be 



I log rx . i + J log ry ,j-\-~K log rz . k 



= I log a? .i+ J log y . j+lL logs . 7c-\~logr(Ii-\-Jj+Kk). 



Thus the result of increasing the brilliancy of any light must be 

 to add to the sensation a variable amount of a constant sensation, 

 li+Jj+Kk; and all very bright light will tend toward the 

 same colour, which may therefore be called the colour of brightness. 

 Moreover, if the three primary colours be mixed in the proportions 

 in which each by itself is just perceptible, the sensation produced 

 will be 



logr(Li+Jj + Kk) 9 



and can only differ by more or less. 



Now I find in fact that all colours are yellower when brighter. 

 If two continuous rectangular spaces be illuminated with the same 

 homogeneous light, uniformly over each, but unequally in the two, 

 they will appear of different colours. 



