374 Mr. H. R. Droop an 



followed that every such colour and shade could be produced 

 by three colour-sensations, each of which, when excited, con- 

 veyed to the brain the impression of a homogeneous colour. 



Helmholtz arrived at the same conclusion by proving (see 

 Handbuch der physiologischen Optik, p. 282, ed. 1867) that 

 any given colour could be produced by combining a certain 

 quantity of white with some particular colour of the spectrum. 

 From which he deduced that every colour and shade of colour 

 depended on only three independent variables, viz. the quan- 

 tity of the spectrum-colour, the quantity of white, and the 

 length of wave of the spectrum-colour. But though the theory 

 of three colour-sensations was the simplest and most obvious 

 explanation of the experimental facts thus established, it is 

 not (as has been commonly assumed) the only theory capable 

 of explaining them. They would be equally well explained 

 by supposing that there are four, five, or more colour-sensa- 

 tions connected by a sufficient number of linear equations of 

 condition to reduce the number of independent variables to 

 three. Obviously this will satisfy all that Helmholtz estab- 

 lished. That it will also explain the law established by Max- 

 well may be shown as follows. 



Suppose that there are four colour-sensations, R, Y, G, 

 and B (the red, yellow, green, and blue sensations), and that 

 each of them is expressed as a linear function of the three 

 standard colours, V, C, and U, as every colour seen by a 

 normal human eye can be expressed. 



Then we shall have four equations of the form 

 R > =v r Y + c r C+u r U, 



B = v b Y +c b G + u b JJ. ^ 



And when we eliminate V, C, and U between these four 

 equations we shall get a linear relation between R, Y, G, and 



B, which is the condition that these four colour-sensations 

 should be capable of being expressed as linear functions of V, 



C, and U, i. e. should be colour-sensations coexisting in a 

 normal eye. 



If we supposed five colour-sensations, we should have five 

 equations (A) between which to eliminate V, C, and U, and 

 should get two linear equations between the five colour- 

 sensations. 



The proposition that four colour-sensations with a linear 

 relation between them will satisfy Maxwell's law may also be 

 tested in another way, viz. by assuming that there are four 

 colour-sensations connected by a linear equation 



rR + */Y + (?G + &B = 0, ..... (1) 



(A) 



