STUDIES IN SPECIAL SENSE PHYSIOLOGY 389 



a combination which corresponds to a sensation of whiteness. As 

 we tend to assign a unique position to white in our scale of 

 sensations, it is customary to complete the mixing laws by the 

 following addition : 



3. Any light mixture whatever can be matched by a mixture of 

 a definite homogeneous light (or a definite purple) and white light. 

 That our results may be as general as possible, it is well to note 

 that there is no necessity to accord a special place to white, 

 although it is convenient in practice. 1 



We see then that the mixing experiments give us variations in 

 colour tone and variations in whiteness, that is, two variables, so 

 that our results ought to be expressible graphically by some plane 

 figure. We have also seen that we can pass from red to violet 

 through the spectral colours and back again to red through purple, 

 so that our graph should be a closed figure. Finally in virtue of 

 the fact that the position of any mixed colour depends directly 

 upon the relative proportions of its components, we infer that the 

 method of determining the position of the centre of inertia of 

 masses might be adapted to the task of ascertaining the position 

 of a mixed colour, given the nature and proportions of its 

 constituents. 



If three colours, A, B, C, none of which can be mixed from the 

 other two, be represented by three points in a plane, then, on 

 assigning to them values in terms of any unit, the situations and 

 quantitative values of their mixtures can be ascertained. Thus a 

 colour mixed from a units of A and b units of B will lie on the 

 line A B at the point at which the centre of gravity of two masses 

 aA and bB (representing the proportions of each colour in the 

 mixture) would be situated. 



In order to establish the correctness of this method it is 

 necessary to prove that, given the experimental laws of colour- 

 mixing, as above defined, this construction is valid in all possible 

 cases i.e. that the situation of a mixed colour, in a diagram, 

 coincides with that of the centre of gravity of two equivalent 

 masses when (1) The two constituents can be mixed from the 

 three chosen colours ; (2) when one can and one cannot so be 

 mixed ; (3) when neither can so be mixed. 



The proof is too long for insertion in this essay, but it is quite 

 straightforward ( 9 ). We can show that the co-ordinates of the point 



1 Cf. ou this jioiiit. J. v. Krii-.s, Nagel's Handb., vol. iii., p. 116. 



