1891.] The Numerical Registration of Colour. 



and mixing them, we can give the same impression to the eye that 

 any compound colour gives, and that of any intermediate simple 

 spectrum colour but very slightly diluted with white light. With 

 these same three colours, but in different proportions, we can also 

 give the impression of white light to the eye. The intermediate 

 spectrum colours between the green and the violet rays selected, 

 when slightly diluted, are imitated by mixing these rays together in 

 different proportions, and similarly those lying between the red and 

 the green by mixing together these rays in different proportions 

 and there is some ray present in the spectrum which, when very 

 slightly diluted with white light, has the same colorific effect on the 

 eye as the mixtures of the pairs V and G and G and R in any pro- 

 portions whatever. 



Let the luminosities of the rays R, G, and V, which give the im- 

 pression of white light, be a, &, and c units respectively, and p, g, and 

 r those which give that of the colour which has to be registered and 

 reproduced. We then get the following equations where W is 

 white, w its luminosity, Z the colour, and z its luminosity 



wW ................ (i); 



pR + qG + rV =zZ .................. (ii). 



Then evidently 



(a + J + e) = w, and 



Let p = ata, q = fib, r = <ye. 

 we may write (ii) as 



(iii). 



Tow, either , ft, or 7 must be smaller than the other two. As an 

 iple, if a be the smallest, we multiply (i) by , when we get 



= atwW .............. (iv). 



Subtracting (iv) from (iii), we get 



(ft-*) bG+ (<y ) cV = zZ-*wW. 



Now, it has already been stated that between Fand G there is some 

 ,y which gives the same sensation of colour, mixed with a very small 

 >ntity of white light, as the above mixture of Fand G let us call 

 it X and its luminosity x \x being evidently equal to (ft )& + 

 (<y )c], and p. the luminosity of the small quantity of white 

 added. 



We then get zZ = xX + (/*+*) W. 



II 



