RESEARCHES BASED UPON THE THEORY 237 



produce any appreciable effect ; hence, in what follows, the effect of the 

 red and green sensations on the luminosity will alone be considered. 



" The easiest way to show the manner in which the luminosity 

 curve of a colour-deficient person is obtained will be to consider a 

 particular case, say, one where the red sensation is deficient to such 

 an extent that all the ordinates of the red sensation curve are only 

 half the normal. Such a person may be said to possess half-normal 

 red sensation and will be indicated by the symbol 0-5 RS. Since each 

 of the ordinates of the red sensation curve is half the normal, the total 

 area of that curve will also be half the normal. As in the light from 

 the crater of the electric arc the areas of the red and green sensation 

 curves are as 579 to 248, it follows that the areas for the 0*5 RS are as 

 290 to 248. 



" Now suppose such a person determines the luminosity of a colour 

 of which the wave-length is A, and that A;, and A,^ are the ordinates of the 

 normal red and green sensation curves for this colour, the corresponding 

 ordinates for the observer will be hK, and A^,. The total sensation 

 produced by the colour will be the sum of the two sensations, that is, 

 for the normal it will be A,, -f A^, and for the observer (0-5 RS) -|A,. -1- A^. 



" The sensation produced by the comparison white in the luminosity 

 measurement will be proportional to the sum of the areas of the red 

 and green sensation curves. Hence, if we represent the areas of these 

 curves for the normal by Ur and Zg respectively, the sensations produced 

 by the white for the normal will be Ur + Eg, and for the colour-deficient 

 will be \Er -\- Eg. 



" Thus the brightness of the coloured hght is for the 0-5 RS observer 



reduced in the ratio (|A,. + \g)l{K + A^,), while that of the white is 



reduced in the ratio {\Er + Eg)l{Er + Eg). Let w be the intensity of 



the white when the normal observer makes the luminosity setting and 



w' the intensity of the white when the colour-deficient observer makes 



the setting. Then we have 



w = a (A,. + A,,) (1) 



and w' ^-^-^^ -^ a (|A, + A,) (2), 



where a is a constant which depends on the unit used to measure the 

 intensity of the white light. 



" Thus the ratio of the colour-deficient observer's luminosity to that 

 of the normal is given by 



^(/ _ ^Xr + A„ Er + E g 



w A, + A, "^lEr+Eg ^'^'- 



