412 Dr. R. A. Houstoun 



on a 



This table states, for example, that the percentages of R, 

 G, and B energy in the mixture giving the same hue as 

 X = 5 128 are —50, 111, and 39 respectively. The composition 

 of white light according to energy is 41 R, 31 Gc, and 28 B, 

 so that, when the results are represented this way, the close 

 proximity of the white with the limiting curve is avoided. 

 The violet end, which is difficult to measure, is also repre- 

 sented on a much reduced scale. 



§ 3. Let us suppose that two colours are mixed, and that 

 it is required to determine the colour of the mixture. Let 

 each colour be represented by its energy curve in terms of 

 any arbitrary spectrum-scale s. Let the centroids of the 

 two energy-curves be at s x and s 2 , and let their areas, i. e. 

 the intensities of the two colours, be denoted by Ij_ and I 2 . 

 The question arises as to how the shape of each curve is to 

 be specified. The most natural way is by means of the 

 square of the radius of gyration of the area about the ordinate 

 through the centroid. This is in accordance with statistical 

 practice ; in fitting curves to observations the statisticians 

 are accustomed to consider first, second, third, etc. moments ; 

 when the area is known, the first moment specifies the 

 centroid, and the second the square of the radius of gyration. 

 The radius of gyration is the " standard deviation " of the 

 statistician. The colour-perceiving centre in the brain is so 

 badly developed that it is not necessary to characterize the 

 shape of the energy-curve any further than by the second 

 moment. 



Let ki 2 , h 2 denote the squares of the radius of gyration 

 for the two component colours, and let s, I, and ¥ specify 

 the mixture. Then 



I = I 1 + I 2 , s= sli + S ^ 



an( 



' + ii+i, 



Newton's colour-diagram follows naturally from these 

 equations. For let s l9 s 2 specify the abscissae, and s^ + k x 2 

 and s 2 2 + k 2 2 the ordinates of two points on a plane, and 

 place particles of masses 1 1 and I 2 at these points ; then it is 

 clear that s and s 2 -j-P denote the abscissa and ordinate of 

 their centroid. 



Let us suppose that k 2 is the same for all the spectrum 

 colours. Then if we plot them on the colour-diagram we 

 have 



x = s, y = s 2 -\-k 2 , i. e. o?=y — k 2 , 



the equation to a parabola. This is in accordance with fig. 2. 



