ON THE THEORY OF COMPOUND COLOURS. 



429 



all the others, and therefore requires to be carefully observed. There are twenty 

 observations of this equation, the mean of which gives 



18-6 (24) + 31-4 (44) + 30-5 (68) = W* (16) 



as the standard equation. 



We may use the twenty observations of this equation as a means of 

 determining the relations between the errors in the different colours, and thus 

 of estimating the accuracy of the observer in distinguishing colours. 



The following Table gives the result of these operations, where R stands 

 for (24), G for (44), and B for (68): 



TABLE V. Mean Errors in the Standard Equation. 



(G-B)=-99 

 (B-R)=-85 

 (R-G)=-86 



(G + B) = 2-31 



(B+R) = l-59 



R + G) = l-57 



(R)= -54 

 (G) = l-22 

 (B) = M5 



The first column gives the mean difference between the observed value of 

 each of the colours and the mean of all the observations. The second column 

 shews the average error of the observed differences between the values of the 

 standards, from the mean value of those differences. The third column shews 

 the average error of the sums of two standards, from the mean of such sums. 

 The fourth column gives the square root of the sum of the squares of the 

 quantities in the first column. I have also given the average error of the 



sum of R, G and B, from its mean value, and the value of ./R' 



It appears from the first column that the red is more accurately observed 

 than the green and blue. 



IX. Relative Accuracy in Observations of Colour and of Brightness. 



If the errors in the different colours occurred perfectly independent of each 

 other, then the probable mean error in the sum or difference of any two colours 

 would be the square root of the sum of their squares, as given in the fourth 

 column. It will be seen, however, that the number in the second column is 

 always less, and that in the third always greater, than that in the fourth ; 

 shewing that the errors are not independent of each other, but that positive 

 errors in any colour coincide more often with positive than with negative errors 



