268 O. JS r . Rood— Color System. 



angular positions of these colors were not arbitrarily assumed, 

 but determined from the mixture equation and the ascertained 

 coefficients. With the aid of this triangle and color equations 

 experimentally obtained, I plotted in the usual way the posi- 

 tions of five of the discs used in the building up process, and 

 calculated their coefficients with the following result : 



Direct coef. Calculated. 



Gl 1-119 1-109 



01 1-221 1-231 



P12 1-229 1-257 



G18 -S67 -892 



Pi : -571 -566 



GYo -806 -795 



GY5, a greenish yellow, was quite beyond the limits of the 

 triangle. 



This agreement shows that the zig-zag process employed by 

 me is homogeneous with that ordinarily used in Newton's 

 diagram, and from this it follows that it is not necessary to 

 determine by my method coefficients for a greater number of 

 discs than will furnish a properly shaped triangle, and that the 

 remainder of the work can be done by the older method. It 

 may here be remarked that in obtaining the fundamental equa- 

 tion for the construction of the diagram and those for locating 

 the colors, it is necessary to exercise far more suspicious care 

 than is the case in the direct determinations of the coefficients. 

 Although a pure gray is always attainable, theoretically, yet it 

 seldom is obtained quite to the satisfaction of the observer ; 

 the best way is to employ on the same axis duplicate sets of 

 discs separated by the comparison gray, to vary the manipula- 

 tion and multiply the observations. The work having pro- 

 gressed thus far it becomes possible to ascertain the coefficient 

 of any colored surface and to assign it a position in the dia- 

 gram. 



It may be remarked that the angular positions assigned to 

 colors by the method just described agree in their main fea- 

 tures with those given by me in a diagram on page 250 of 

 " Modern Chromatics," which is founded on contrast observa- 

 tions, the main differences being in the angular positions 

 assigned in the diagram to violet and blue-violet ; these would 

 have to be moved about 15° to the right, i. e., nearer to the 

 other blues to make them coincide with positions furnished by 

 this system. 



I give here some of the coefficients obtained : the vermilion 

 with a coefficient of 1 had only a moderate brilliancy, being 

 made of English vermilion applied to card-board as a paste : 

 since then I have found in the shops a red, supposed to be 

 vermilion, with a coefficient as high as 1*1 74. 



