The coloring of a satisfactory set of disks to represent the thirty-six pure spectrum colors and hues was a matter of extreme difficulty, many hundreds having been painted and discarded before the desired result was achieved. Several serious problems were involved, the matter of change of hue through chemical reaction of the combined pigments or dyes[11] (especially the latter) being almost as troublesome as that of securing the proper degree of difference between each adjoining pair of hues. The method by which satisfactory results were finally secured was as follows: First, six disks were colored to represent each of the fundamental spectrum colors, according to the author's conception of them.[12] These six disks were then placed against a suitable background (a neutral gray), in spectrum sequence, with wide intervals for the accommodation of connecting series of disks, which were then colored so as to represent an apparently even transition from one to the other. When this very difficult task had been done as well as the eye alone could judge, each intermediate was then measured on the color-wheel and the relative proportions (in percentages) of its two component colors recorded. After this had been done for all the intermediate hues each series (the red-orange, orange-yellow, yellow-green, green-blue, blue-violet, and violet-red) was taken separately and a curve constructed on cross-section paper from the recorded ratios. These curves were found to be in all cases more or less irregular or unsymmetrical, but nevertheless were sufficiently near correct to serve as a basis for a symmetrical curve; and after the points out of proper line were suitably relocated the two component colors were correspondingly readjusted on the color-wheel and each faulty disk corrected (or a new one painted) until it exactly matched the required combination. The scales representing the tints and shades of each color, and also the gray or broken colors were similarly determined by corrected curves.[13] By the method adopted of running each of the thirty-six spectrum hues through a scale of tints and shades, and repeating the combination through several series modified by increasing increments of neutral gray, practically the entire possible range of color variation is covered,[14] rendering it an easy matter to locate in the plates, either among the colors actually shown or in an intermediate space, any color which it is desired to match; and where short distinctive names have not been found (their place being, tentatively, supplied by compound names), as, necessarily, must often be the case, any color or intermediate between any two colors, either as to hue, tint, or shade, may be readily designated by the very simple system of symbols (numerals and letters) employed.[15]