The scales (both horizontal and vertical) of the present work are all prepared directly from definite color-wheel formulæ, based on carefully calculated curves; the thirty-six pure spectrum hues, represented by the middle horizontal line of color-squares on Plates I-XII (together with an equal number of intermediates represented by blank spaces), requiring a separate curve and consequently different relative proportions of the two component colors for each series of hues—that is, the series from red to orange, orange to yellow, yellow to green, green to blue, blue to violet, and violet to red, respectively; but the progressive increments of white in the scales of tints, black in those of shades, and neutral gray in the several series of broken colors are exactly the same in every case. The first series of Plates (I-XII) shows the pure, full spectrum colors and intermediate hues (middle horizontal line, nos. 1-72),[9] each with its vertical scale of tints (upward, _a-g_) and shades (downward, _h-n_), the increments of white for the tints being 9.5, 22.5, and 45 per cent., respectively, those of black in the shades being 45, 70.5, and 87.5 per cent. The remaining Plates show these same thirty-six colors or hues in exactly the same order and similarly modified (vertically) by precisely the same progressive increments of white (upward) and black (downward), but all the colors are dulled by admixture of neutral gray; the first series (1′-72′, Plates XIII-XXVI) containing 32 per cent. of neutral gray, the second (1′′-72′′, Plates XXVII-XXXVIII) 58 per cent., the third (1′′′-72′′′, Plates XXXIX-XLIV) 77 per cent., and the fourth (1′′′′-72′′′′, Plates XLV-L) 90 per cent. The last three Plates (LI-LIII) show the six spectrum colors[10] (also purple, the intermediate between violet and red) still further dulled by admixture of 95.5 per cent. of neutral gray, these being in reality colored grays; to which are added a scale of neutral gray and one of carbon gray, the former being the gray resulting from mixture of the three primary colors (red 32, green 42, violet 26 per cent., which in relative darkness equals black 79.5, white 20.5 per cent.); the latter being the gray produced by mixture of lamp black and Chinese white, and the scale a reproduction of that in the author's first "Nomenclature of Colors" (1886, Plate II, nos. 2-10). It should be emphasized that in all cases except the scale of carbon grays, only the disks representing the middle horizontal series of colors (both pure and broken) have been used, in combination with a black and a white disk, respectively, to make the colors of the vertical scales of tints and shades.