1st Radius = ⁹/₁₀ of Red + ¹/₁₀ of Black. 2nd ” = ⁸/₁₀ ” + ²/₁₀ ” 3rd ” = ⁷/₁₀ ” + ³/₁₀ ” 4th ” = ⁶/₁₀ ” + ⁴/₁₀ ” 5th ” = ⁵/₁₀ ” + ⁵/₁₀ ” 6th ” = ⁴/₁₀ ” + ⁶/₁₀ ” 7th ” = ³/₁₀ ” + ⁷/₁₀ ” 8th ” = ²/₁₀ ” + ⁸/₁₀ ” 9th ” = ¹/₁₀ ” + ⁹/₁₀ ” These proportions relate to the effect of the mixtures upon the eye, and not to the material quantity of the red and black substances. 145. We see then—1. That each of these _tones_, 15, composed of colour and black, reduced by white and deepened by black, gives a scale of twenty tones, so much the more broken as they are nearer the scale of normal black. 2. That the quadrant by its movement upon the axis of the circle, represents the scales of every colour except red, broken by black. These broken scales are equidistant, and are formed of equidistant tones. 3. That all the colours are thus contained in a circle, whose plan comprehends the pure colours; the central space, black; and the intermediate space the pure colours, broken by the various proportions of black. 146. The diagram, as just described, thus represents the lowering of pure colours by white, and their gradation by black; their modifications by their mutual mixtures, the modification of hues, and the modification of breaking. We will presently inquire into the possibility of realizing it by means of coloured materials. 147. We have presumed—1. That the normal tone of each of the scales is as pure as possible. 2. That the tones bearing the same number in all the scales,—both those of the pure colours and those of the broken colours,—are, to the sight, of equal depth. 3. That if three tones, of the same number, be taken in three consecutive scales, the tone of the intermediate scale is the mean between the colours of the extreme scales. It is thus easy to explain the modifications of a pure colour commencing with its normal tone. 148. These modifications are so produced that—1. _The Pure Colour never leaves its Scale._—The modification is in the direction of the radius of the circle—proceeding from the normal tone towards the centre, it gains white; while proceeding from the normal tone towards the circumference, it gains black.