134. In order to represent all the modifications that I have called _tones_ and _hues_ of colours, as well as the relations which exist between those that are complementary to each other, I have devised the following diagram (Plate 7). From a centre, _c_, I describe two circumferences, _y_ Y. I divide each of these by means of three rays, _c a_, _c b_, _c d_, into arcs of 120 degrees each. I divide the portion of each ray comprised between the two circles _y_ Y into twenty parts, which represent as many tones of the colours red, yellow, and blue. 135. In each of the scales of these three colours there is one tone, which, when pure, represents the colour of the scale to which it relates. I therefore call it the _normal tone of that scale_. If we represent a unit of surface _s_, entirely covered by the pigment which reflects the normal colour, and if we suppose that this colouring matter is equally distributed over the surface _a_ 1, we shall represent the tones superior to the normal tone by the unit of surface covered with 1 of the normal colour, plus the quantities of black increasing with the number of tones; and we shall represent the inferior tones by the unit of surface covered with a fraction of the quantity 1, constituting the normal tone, mixed with (——) quantities of black, as the tone has a less elevated number. If the tone 15 of the red scale be the normal tone, the normal tone of the yellow scale will have a lower number, while the normal tone of the blue scale will have a higher number. This depends upon the unequal lightness of the colours. 136. If each arc of 120° be divided into two of 60° and if radii pass through the points of division, beginning at _y_, there will be represented twenty tones of the orange, green, and violet scales, the colours at the extremities of each diameter being complementary to one another. Each arc of 60° might be divided into arcs of 30°, and thus would be obtained radii representing twenty tones of scales, which I shall call orange-red, orange-yellow, greenish-yellow, greenish-blue, bluish-violet, and violet-red. 137. By dividing each arc into five, for example, by means of five radii, which I divide into twenty parts each, beginning at the circumference _y_, I shall obtain sixty new scales. 138. Beginning with red, I designate them as follows:—