158. 3. The normal tone of a pure colour represented by a quantity equal to 1, covering the unit of surface, is the commencement of the normal tones and scales proceeding towards black; these normal tones being represented by black and a quantity of colour less than unity, constituting the mixtures which cover a unit of surface s, and colour it of a tone which has the same number as the normal tone of the pure scale to which it relates. It is understood that in proceeding from this tone to the corresponding tone of normal black, we may insert an unlimited number of mixtures of colour and black. 159. The modifications of colours, thus indicated by the diagram, render it extremely easy to understand the definitions given above (123) of the words, scales, tones, hues, pure and broken colours. 160. 2. _It affords the means of knowing the complementaries of every colour, since the names written at the two extremities of any one diameter indicate the colours complementary to each other._ 161. EXAMPLES.—_a._ Suppose it be required to know the mutual influence of _blue and yellow_; at one extremity of a diameter we read the word _blue_, and at its opposite end, the word _orange_; showing that blue tends to give orange to yellow. Again, at the end of another diameter we read the word yellow, and at its opposite, the word violet; by which we see that yellow tends to give violet to blue. 162. _b._ Suppose _green and blue_ be contiguous; at one extremity of a diameter we read the word green, and at its opposite end, red; showing that green tending to give red to blue, must render it more violet. Again, at one end of a diameter we read the word blue, and at its opposite end, orange. But what arises from the mixture of green and orange? The orange will tend to neutralize its complementary, blue, in the green; and as it is always too feeble to neutralize all the blue, its influence will be limited to neutralizing a portion of it; whence it results that green, contiguous to blue, will appear more yellow than it really is. 163. _c._ Let _green and yellow_ be contiguous, we shall see in like manner that the green, by imparting red to the yellow, will render it orange; and that violet, the complementary of yellow, by neutralizing some yellow in the green, will make the green appear bluer, or less yellow. 164. 3. _A third advantage of this diagram, which distinguishes it from other chromatic diagrams, is, that it affords the preceding advantages, without being coloured._ 165. 4. _A fourth advantage is that of its manifesting to all artists who use coloured materials of a definite size, especially the workers of tapestry, carpets and the like, the relation of number which must exist between the tones of the various scales which they work together._ SECTION III. _Harmony of Colours._