APPENDIX TO CHAPTER XIV. COLOUR-DIAGRAMS. FOLLOWING a suggestion of Newton's, Maxwell constructed a diagram in which the colours of pigments and many natural objects can be laid down in accordance with certain principles and assumptions presently to be explained. Now, although some of the assumptions are arbitrary, yet if they are accepted a chart is obtained which presents many valuable features for the student of colour. The nature and scope of this colour-diagram will perhaps best be made evident by tracing the actual construction of one as made by the present writer. Following Maxwell, vermilion, emerald-green, and artificial ultramarine-blue were assumed as the three fundamental colours, and positions at the three angles of an equilateral triangle assigned to them. The length of each side of the triangle was 200 divisions of the scale employed. The first step was to determine the position of white in the triangle. For this purpose disks of vermilion, emerald-green, and ultramarine were combined as shown in Fig. 101, smaller central disks of black and white being placed on the FIG. 101.-Compound Disk of Vermilion, Emerald-green, Ultramarine, White and Black, arranged for the production of Grey. same axis. It was found, when the colours were mixed by rapid rotation, that 36 46 parts of vermilion, with 33·76 of emerald-green and 29.76 of ultramarine, gave a grey similar to that obtained by mixing 28.45 parts of white with 71.55 of black. In the experiment 24.5 parts of white were actually obtained; but this was cor rected by adding to it the white due to the black disk, it having been previously ascertained that, if the luminosity of the white paper composing the white disk was taken as 100, that of the black disk was 5.24. The same correction was made in all the cases that follow. The equation then reads: 36.46 R + 33.76 G + 29.76 B = 28:45 W......(1). The next step is to divide up the line R G, Fig. 103, in the ratio of 36.46 to 33.76: (36:46 +33.76): 36 46 :: 200: 103.5. That is, if we mix vermilion and emerald-green in the proportion of 36-46 to 33.76, the mixture-point (a) lies on the line RG, and is 103.5 divisions distant from G, Fig. 103. This point is the position of the complement of the fundamental ultramarine, B. We now connect this point (a) with B by a straight line, find the length of the line to be 173-5 divisions, and seek the mixture-point of 36.46 R + 33.76 G and 29.76 B, which is obtained by the following proportion: [(36:46 +33.76) + 29.76]: 2976; 1735: 51.64. This mixture-point is the position of white; for vermilion, emerald-green, and ultramarine, when mixed in the above proportions, produce white. Hence, white (W, Fig. 103) will be on the line a B, 51.64 divisions from a. (It evidently must be somewhere on this line, for at the two extremities of the line are colours which are complementary, and there must be a mixture-point on the line which is white.) It will be noticed that in this proceeding the colours have been heated, according to Newton's suggestion, as though they were weights acting on the ends of lever-arms, and these arms have been taken of such lengths as to bring the system into equilibrium. It will also be observed that it has been assumed that the pigments, vermilion, emerald-green, and ultramarine, have the same intensity, or that equal areas of them have the same weight. Thus, 36·46 parts of vermilion and 33·76 of emerald-green, acting on a lever-arm 51·64 divisions in length, balance 29-76 parts of ultramarine acting on an arm with a length of 121.86 divisions. The lever-arms of the vermilion and emerald-green passing through W are also similarly balanced, and the whole system is in equilibrium. The white or grey which was obtained in equation (1) was the equivalent of 100 parts of colour; by multiplying 28·45 by 3·51 we obtain 100, and we set these 100 grey units in the place of 28.45 W in equation (1), and obtain what Maxwell calls the corrected value of the white. The factor 3.51 is called the coefficient of the white, and is used to establish a relation between equation (1) and those that follow. The coefficients of vermilion, emerald-green, and ultramarine have at the outset been assumed as 1, and hence in its corrected form equation (1) reads thus: 36.46 R+33.76 G + 29.76 B = 100 w...... We have now laid down upon our colour-diagram the position of our three fundamental colours and that of white, and are prepared to assign positions to all other pigments or mixtures of pigments. For example, to determine the position of pale chromeyellow, a disk covered with this pigment is to be combined with disks of emerald-green and ultramarine, and set in rotation (Fig. FIG. 102.-Compound Disk of Chrome-yellow, Emerald-green, Ultramarine, White, and Black, arranged so as to give a pure Grey by rotation. 102). This experiment was made, and the following equation obtained: 26.9 Y + 12.5 G + 60·6 B=324 W + 67·6 b..... ....... .(3). Before using equation (3), it is necessary to bring it into relation with equation (2), and the first step is to express the value of the white in the same manner as in equation (2), viz.: we multiply it by the coefficient 3·51, and obtain in this way the value of the corrected white, or 113.87. This quantity we substitute in equation (3), which then reads: 26.9 Y +12.5 G + 60'6 B 113 87 w...... = We must now introduce a corrected value for the chrome-yellow, so arranged that we shall have the same number of units, grey or coloured, on both sides of the sign of equality: 113.87(606 + 12·5) = 40·77. 40.77 is then the corrected value of the chrome-yellow, and equation (3) in its corrected form finally reads: 40.77 Y+12.5 G + 60·6 B 113·87 w...... To obtain the coefficient of the chrome-yellow, we divide the corrected value by the original value: We are now prepared to determine the position of chrome-yellow in the diagram. We divide the line B G into two parts having the ratio of 12.5 to 60·6: (12.5 +606): 12.5 :: 200: 34.2. The position, then, of the complement of chrome-yellow is on the line B G, Fig. 103, at the spot marked cobalt, and is distant from B by 34.2 divisions; the distance of this point from W is found by measurement to be 94.1 divisions. We connect the point by a straight line with W, and produce the line some distance beyond; the position of chrome-yellow will be on this line, and may be found by the following proportion: Weight of chrome-yellow : weight of emerald-green and ultramarine :: distance of emeraldgreen and ultramarine : distance of chrome-yellow; or, 40.77: (60·6 + 12·5):: 94·1 : 168 7. Chrome-yellow is consequently distant from the neutral point or white 1687 divisions; we insert it in the diagram along with its coefficient 1.51. By a corresponding process the positions and coefficients of a number of the more ordinary colours have been laid down in the diagram. See Fig. 103. If the diagram is examined, it will be found that along any single radius the pale colours, or those mixed with much white, are located nearer W than those that are more free from such admixture; it will also be noticed that the more luminous colours have higher coefficients. By the aid of this diagram we obtain relative measures of the luminosity and saturation of colours on the same or on closely adjacent radii; the FIG. 103.-Maxwell's Colour-Diagram as constructed by O. N. R. colours also have angular positions assigned to them, so that they are fairly defined as to angular position, intensity, and greater or less freedom from white. It is, however, to be remarked that the construction rests upon several more or less arbitrary assumptions, as: 1. That vermilion, emerald-green, and ultramarine-blue really correspond to the three fundamental colours. If we substitute in place of them other colours, such as red lead, grass-green, and violet, we obtain different |