The geometrical solution of colour mixture problems

Starting from the experimental fact that any colour can be uniquely expressed by a trichromatic equation, provided negative coefficients may enter, it is shown that all problems of colour mixture are amenable to an exact system of geometrical calculation. The particular methods described in the paper are such as to obviate the introduction of stereographic projection and other geometrical complications which enter into previously published methods. This simplification is effected by conducting the actual colour mixture part of any calculation in the quantity units of one trichromatic system, leaving the relative magnitudes of the various systems of units, where more than one system is involved, to be accounted for by the introduction of suitable coefficients in the purely arithmetical part of the work. The problems dealt with are: Mixtures of two colours. Mixtures of three colours. Mixtures of four or more colours. Transformation of data from one trichromatic system to another, either directly or by means of general equations of transformation. Transformation of data between the trichromatic and monochromatic systems of specification. Calculation of colour from energy distribution of stimulus. Graphical solutions are described for all these problems, non-graphical solutions being also given for all cases in which they are applicable. The graphical solutions are described in relation to rectangular co-ordinates so that they may be carried out on ordinary graph paper without the necessity of specially prepared charts. The methods are illustrated by a number of worked examples specially designed to show how various types of data which may enter into a practical problem may be reduced to a form suitable for solution, and how the result of the colour calculation can be reconverted to the form in which the answer is required.