62 
PROFESSOE J. C'LEEK ISLAXVTELL ON 
§ III. Mathematical Theory of Netttox’s Diagram of Colours. 
Newton’s diagram is a plane figure, designed to exhibit the relations of colours to 
each other. 
Every point in the diagram represents a colour, simple or compound, and we may 
conceive the diagram itself so painted, that every colour is found at its coiTesponding 
point. Any colour, differing only in quantity of illumination fi’om one of the colours 
of the diagram, is referred to it as a unit, and is measured by the ratio of the illumina- 
tion of the given colour to that of the corresponding colour in the diagram. In this 
way the quantity of a colour is estimated. The resultant of mixing any two colours of 
the diagram is found by dividing the hne joining them inversely as the quantity of each ; 
then, if the sum of these quantities is unity, the resultant will have the illumination as 
well as the colour of the point so found ; but if the sum of the components is different 
from unity, the quantity of the resultant will be measured by the sum of the components. 
This method of determining the position of the resultant colour is mathematically 
identical with that of finding the centre of gravity of two weights, and placing a weight 
equal to their sum at the point so found. We shall therefore speak of the resultant 
tint as the sum of its components placed at their centre of gravity. 
By compounding this resultant tint with some other colour, we may find the position 
of a mixture of three colours, at the centre of gravity of its components ; and by taking 
these components in different proportions, we may obtain colours corresponding to eveiy 
part of the triangle of which they are the angular points. In this way, by taking any 
three colours we should be able to construct a triangular portion of Newton’s diagram bv 
painting it with mixtures of the three colours. Of course these mixtures must be made 
to correspond with optical mixtures of light, not with mechanical mixtures of pigments. 
Let us now take any colour belonging to a point of the diagram outside this triangle. 
To make the centre of gravity of the three weights coincide mth this point, one or more 
of the weights must be made negative. This, though following from mathematical prin- 
ciples, is not capable of direct physical interpretation, as we cannot exhibit a negative 
colour. 
The equation between the three selected colours, x, y, z, and the new colour u, may 
in the first case be written 
u=x-\-y-\-z, (1.) 
.r, y, z being the quantities of colour required to produce ii. In the second case suppose 
that z must be made negative, 
u—x-{-y—z (2.) 
As we cannot realize the term —2 as a negative colour, we transpose it to the other side 
of the equation, which then becomes 
uJ^z=x-\-y, (3.) 
which may be interpreted to mean, that the resultant tint* u-\-z., is identical nith the 
resultant, x-\-y. We thus find a mixture of the new colour with one of the selected 
colours, which is chromatically equivalent to a mixture of the other two selected colours. 
