THE THEOEY OF COMPOUND COLOUES. 
63 
When the equation takes the form 
u=x—y—z, ( 4 .) 
tivo of the components being negative, we must transpose them thus, 
u+y-Yz=x, ( 5 .) 
which means that a mixture of certain proportions of the new colour and two of the three 
selected, is chromatically equivalent to the third. We may thus in all cases find the 
relation between any three colours and a fourth, and exhibit this relation in a form 
capable of experimental verification ; and by proceeding in this way we may map out 
the positions of all colom's upon Newtox’s diagram. Every colour in nature will then 
he defined by the position of the corresponding colour in the diagram, and by the ratio 
of its illumination to that of the colour in the diagram. 
§ ly. Method of rejyresenting Colours hy Straight Lines drawn from a Point. 
To extend our ideas of the relations of colours, let us form a new geometrical concep- 
tion by the aid of solid geometry. 
Let us take as origin any point not in the plane of the diagram, and let us draw lines 
through this point to the different points of the diagram ; then the direction of any of 
these hues will depend upon the position of the point of the diagram through which it 
passes, so that we may take this line as the representative of the corresponding colour 
on the diagram. 
Ill order to indicate the quantity of this colour, let it be produced beyond the plane 
of the diagram in the same ratio as the given colour exceeds in illumination the colour 
on the diagram. In this way every colour in nature will be represented by a line drawn 
through the origin, whose direction indicates the quality of the colour, while its length 
indicates its quantity. 
Let us find the resultant of two colours by this method. 
Let O be the origin and be a section of the plane 
of the diagram by that of the paper. Let OP, OQ be 
lines representing colours, A, B the corresponding points in the diagram ; then the 
quantity of P \yil be and that of Q will be 0^ = 2'- resultant of these 
will be represented in the diagram by the point C, where AC : CB :: q :j), and the quantity 
of the resultant will be ^+5', so that if we produce OC to R, so that OR=(2?+5^)OC, 
the line OR will represent the resultant of OP and OQ in direction and magnitude. It 
is easy to prove, from this construction, that OR is the diagonal of the parallelogram of 
which OP and OQ are two sides. It appears therefore that if colours are represented 
in quantity and quality by the magnitude and direction of straight lines, the rule for the 
composition of colours is identical with that for the composition of forces in mechanics. 
This analogy has been well brought out by Professor Geassmaxn in Poggexdoefe’s 
‘ Annalen,’ Bd. Ixxxix. 
K 2 
