418 ON THE THEORY OF COMPOUND COLOURS. 



this relation in a form capable of experimental verification ; and by proceeding 

 in this way we may map out the positions of all colours upon Newton's diagram. 

 Every colour in nature will then be 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. 



IV. Method of representing Colours by Straight Lines drawn from a Point. 



To extend our ideas of the relations of colours, let us form a new geome- 

 trical conception 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 lines 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. 



In 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 be the origin and AB be a section 

 of the plane of the diagram by that of the paper. 

 Let OP, OQ be lines representing colours, A, B the 



OP 

 corresponding points in the diagram ; then the quantity of P will be J^A = P> 



and that of Q will be 775 = 2- The resultant of these will be represented in 



the diagram by the point C, where AC: CB :: q : p, and the quantity of the 

 resultant will be p + q, so that if we produce OC to R, so that OR = (p + q)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 



