332 Prof. Challis's Theory of the Composition of Colours 



rays do not give rise to such dispersion. By taking into account 

 that absorption generates in greater or less degree epipolic dis- 

 persion, all the phsenomena witnessed by the two experimenters 

 may, 1 think, be explained consistently with the principle that a 

 ray of definite refrangibility is uncompounded. I proceed now 

 with the theory of the composition of colours. 



The analytical formula which expresses that a ray is com- 

 pounded of two or more simple rays is the following : — 



t;=»isin — (a?— «/4-c)+m'sin^(ar — ff^ + c')+ &c. 



Assuming now that composition of colours corresponds to com- 

 position of setherial undulations, the following explanations are 

 given by the undulatory hypothesis of the leading facts which ob- 

 servation has established respecting the composition of colours: — 



(1) The general fact of the composition and resolution of 

 colours is explained by the principle of the coexistence of small 

 vibrations on which the above formula depends. 



(2) The result of compounding any number of undulations 



for which \ is the same, is a series of undulations expressed by 



o__ 



the formula V=M sin— - (a?— «^4-C), in which V is the alge- 



braic sum of the separate velocities, and M is a function of m, 

 m'y &c., and of the phases c, cf, &c. of the component undula- 

 tions. Accordingly it is found by experiment that the compo- 

 sition of rays of a given colour produces a compound ray of the 

 same colour. The coefiicient M, which involves c, c*, &c., must, 

 however, be distinguished from the coefficient m of a simple 

 series of undulations. 



(3) If the values of v at a given time be represented by the 

 ordinates of a curve of which the abscissae are the values of so^ 

 this curve will in general cut the axis of ^ in a great number of 

 points with irregular intervals between them. When this is the 

 case, the result of the composition of the different rays is white 

 light, and the degree of whiteness is greater the greater the irre- 

 gularity. There is here a strict analogy to sound-sensations* 

 As sounds are not all musical, so light is not all coloured. It 

 may be admitted, that as colour in a simple ray is due to regu- 

 larity of wave-intervals, so in every instance of the production 

 of colour, the sensation is due to some species of regularity of 

 recurrence in the waves. It may also be remarked, that the 

 irregularity to which whiteness is due exists whatever epoch be 

 selected, and consequently that whiteness is independent of the 

 phases of the component undulations. This is known to be the 

 case from experience. 



. (4) The effect of compounding two simple colours is expressed 



