544 FOURTH REPORT — 1834. 



Theoretical Explanations of some Facts relating to the Com- 

 position of the Colours of the Spectrum. By the Rev. James 

 Challis. 



A ray of homogeneous light, in the unclulatory hypothesis, 

 consists of the isochronous undulations of an elastic medium ; and 

 the velocity at a given instant, of the undulating particles situ- 

 ated on a straight line drawn in the direction in which the light 



— — \- c\,x being 



the distance of any point on the line from a fixed point. The 

 condition of homogeneity is, that m and X be constant : the 

 colour depends on A. 



If two rays be combined, for which m is the same and X dif- 

 ferent, the compound ray, by the principle of the coexistence 

 of small vibrations, is expressed by 



—— + c I -I- ?« sin ( —J- + c' y, 



r, {it X \ . /it X _ \ 



2m cosi -J- -h c, I sm ( -r — I- c^J- 



In the spectrum the greatest and least values of X are to each other 

 nearly in the ratio of 3 to 2, so that "^ ( X ~ "x* ) ^^ ^^ ^^^^^ ®*1"^^ 



to t: — , and I at least equal to 6 X. Hence in the periodic func- 

 o X 



tion cos ( ^ — H <?i ) the periods recur much less frequently than 



those of the other factor, sin ( — + cA, in which L is an har- 

 monic mean between X and X'. It does not appear that the eye 

 can appreciate periods of slower recurrence than those corre- 

 sponding to the rays of the spectrum. We may, therefore, con- 

 clude that the periodicity of cos \—j- + cA would not be per- 

 ceived, and that the eye would be sensible only of that of the 

 other factor. The compound ray will therefore be of an inter- 

 mediate colour. 



