336 Prof. Challis's Theoiy of the Composition of Colours 



fore be ascribed to a large value of fi, that is, to a large diflference 

 of intriusic brightness in the two kinds of rays. / ju .,li ui /it 

 (7) The following is, according to this theory, the explanation 

 of the conjplementiu'y colours of the solar spectrum. We have 

 seen that when the ratio of X to \' for two colours does not differ 

 much from a ratio of equality, the result of combining the colours 

 is an intermediate colour with a mixture of whiteness. In pro- 

 portion as that ratio deviates more from a ratio of equality, the 

 whiteness will increase, because those points of intersection of the 



(2'n'x \ 

 —J- +^2 ) 



in art. (4) will be brought nearer to each other and produce a 

 greater amount of irregularity. Consequently there must be 

 some ratio of \ to X' for which the whiteness so predominates as 

 to destroy all colour. "When this ratio is reached, the colours 

 become complementary. Since we are dealing v^th sensations, it 

 is not too much to assume that sensations produced by undula- 

 tions of the aether have some analogy to sensations produced by 

 undulations of the air. Respecting musical sounds, we know 

 that if \ and X' for two such sounds differ very little from each 

 other, the result of the combination is to the sense musical. On 

 increasing the difference, beats begin to be heard, which corre- 

 spond to incipient whiteness. On still further increasing the 

 difference, we reach complete discord, or unmusical noise, answer- 

 ing to perfect whiteness. M. Helmholtz has given (Poggendorff^s 

 Annalen, vol. xciv.) the following interesting results respecting 

 the ratio of the wave-lengths of complementary colours :- 

 >inRf}n''0'^ '3iM iu 'yr> 'nit to >•>! 



•■•,'An jiiT 



>lJr;'Ki.'/-3iW lO il'ii { 



These experimental results show that the ratio of the wave- 

 lengths of the complementary colours of the spectrum varies from 

 about the ratio of 4 to 3 for red and green-blue, to about the ratio 

 of 6 to 5 for gold-yellow and blue. The production of whiteness 

 with a less difference of wave-lengths in one combination than 

 in another would, according to this theory, be due to a greater 

 difference of intrinsic brightness of the component rays. We 

 have already given a probable reason for concluding that this 

 difference may be greatest when yellow, the predominant colour 



