1 873.] Colours and their Relations. 97 



1*5, will correspond to the sol of both scales. So, also, if 

 the green be divided by the orange, the quotient 1*2, is equal 

 to mib , or the minor third of the harmonic scale ; while the 

 violet divided by the green gives 1*25, corresponding to its 

 major third. 



Beyond these points of correspondence, in themselves not 

 a little remarkable, there is no analogy between the scale of 

 colour and the musical scales. The analogy is closest in 

 the case of the harmonic scale ; but there is this funda- 

 mental difference, that, whereas there are in that scale three 

 interlaced arithmetical progressions, with diverse common 

 differences, the colour scale consists of a single perfect 

 arithmetical progression ; so that, in their integrity, the two 

 scales are irreconcilable. It is thus evident that the 

 analogy between the two scales, so far from being perfect, 

 consists only in this, that both are founded on a mathema- 

 tical basis ; but the colour scale forms a series much more 

 simple and symmetrical than does either the Pythagorean 

 or the harmonic musical scale. 



These mathematical relations, subsisting among the mean 

 rays of each pure colour of the spectrum, become all the 

 more interesting when viewed in connection with those sub- 

 sisting among the principal fixed lines of the normal spec- 

 trum, as respects their relative wave-lengths. For the 

 purpose of a comparison of the one set of relations with 

 the other, the latter may here be given as deduced from the 

 very accurate observations of M. Angstrom. Assuming the 

 more refrangible E as the centre of the system, and calling 

 the value of its wave-length 10, the relative wave-lengths 

 corresponding to the other fixed lines A, B, C, the less re- 

 frangible D, F, G, and the more refrangible H, may be 

 found by the following formulae : — 



to 



2A 2 -6A ..... 



. = 3 E 2 + 3E 



(b) 



(6A 2 -A)-(6B 2 + 2B) . 



. = E 2 + gE 



(c) 



(4B 2 + 2B)-( 4 C 2 -2C) . 



. = E 2 + E 



(d) 



(6C 2 -C)-(6D 2 + 6D . 



. = E 2 



(/) 



C 2 + ( 2 F 2 -6F) . . . 



. = 2E 2 + 7E 



(g) 



( 4 G 2 + 4 G)-(C 2 + 2C) . 



. = E 2 + 2E 



(h) 



( 2 F 2 + 6F)-(H 2 + 4 H) . 



. = E 2 + 4 E 



The relative values of the eight wave-lengths, as given by 

 observation, and as calculated from the foregoing equations, 

 are as follows : — 



vol. in. (n.s.) 



