1873 -J Colours and their Relations. 99 



1 : 1*35017. But while in the first case the discrepancy 

 might be attributed to errors of observation, it cannot be so 

 attributed in the case of the calculated wave-lengths : for 

 these could not be altered, even to so trifling an extent as to 

 make the ratio exactly 1 : 1*35, without destroying the 

 whole symmetry of the formulas. It is accordingly far 

 more probable that the ratio between F and C is as 1 : 1*35017 

 than exactly 1 : 1*35 — a relation which would involve the 

 conclusion that all the foregoing nicely balanced formulae 

 have no true mathematical basis, but arise out of mere 

 arithmetical coincidences. Moreover, the ratio 1 : 1*35 does 

 not correspond to that of any musical interval. The case is 

 different with the relation between F and Hy 4 , which is so 

 nearly that of a Pythagorean minor third that the difference 

 might be ascribed to errors of observation. If the calculated 

 value of F be divided by the ratio of this minor third 32-^27, 

 it will give for the wave-length of Hy 4 4101*258 ; whereas 

 Angstrom makes the observed value \\o\'2 — the difference 

 0*058 lying much within the limits of probable error, so 

 that the true relation between F and Hy 4 may very probably 

 be that of this minor third. But it is the minor third 

 proper to melody — not that proper to harmony, the ratio 

 of which is 6-J-5. 



With respect to the other principal fixed lines, generally, 

 — those namely embraced in the foregoing formulae, — it may 

 be affirmed that none of them stand to each other in a ratio 

 corresponding to any of those found in the three several 

 musical scales. Nevertheless, each of the lines stands in a 

 relation of that kind to one or more other lines of the 

 spectrum, within the probable limits of error of observation. 

 These relations are shown in the annexed table, of which 

 the first column contains the letter designating the fixed 

 line ; the second, the sign of multiplication or division. 

 The next three columns the name of the musical interval in 

 one or other of the three scales — the Ideal, the Pythagorean, 

 the Harmonic, by which the wave-length of the fixed line 

 is multiplied or divided. The sixth column contains the 

 wave-length resulting from this multiplication or division. 

 The seventh contains the corresponding wave-length in 

 Angstrom's scale, to which it is nearest. The eighth shows 

 the differences, plus or minus, between the two — these all 

 lying within the limits of probable errors of observation. 

 The ninth contains the names of the elements to-which the 

 wave-lengths are respectively due, and the tenth the colour 

 of the region of the spectrum in which each wave-length 

 occurs. 



