2 6o SCIENCE PROGRESS 



additional colours, and finds that the spaces occupied are con- 

 nected with the lengths of a vibrating string giving the notes 

 of the octave. This is illustrated by a figure which is practic- 

 ally the same as the fig. 4 from the Opticks, which we have 

 reproduced . Only here the statements are rather more definite ; 

 the notes of the octave are referred to as sol, la, fa, ut, re, mi, 

 fa, sol ; the spaces /mkCK and S/3ay of fig. 4 are said to give the 

 two semitones, while the three spaces in the middle occupied 

 by blue, green and yellow, and the end spaces occupied by violet 

 and red, give the five tones. Also the purest part of each colour 

 is now said to be in the middle of its space. 



In the next section Newton states that owing to its not 

 being possible to observe the limits of the colours sufficiently 

 accurately, they may really differ slightly from the positions 

 given above, and he consequently suggests another distribu- 

 tion ; put " eleven mean proportionals " between the ends of 

 the spectrum and let a/3, yS, e£, yd, lk, and \/j, in fig. 4 be 

 respectively the second, third, fifth, seventh, ninth, and tenth 

 of these proportionals, i.e. multiply XM in fig. 4 by V2 to the 

 second, third, fifth, seventh, ninth, and tenth powers, and this 

 distribution also satisfies the observations within experimental 

 error. To compare the two distributions he supposes OM = 

 1 80 ; then according to the first one the limits of the colours are 

 at 



36O, 32O, 3OO 27O, 24O, 2l6, 202|, 180, 



and according to the second 



360, 321, 303, 270, 240, 214, 202, 180. 



Then there are two extremely interesting sentences comparing 

 the merits of the two distributions which may be freely ren- 

 dered as follows : 



" I really prefer the former one, not because it agrees with 

 experiment better, but because it may perhaps suggest analo- 

 gies between harmonies of sounds and harmonies of colours 

 (such as are not wholly unknown to the painters, but which I 

 have not yet studied sufficiently myself — qualium pictores non 

 penitus ignari sunt, sed ipse nondum satis perspectas habeo). 

 Such a connection appears more plausible if we note that the 

 affinity between the extreme red and violet, the ends of the 

 spectrum, is of the same kind as between the first and last notes 

 of the octave." 



