called shades. Of compound colours, distinct from all the primary ones, I shall speak below.
Fifthly, It is remarkable here, that the order of the five tones and two semi-tones of an octave, which corresponds to the order of the seven primary colours, is the second in absolute perfection (which I have from a MS. paper of Sir Isaac Newton’s on music, not yet published), and the first in relative, i.e. of those, in which the semi-tones are at equal distances from the middle or extremes; which circumstance is evidently necessary in the order of the colours. For if distinct colours arise from ratios, and a half-note colour arise next after the red, if you begin at one end, a corresponding one ought to appear next after the violet, if you begin at the other. The sameness of the ratios that must arise, makes this necessary, on supposition, that the distinction of colours is founded on ratios.
Sixthly, If the distinction of colours arise from the ratios of vibrations, the colours may be expected to be broader where the vibrations are more numerous, because a greater addition must be made to a greater number, in order to make an equal ratio. And there is a certain breadth for each of the colours respectively, which suits each set of ratios of vibrations that they can be supposed to bear to one another, according to any supposed law of increase of the vibrations in passing from one end of the solar image to the other. Since therefore the breadth of the seven primary colours, as determined by Sir Isaac Newton, suits the simplest ratios possible, according to the simplest law of increase possible, as has been explained above, we seem to have from thence an argument both for the doctrine of vibrations in general, and for the particular ratios of vibrations here alleged. And there are two things in this matter which deserve particular notice. First, that Sir Isaac Newton’s Spectrum was about ten inches long; and consequently, the breadths of the seven primary colours, red, orange, yellow, green, blue, indigo, violet, in inches, 1.25; 0.75; 1.33; 1.66; 1.66; 1.11; 2.22; which magnitudes are so considerable, that a small error in fixing the limit of a colour does not much affect their mutual ratios. Secondly, that the limits of the colours were determined in a way, that had no dependence on any hypothesis, and the operation repeated several times. However, it may perhaps be worth the time and pains of some curious experimenter, to examine the breadths of the seven primary colours afresh, and compare them with the hypothesis here proposed.
Seventhly, When all the rays reflected from any natural body are near to each other, as in the yellows of the second order, and in the blues and greens of the third, we may suppose, that the slower vibrations are accelerated by the quicker, and the quicker retarded by the slower, so as to compose an intermediate colour, scarce differing from homogeneal light in appearance of purity; just as in a bell, the slower vibrations of the wider part, and the
