[Greek: e]X, [Greek: e]X, [Greek: g]X, [Greek: a]X, MX, to be in
proportion to one another, as the Numbers, 1, 8/9, 5/6, 3/4, 2/3, 3/5,
9/16, 1/2, and so to represent the Chords of the Key, and of a Tone, a
third Minor, a fourth, a fifth, a sixth Major, a seventh and an eighth
above that Key: And the Intervals M[Greek: a], [Greek: ag], [Greek: ge],
[Greek: ee], [Greek: ei], [Greek: il], and [Greek: l]G, will be the
Spaces which the several Colours (red, orange, yellow, green, blue,
indigo, violet) take up.
[Illustration: FIG. 4.]
[Illustration: FIG. 5.]
Now these Intervals or Spaces subtending the Differences of the
Refractions of the Rays going to the Limits of those Colours, that is,
to the Points M, [Greek: a], [Greek: g], [Greek: e], [Greek: e], [Greek:
i], [Greek: l], G, may without any sensible Error be accounted
proportional to the Differences of the Sines of Refraction of those Rays
having one common Sine of Incidence, and therefore since the common Sine
of Incidence of the most and least refrangible Rays out of Glass into
Air was (by a Method described above) found in proportion to their Sines
of Refraction, as 50 to 77 and 78, divide the Difference between the
Sines of Refraction 77 and 78, as the Line GM is divided by those
Intervals, and you will have 77, 77-1/8, 77-1/5, 77-1/3, 77-1/2, 77-2/3,
77-7/9, 78, the Sines of Refraction of those Rays out of Glass into Air,
their common Sine of Incidence being 50. So then the Sines of the
Incidences of all the red-making Rays out of Glass into Air, were to the
Sines of their Refractions, not greater than 50 to 77, nor less than 50
to 77-1/8, but they varied from one another according to all
intermediate Proportions. And the Sines of the Incidences of the
green-making Rays were to the Sines of their Refractions in all
Proportions from that of 50 to 77-1/3, unto that of 50 to 77-1/2. And
by the like Limits above-mentioned were the Refractions of the Rays
belonging to the rest of the Colours defined, the Sines of the
red-making Rays extending from 77 to 77-1/8, those of the orange-making
from 77-1/8 to 77-1/5, those of the yellow-making from 77-1/5 to 77-1/3,
those of the green-making from 77-1/3 to 77-1/2, those of the
blue-making from 77-1/2 to 77-2/3, those of the indigo-making from
77-2/3 to 77-7/9, and those of the violet from 77-7/9, to 78.
72