the same Colour, and degree of Colour from
one End of this Line to the other. I delineated therefore in a Paper the
Perimeter of the Spectrum FAP GMT, and in trying the third Experiment of
the first Part of this Book, I held the Paper so that the Spectrum might
fall upon this delineated Figure, and agree with it exactly, whilst an
Assistant, whose Eyes for distinguishing Colours were more critical than
mine, did by Right Lines [Greek: ab, gd, ez,] &c. drawn cross the
Spectrum, note the Confines of the Colours, that is of the red M[Greek:
ab]F, of the orange [Greek: agdb], of the yellow [Greek: gezd], of the
green [Greek: eethz], of the blue [Greek: eikth], of the indico [Greek:
ilmk], and of the violet [Greek: l]GA[Greek: m]. And this Operation
being divers times repeated both in the same, and in several Papers, I
found that the Observations agreed well enough with one another, and
that the Rectilinear Sides MG and FA were by the said cross Lines
divided after the manner of a Musical Chord. Let GM be produced to X,
that MX may be equal to GM, and conceive GX, [Greek: l]X, [Greek: i]X,
[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 Re