ed. And first to
shew how the Colours in the fourth and eighteenth Observations are
produced, let there be taken in any Right Line from the Point Y, [in
_Fig._ 6.] the Lengths YA, YB, YC, YD, YE, YF, YG, YH, in proportion to
one another, as the Cube-Roots of the Squares of the Numbers, 1/2, 9/16,
3/5, 2/3, 3/4, 5/6, 8/9, 1, whereby the Lengths of a Musical Chord to
sound all the Notes in an eighth are represented; that is, in the
Proportion of the Numbers 6300, 6814, 7114, 7631, 8255, 8855, 9243,
10000. And at the Points A, B, C, D, E, F, G, H, let Perpendiculars
A[Greek: a], B[Greek: b], &c. be erected, by whose Intervals the Extent
of the several Colours set underneath against them, is to be
represented. Then divide the Line _A[Greek: a]_ in such Proportion as
the Numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, &c. set at the Points of
Division denote. And through those Divisions from Y draw Lines 1I, 2K,
3L, 5M, 6N, 7O, &c.

Now, if A2 be supposed to represent the Thickness of any thin
transparent Body, at which the outmost Violet is most copiously
reflected in the first Ring, or Series of Colours, then by the 13th
Observation, HK will represent its Thickness, at which the utmost Red is
most copiously reflected in the same Series. Also by the 5th and 16th
Observations, A6 and HN will denote the Thicknesses at which those
extreme Colours are most copiously reflected in the second Series, and
A10 and HQ the Thicknesses at which they are most copiously reflected in
the third Series, and so on. And the Thickness at which any of the
intermediate Colours are reflected most copiously, will, according to
the 14th Observation, be defined by the distance of the Line AH from the
intermediate parts of the Lines 2K, 6N, 10Q, &c. against which the Names
of those Colours are written below.

[Illustration: FIG. 6.]

But farther, to define the Latitude of these Colours in each Ring or
Series, let A1 design the least thickness, and A3 the greatest
thickness, at which the extreme violet in the first Series is reflected,
and let HI, and HL, design the like limits for the extreme red, and let
the intermediate Colours be limited by the intermediate parts of the
Lines 1I, and 3L, against which the Names of those Colours are written,
and so on: But yet with this caution, that the Reflexions be supposed
strongest at the intermediate Spaces, 2K, 6N, 10Q, &c. and from thence
to decrease gradually towards these limits, 1I, 3L, 5M, 7O, &c. on
either si