transmits the same bright Light of the second Ring; if tripled, it
transmits that of the third, and so on; the bright yellow Light in all
these cases being in its Fits of Transmission. And therefore if its
thickness be multiplied 34386 times, so as to become 1/4 of an Inch, it
transmits the same bright Light of the 34386th Ring. Suppose this be the
bright yellow Light transmitted perpendicularly from the reflecting
convex side of the Glass through the concave side to the white Spot in
the center of the Rings of Colours on the Chart: And by a Rule in the
7th and 19th Observations in the first Part of this Book, and by the
15th and 20th Propositions of the third Part of this Book, if the Rays
be made oblique to the Glass, the thickness of the Glass requisite to
transmit the same bright Light of the same Ring in any obliquity, is to
this thickness of 1/4 of an Inch, as the Secant of a certain Angle to
the Radius, the Sine of which Angle is the first of an hundred and six
arithmetical Means between the Sines of Incidence and Refraction,
counted from the Sine of Incidence when the Refraction is made out of
any plated Body into any Medium encompassing it; that is, in this case,
out of Glass into Air. Now if the thickness of the Glass be increased by
degrees, so as to bear to its first thickness, (_viz._ that of a quarter
of an Inch,) the Proportions which 34386 (the number of Fits of the
perpendicular Rays in going through the Glass towards the white Spot in
the center of the Rings,) hath to 34385, 34384, 34383, and 34382, (the
numbers of the Fits of the oblique Rays in going through the Glass
towards the first, second, third, and fourth Rings of Colours,) and if
the first thickness be divided into 100000000 equal parts, the increased
thicknesses will be 100002908, 100005816, 100008725, and 100011633, and
the Angles of which these thicknesses are Secants will be 26 13 , 37
5 , 45 6 , and 52 26 , the Radius being 100000000; and the Sines of
these Angles are 762, 1079, 1321, and 1525, and the proportional Sines
of Refraction 1172, 1659, 2031, and 2345, the Radius being 100000. For
since the Sines of Incidence out of Glass into Air are to the Sines of
Refraction as 11 to 17, and to the above-mentioned Secants as 11 to the
first of 106 arithmetical Means between 11 and 17, that is, as 11 to
11-6/106, those Secants will be to the Sines of Refraction as 11-6/106,
to 17, and by this Analogy will give these Sines. So then, if the
obliquities of the Rays to the concave Surface of the Glass be such that
the Sines of their Refraction in passing out of the Glass through that
Surface into the Air be 1172, 1659, 2031, 2345, the bright Light of the
34386th Ring shall emerge at the thicknesses of the Glass, which are to
1/4 of an Inch as 34386 to 34385, 34384, 34383, 34382, respectively. And
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