he
Diameters of the Rings made by the Rays in the Extremities and Limits of
the seven Colours, red, orange, yellow, green, blue, indigo, violet,
proportional to the Cube-roots of the Numbers, 1, 8/9, 5/6, 3/4, 2/3,
3/5, 9/16, 1/2, which express the Lengths of a Monochord sounding the
Notes in an Eighth: For by this means the Diameters of the Rings of
these Colours will be found pretty nearly in the same Proportion to one
another, which they ought to have by the fifth of these Observations.

And thus I satisfy'd my self, that these Rings were of the same kind and
Original with those of thin Plates, and by consequence that the Fits or
alternate Dispositions of the Rays to be reflected and transmitted are
propagated to great distances from every reflecting and refracting
Surface. But yet to put the matter out of doubt, I added the following
Observation.

_Obs._ 9. If these Rings thus depend on the thickness of the Plate of
Glass, their Diameters at equal distances from several Speculums made of
such concavo-convex Plates of Glass as are ground on the same Sphere,
ought to be reciprocally in a subduplicate Proportion of the thicknesses
of the Plates of Glass. And if this Proportion be found true by
experience it will amount to a demonstration that these Rings (like
those formed in thin Plates) do depend on the thickness of the Glass. I
procured therefore another concavo-convex Plate of Glass ground on both
sides to the same Sphere with the former Plate. Its thickness was 5/62
Parts of an Inch; and the Diameters of the three first bright Rings
measured between the brightest Parts of their Orbits at the distance of
six Feet from the Glass were 3.4-1/6.5-1/8. Inches. Now, the thickness
of the other Glass being 1/4 of an Inch was to the thickness of this
Glass as 1/4 to 5/62, that is as 31 to 10, or 310000000 to 100000000,
and the Roots of these Numbers are 17607 and 10000, and in the
Proportion of the first of these Roots to the second are the Diameters
of the bright Rings made in this Observation by the thinner Glass,
3.4-1/6.5-1/8, to the Diameters of the same Rings made in the third of
these Observations by the thicker Glass 1-11/16, 2-3/8. 2-11/12, that
is, the Diameters of the Rings are reciprocally in a subduplicate
Proportion of the thicknesses of the Plates of Glass.

So then in Plates of Glass which are alike concave on one side, and
alike convex on the other side, and alike quick-silver'd on the convex
sides, and