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 differ in nothing but their thickness, the Diameters of the Rings are reciprocally in a subduplicate Proportion of the thicknesses of the Plates. And this shews sufficiently that the Rings depend on both the Surfaces of the Glass. They depend on the convex Surface, because they are more luminous when that Surface is quick-silver'd over than when it is without Quick-silver. They depend also upon the concave Surface, because without that Surface a Speculum makes them not. They depend on both Surfaces, and on the distances between them, because their bigness is varied by varying only that distance. And this dependence is of the same kind with that which the Colours of thin Plates have on the distance of the Surfaces of those Plates, because the bigness of the Rings, and their Proportion to one another, and the variation of their bigness arising from the variation of the thickness of the Glass, and the Orders of their Colours, is such as ought to result from the Propositions in the end of the third Part of this Book, derived from the Phænomena of the Colours of thin Plates set down in the first Part.
There are yet other Phænomena of these Rings of Colours, but such as follow from the same Propositions, and therefore confirm both the Truth of those Propositions, and the Analogy between these Rings and the Rings of Colours made by very thin Plates. I shall subjoin some of them.
Obs. 10. When the beam of the Sun's Light was reflected back from the Speculum not directly to the hole in the Window, but to a place a little distant from it, the common center of that Spot, and of all the Rings of Colours fell in the middle way between the beam of the incident Light, and the beam of the reflected Light, and by consequence in the center of the spherical concavity of the Speculum, whenever the Chart on which the Rings of Colours fell was placed at that center. And as the beam of reflected Light by inclining the Speculum receded more and more from the beam of incident Light and from the common center of the colour'd Rings between them, those Rings grew bigger and bigger, and so also did the white round Spot, and new Rings of Colours emerged successively out of their common center, and the white Spot became a white Ring encompassing them; and the incident and reflected beams of Light always fell upon the opposite parts of this white Ring, illuminating its Perimeter like two mock Suns in the opposite parts of an Iris. So then the Diameter of this Ring, measured from the middle of its Light on one side to the middle of its Light on the other side, was always equal to the distance between the middle of the incident beam of Light, and the middle of the reflected beam measured at the Chart on which the Rings appeared: And the Rays which form'd this Ring were reflected by the Speculum in Angles equal to their Angles of Incidence, and by consequence to their Angles of Refraction at their entrance into the Glass, but yet their Angles of Reflexion were not in the same Planes with their Angles of Incidence.
Obs. 11. The Colours of the new Rings were in a contrary order to those of the former, and arose after this manner. The white round Spot of Light in the middle of the Rings continued white to the center till the distance of the incident and reflected beams at the Chart was about 7/8 parts of an Inch, and then it began to grow dark in the middle. And when that distance was about 1-3/16 of an Inch, the white Spot was become a Ring encompassing a dark round Spot which in the middle inclined to violet and indigo. And the luminous Rings encompassing it were grown equal to those dark ones which in the four first Observations encompassed them, that is to say, the white Spot was grown a white Ring equal to the first of those dark Rings, and the first of those luminous Rings was now grown equal to the second of those dark ones, and the second of those luminous ones to the third of those dark ones, and so on. For the Diameters of the luminous Rings were now 1-3/16, 2-1/16, 2-2/3, 3-3/20, &c. Inches.
When the distance between the incident and reflected beams of Light became a little bigger, there emerged out of the middle of the dark Spot after the indigo a blue, and then out of that blue a pale green, and soon after a yellow and red. And when the Colour at the center was brightest, being between yellow and red, the bright Rings were grown equal to those Rings which in the four first Observations next encompassed them; that is to say, the white Spot in the middle of those Rings was now become a white Ring equal to the first of those bright Rings, and the first of those bright ones was now become equal to the second of those, and so on. For the Diameters of the white Ring, and of the other luminous Rings encompassing it, were now 1-11/16, 2-3/8, 2-11/12, 3-3/8, &c. or thereabouts.
When the distance of the two beams of Light at the Chart was a little more increased, there emerged out of the middle in order after the red, a purple, a blue, a green, a yellow, and a red inclining much to purple, and when the Colour was brightest being between yellow and red, the former indigo, blue, green, yellow and red, were become an Iris or Ring of Colours equal to the first of those luminous Rings which appeared in the four first Observations, and the white Ring which was now become the second of the luminous Rings was grown equal to the second of those, and the first of those which was now become the third Ring was become equal to the third of those, and so on. For their Diameters were 1-11/16, 2-3/8, 2-11/12, 3-3/8 Inches, the distance of the two beams of Light, and the Diameter of the white Ring being 2-3/8 Inches.