eight or nine Inches distance from the Glass, almost perpendicularly over it, and the Glass was 1/6 of an Inch thick, and thence it is easy to collect that the true Diameter of the Ring between the Glasses was greater than its measur'd Diameter above the Glasses in the Proportion of 80 to 79, or thereabouts, and by consequence equal to 16/79 parts of an Inch, and its true Semi-diameter equal to 8/79 parts. Now as the Diameter of the Sphere (182 Inches) is to the Semi-diameter of this fifth dark Ring (8/79 parts of an Inch) so is this Semi-diameter to the thickness of the Air at this fifth dark Ring; which is therefore 32/567931 or 100/1774784. Parts of an Inch; and the fifth Part thereof, viz. the 1/88739 Part of an Inch, is the Thickness of the Air at the first of these dark Rings.
The same Experiment I repeated with another double convex Object-glass ground on both sides to one and the same Sphere. Its Focus was distant from it 168-1/2 Inches, and therefore the Diameter of that Sphere was 184 Inches. This Glass being laid upon the same plain Glass, the Diameter of the fifth of the dark Rings, when the black Spot in their Center appear'd plainly without pressing the Glasses, was by the measure of the Compasses upon the upper Glass 121/600 Parts of an Inch, and by consequence between the Glasses it was 1222/6000: For the upper Glass was 1/8 of an Inch thick, and my Eye was distant from it 8 Inches. And a third proportional to half this from the Diameter of the Sphere is 5/88850 Parts of an Inch. This is therefore the Thickness of the Air at this Ring, and a fifth Part thereof, viz. the 1/88850th Part of an Inch is the Thickness thereof at the first of the Rings, as above.
I tried the same Thing, by laying these Object-glasses upon flat Pieces of a broken Looking-glass, and found the same Measures of the Rings: Which makes me rely upon them till they can be determin'd more accurately by Glasses ground to larger Spheres, though in such Glasses greater care must be taken of a true Plane.
These Dimensions were taken, when my Eye was placed almost perpendicularly over the Glasses, being about an Inch, or an Inch and a quarter, distant from the incident Rays, and eight Inches distant from the Glass; so that the Rays were inclined to the Glass in an Angle of about four Degrees. Whence by the following Observation you will understand, that had the Rays been perpendicular to the Glasses, the Thickness of the Air at these Rings would have been less in the Proportion of the Radius to the Secant of four Degrees, that is, of 10000 to 10024. Let the Thicknesses found be therefore diminish'd in this Proportion, and they will become 1/88952 and 1/89063, or (to use the nearest round Number) the 1/89000th Part of an Inch. This is the Thickness of the Air at the darkest Part of the first dark Ring made by perpendicular Rays; and half this Thickness multiplied by the Progression, 1, 3, 5, 7, 9, 11, &c. gives the Thicknesses of the Air at the most luminous Parts of all the brightest Rings, viz. 1/178000, 3/178000, 5/178000, 7/178000, &c. their arithmetical Means 2/178000, 4/178000, 6/178000, &c. being its Thicknesses at the darkest Parts of all the dark ones.
Obs. 7. The Rings were least, when my Eye was placed perpendicularly over the Glasses in the Axis of the Rings: And when I view'd them obliquely they became bigger, continually swelling as I removed my Eye farther from the Axis. And partly by measuring the Diameter of the same Circle at several Obliquities of my Eye, partly by other Means, as also by making use of the two Prisms for very great Obliquities, I found its Diameter, and consequently the Thickness of the Air at its Perimeter in all those Obliquities to be very nearly in the Proportions express'd in this Table.