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 therefore, if the thickness in all these Cases be 1/4 of an Inch (as it is in the Glass of which the Speculum was made) the bright Light of the 34385th Ring shall emerge where the Sine of Refraction is 1172, and that of the 34384th, 34383th, and 34382th Ring where the Sine is 1659, 2031, and 2345 respectively. And in these Angles of Refraction the Light of these Rings shall be propagated from the Speculum to the Chart, and there paint Rings about the white central round Spot of Light which we said was the Light of the 34386th Ring. And the Semidiameters of these Rings shall subtend the Angles of Refraction made at the Concave-Surface of the Speculum, and by consequence their Diameters shall be to the distance of the Chart from the Speculum as those Sines of Refraction doubled are to the Radius, that is, as 1172, 1659, 2031, and 2345, doubled are to 100000. And therefore, if the distance of the Chart from the Concave-Surface of the Speculum be six Feet (as it was in the third of these Observations) the Diameters of the Rings of this bright yellow Light upon the Chart shall be 1'688, 2'389, 2'925, 3'375 Inches: For these Diameters are to six Feet, as the above-mention'd Sines doubled are to the Radius. Now, these Diameters of the bright yellow Rings, thus found by Computation are the very same with those found in the third of these Observations by measuring them, _viz._ with 1-11/16, 2-3/8, 2-11/12, and 3-3/8 Inches, and therefore the Theory of deriving these Rings from the thickness of the Plate of Glass of which the Speculum was made, and from the Obliquity of the emerging Rays agrees with the Observation. In this Computation I have equalled the Diameters of the bright Rings made by Light of all Colours, to the