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
Diameters of the Rings made by the bright yellow. For this yellow makes
the brightest Part of the Rings of all Colours. If you desire the
Diameters of the Rings made by the Light of any other unmix'd Colour,
you may find them readily by putting them to the Diameters of the bright
yellow ones in a subduplicate Proportion of the Intervals of the Fits of
the Rays of those Colours when equally inclined to the refracting or
reflecting Surface which caused those Fits, that is, by putting the
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.
173