Charges ought to be as the square Roots of their lengths; and this
answers to Experience, as is well known. For Instance, a Telescope of 64
Feet in length, with an Aperture of 2-2/3 Inches, magnifies about 120
times, with as much distinctness as one of a Foot in length, with 1/3 of
an Inch aperture, magnifies 15 times.
[Illustration: FIG. 28.]
Now were it not for this different Refrangibility of Rays, Telescopes
might be brought to a greater perfection than we have yet describ'd, by
composing the Object-glass of two Glasses with Water between them. Let
ADFC [in _Fig._ 28.] represent the Object-glass composed of two Glasses
ABED and BEFC, alike convex on the outsides AGD and CHF, and alike
concave on the insides BME, BNE, with Water in the concavity BMEN. Let
the Sine of Incidence out of Glass into Air be as I to R, and out of
Water into Air, as K to R, and by consequence out of Glass into Water,
as I to K: and let the Diameter of the Sphere to which the convex sides
AGD and CHF are ground be D, and the Diameter of the Sphere to which the
concave sides BME and BNE, are ground be to D, as the Cube Root of
KK--KI to the Cube Root of RK--RI: and the Refractions on the concave
sides of the Glasses, will very much correct the Errors of the
Refractions on the convex sides, so far as they arise from the
sphericalness of the Figure. And by this means might Telescopes be
brought to sufficient perfection, were it not for the different
Refrangibility of several sorts of Rays. But by reason of this different
Refrangibility, I do not yet see any other means of improving Telescopes
by Refractions alone, than that of increasing their lengths, for which
end the late Contrivance of _Hugenius_ seems well accommodated. For very
long Tubes are cumbersome, and scarce to be readily managed, and by
reason of their length are very apt to bend, and shake by bending, so as
to cause a continual trembling in the Objects, whereby it becomes
difficult to see them distinctly: whereas by his Contrivance the Glasses
are readily manageable, and the Object-glass being fix'd upon a strong
upright Pole becomes more steady.
Seeing therefore the Improvement of Telescopes of given lengths by
Refractions is desperate; I contrived heretofore a Perspective by
Reflexion, using instead of an Object-glass a concave Metal. The
diameter of the Sphere to which the Metal was ground concave was about
25 _English_ Inches, and by consequence the length of the Instrument
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