glass of a fourteen Foot Telescope, made by
an Artificer at _London_, I once mended considerably, by grinding it on
Pitch with Putty, and leaning very easily on it in the grinding, lest
the Putty should scratch it. Whether this way may not do well enough for
polishing these reflecting Glasses, I have not yet tried. But he that
shall try either this or any other way of polishing which he may think
better, may do well to make his Glasses ready for polishing, by grinding
them without that Violence, wherewith our _London_ Workmen press their
Glasses in grinding. For by such violent pressure, Glasses are apt to
bend a little in the grinding, and such bending will certainly spoil
their Figure. To recommend therefore the consideration of these
reflecting Glasses to such Artists as are curious in figuring Glasses, I
shall describe this optical Instrument in the following Proposition.

_PROP._ VIII. PROB. II.

_To shorten Telescopes._

Let ABCD [in _Fig._ 29.] represent a Glass spherically concave on the
foreside AB, and as much convex on the backside CD, so that it be every
where of an equal thickness. Let it not be thicker on one side than on
the other, lest it make Objects appear colour'd and indistinct, and let
it be very truly wrought and quick-silver'd over on the backside; and
set in the Tube VXYZ which must be very black within. Let EFG represent
a Prism of Glass or Crystal placed near the other end of the Tube, in
the middle of it, by means of a handle of Brass or Iron FGK, to the end
of which made flat it is cemented. Let this Prism be rectangular at E,
and let the other two Angles at F and G be accurately equal to each
other, and by consequence equal to half right ones, and let the plane
sides FE and GE be square, and by consequence the third side FG a
rectangular Parallelogram, whose length is to its breadth in a
subduplicate proportion of two to one. Let it be so placed in the Tube,
that the Axis of the Speculum may pass through the middle of the square
side EF perpendicularly and by consequence through the middle of the
side FG at an Angle of 45 Degrees, and let the side EF be turned towards
the Speculum, and the distance of this Prism from the Speculum be such
that the Rays of the Light PQ, RS, &c. which are incident upon the
Speculum in Lines parallel to the Axis thereof, may enter the Prism at
the side EF, and be reflected by the side FG, and thence go out of it
through the side GE, to the Point T, which mus