,
that the middle of the Glass do always precisely answer to the Brim of this
_Ring_, seeing that the position of the Glass does always change a little
in respect of the _Ring_, in proportion as 'tis worn, and as it must be
pressed because of its inclination. He believes it also very hard, to give
to the _Axis_ or to the _Mandril_, which holds the Glass, that little {59}
_Inclination_, that would be necessary for great Glasses, and to make the
two _Mandrils_ to have one and the same _Plain_, as is necessary. And,
having done all this, he persuades himself, that it is exceedingly
difficult, if not impossible, for two contrary motions, where so many
pieces are, to rest for a long time steddy and firm, as is requisite for
the not swarving from it a hair's thickness, since less than that can
change all.

He goes on, and, seeing that this _Inventor_ speaks of Glasses of a
thousand, & ten thousand foot, which he supposed not impossible to be made
by this _Engine_, discourses of what is necessary for the making Glasses of
such bignesses; which he believes this _Inventor_ may perhaps not have
thought of. Wherefore he affirms, that if the _Table_, made by himself for
the _Apertures_ of Glasses (which is that, that is above delivered) be
continued unto a thousand feet, by taking always the _Subduplicate
proportion_ of _Lengths_, it will be found, that for pretty good ones, the
_Aperture_ must be of 15. Inches; for good ones, more than 18. and for such
as are excellent, more than 21. Inches: whence it may be judged, what piece
of Glass, and of what thickness it must be, to endure the working. But he
proceeds to speak of the _Inclination_, which the _Mandril_ must have upon
the _Plain_ of the _Ring_, when the _Ring_ should have 10. or 12 Inches;
and finds, that it would make but 6 or 7. minutes of inclination, and that
a Glass would have less _Convexity_, and consequently, less difference from
a Glass perfectly plain, than the 7. or 8. part of a Line. And then he
leaveth it to be judged, whether a Glass of such a Length being found, we
ought to hope, that a _Turn_ can be firm enough to keep such a piece of
Glass in the same Inclination, so that a _Mandril_ do not recede some
Minutes from it: and, though even the Glass could be fastned perfectly
perpendicular to the _Mandril_, that those two _Mandrils_ could be put in
one and the same Plain, & that that little Inclination, which is requisite,
could be given, and the _Mandril_ be cont