that was otherwise; as he might presently satisfie himself by a way
I could shew him (if he did not know it) whereby the difference of the
thickness of the sides might be found to the hundreth part of a Line.

As to the exceeding exactness of the _Figure_ of Long _Object-Glasses_,
'tis not doubted, but that it is a matter difficult enough to be attained
any way: but yet, I think, much easier by _Engine_, than by _Hand_; and of
all _Engines_, I conceive, none more plain and simple, than that of a
_Mandril_. And for making _spherical Glasses_ by an _Engine_, I am apt to
think, there hardly can be any way more plain, and more exact, than that
which I have described; wherein there is no other motion, than that of two
such _Mandrils_, which may be made of sufficient strength, length, and
exactness, to perform abundantly much more, than I can believe possible to
be done otherwise than by chance, by a man's hands or strength unassisted
by an _Engine_, the motion and strength being much more certain and
regular. I know very well, that in making a 60. foot Glass by the strength
of the hand, in the common way, not one of ten that are wrought, will
happen to be good, as I have been assured by Mr. _Reeves_; who, I am apt to
think, was the first that made any good of that length. For the _Figure_ of
the _Tool_ in that way is presently vitiated by the working of the Glass,
and without much _gaging_ will not do any thing considerable. Besides, the
strength of a man's hands, applied to it for the working and polishing of
it, is very unequal, and the motions made, are very irregular; but in the
way, I have ventured to propose, by _Mandrils_, the longer the _Glass_ and
_Tool_ are wrought together, the more exact they seem to be and if all
things be ordered, as they should be, the very polishing of the Glass, does
seem most of all rectifie the _Figure_.

As to what he objects, that the Tool does only touch the Glass in a
_Mathematical Circle_; that is true, perhaps, at first, but before the
Glass is wrought down to its true _Figure_, the _Edge_ of the _Tool_ {67}
will be worn or grownd away, so as that a Ring of an inch broad may be made
to touch the _Spherical Surface_ of the Glass; nay, if it be necessary
(without much trouble, especially in the grinding of longer Glasses) the
whole _Concave Surface_ of the _Tool_ may be made to touch a Glass.
Besides, that as to the keeping a quantity of the same sand and Powders of
several finesses, a