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
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, according as the glass wears, the same is possible to be don, as with the same Sand wrought finer by working in the Ordinary way.
The giving the Inclination to the Mandrils, is not at all difficult; though perhaps to determine the length exactly which the Glass so made shall draw, is not so easie: But 'tis no matter, what length the Glass be off, so it be made good, whether 60 or 80 foot, or the like. Nor is it so very difficult, to lay them both in the same Plain. And to keep them steddy, when once fix'd, is most easie.
As to the Calculation of the propriety of a Glass of a thousand foot, perhaps for that particular Length, I had not, nor have as yet calculated, that the Convexity of one of eighteen inches broad, will not be above a seventh part of a Line. But it does not thence follow, that I had not considered the difficulties, that would be in making of it. For, I must tell him, that I can make a Plano convex Glass though its convexity be a smaler sphere than is usual for such a length to be an Object-Glass of about 150 foot in Length, nay of 300 foot, and either longer or shorter, without at all altering the convexity. So that, if he will by any Contrivance he hath, give me a Plano-convex Glass of 20, or 40 foot Diameter, without Veins, and truly wrought of that Figure, I will presently make a Telescope with it, that with a single Ey-glass shall draw a thousand foot: Which Invention, I shall shortly discover, there being, I think, nothing more easie and certain. And if a Plano-convex Glass can be made of any Sphere between twenty and fourty foot radius, so as that both the Convex and Plain side of the Glass be exactly polish'd of a true Figure, I will shortly shew, how therewith may be made a Telescope of any Length, supposing the Glass free from all kind of Veins, or inequality of Refraction.
As for the sliding of the Glass upon the Cement, I see no reason at all for it, at least in the Cement, I make use of, having never observed any such accident in hard Cement.
And for the Bearing of the Ring against one side of the Glass only at a time, I cannot see, why that should produce any inequality, since all the sides of the Glass have successively the same pressure.
His ratiocination concerning a Glass of 300 foot, is much the same with the former, about the difficulty of working a true surface of a convenient figure; which how considerable both that and his Conclusion thereupon (videl. That we are not to expect Glasses of above 300 or 400 foot long at most, and that neither Matter nor Art will go so far) is, may be judged from what I have newly told you of making any Object-Glass of any Length.
And for his good wishes, that those, who promise to make him see Plants or Animals in the Moon (of which I know not any, that has done so, though perhaps there may be some, notwithstanding his Objections, that do not yet think it impossible to be done) had considered, what a Man is able to see with his bare Eye at 60 Leagues distance: I cannot but return him my wishes, that he would consider the difference between seeing a thing through the Gross and Vaporous Air neer the Earth, and through the Air over our heads: Which, if he observe the Moon in the Horizon, and neer the Zenith with a Telescope, he will experimentally find; and, having done so, he will perhaps not be so dissident in this matter.