long, another for all between ten and an hundred, a fourth for all between a hundred and a thousand foot long; and if Curiosity shall ever proceed so far, one for all lengths between a thousand and ten thousand foot long; for indeed the principle is such, that supposing the Mandrils well made, and of a good length, and supposing great care be used in working and polishing them, I see no reason, but that a Glass of a thousand, nay of ten thousand foot long, may be as well made as one of ten; for the reason is the same, supposing the Mandrils and Tools be made sufficiently strong, so that they cannot bend; and supposing the Glass, out of which they are wrought, be capable of so great a regularity in its parts as to refraction:  this hollow Cylinder K is to contain the Sand, and by being drove round very quick to and fro by means of a small Wheel, which may be mov’d with ones foot, serves to grind the Glass:  The other Mandril is shap’d like this, but it has an even neck instead of a taper one, and runs in a Collar, that by the help of a Screw and a joynt made like M in the Figure, it can be still adjustned to the wearing or wasting neck:  into the end of this Mandril is screwed a Chock N on which with Cement or Glew is fastned the piece of Glass Q that is to be form’d; the middle of which Glass is to be plac’d just on the edge of the Ring and the Lath OP is to be set and fixt (by means of certain pieces and screws the manner whereof will be sufficiently evidenc’d by the Figure) in such an Angle as is requisite to the forming of such a Sphere as the Glass is design’d to be of; the geometrical ground of which being sufficiently plain, though not heeded before, I shall, for brevities sake, pass over.  This last Mandril to be made (by means of the former, or some other Wheel) to run round very swift also, by which two cross motions the Glass cannot chuse (if care be us’d) but be wrought into a most exactly spherical Surface.

But because we are certain, from the Laws of refraction (which I I have experimentally found to be so, by an Instrument I shall presently describe) that the lines of the angles of Incidence are proportionate to the lines of the angles of Refraction, therefore if Glasses could be made of those kind of Figures, or some other, such as the most incomparable Des Cartes has invented, and demonstrated in his Philosophical and Mathematical Works, we might hope for a much greater perfection of Opticks then can be rationally expected from spherical ones; for though, caeteris paribus, we find, that the larger the Telescope Object Glasses are, and the shorter those of the Microscope, the better they magnify, yet both of them, beside such determinate dimensions, are by certain inconveniences rendred unuseful; for it will be exceeding difficult to make and manage a Tube above an hundred foot long, and it will be as difficult to inlighten an Object less then an hundred part of an inch distant from the Object Glass.