for, by that means, the longer the Glass be, the bigger aperture will it bear, if the Glasses be of an equal goodness in their kind. Therefore a six will indure a much larger Aperture then a three foot Glass, and a sixty foot Glass will proportionably bear a greater Aperture then a thirty, and will as much excel it also as a six foot does a three foot, as I have experimentally observ'd in one of that length made by Mr. Richard Reives here at London, which will bear an Aperture above three inches over, and yet make the Object proportionably big and distinct; whereas there are very few thirty foot Glasses that will indure an Aperture of more then two inches over. So that for Telescopes, supposing we had a very ready way of making their Object Glasses of exactly spherical Surfaces, we might, by increasing the length of the Glass, magnifie the Object to any assignable bigness. And for performing both these, I cannot imagine any way more easie, and more exact, then by this following Engine, by means of which, any Glasses, of what length soever, may be speedily made. It seems the most easie, because with one and the same Tool may be with care ground an Object Glass, of any length or breadth requisite, and that with very little or no trouble in fitting the Engine, and without much skill in the Grinder. It seems to be the most exact, for to the very last stroke the Glass does regulate and rectifie the Tool to its exact Figure; and the longer or more the Tool and Glass are wrought together, the more exact will both of them be of the desir'd Figure. Further, the motions of the Glass and Tool do so cross each other, that there is not one point of eithers Surface, but has thousands of cross motions thwarting it, so that there can be no kind of Rings or Gutters made either in the Tool or Glass.
The contrivance of the Engine is, only to make the ends of two large Mandrils so to move, that the Centers of them may be at any convenient distance asunder, and that the Axis of the Mandrils lying both in the same plain produc'd, may meet each other in any assignable Angle; both which requisites may be very well Schem. 1. Fig. 3. perform'd by the Engine describ'd in the third Figure of the first Scheme: where AB signifies the Beam of a Lath fixt perpendicularly or Horizontally, CD the two Poppet heads, fixt at about two foot distance, EF an Iron Mandril, whose tapering neck F runs in an adapted tapering brass Collar; the other end E runs on the point of a Screw G; in a convenient place of this is fastned H a pully Wheel, and into the end of it, that comes through the Poppet head C, is screwed a Ring of a hollow Cylinder K, or some other conveniently shap'd Tool, of what wideness shall be thought most proper for the cize of Glasses, about which it is to be imploy'd: As, for Object glasses, between twelve foot and an hundred foot long, the Ring may be about six inches over, or indeed somewhat more for those longer Glasses. It would be convenient also and not very chargeable, to have four or five several Tools; as one for all Glasses between an inch and a foot, one for all Glasses between a foot and ten foot 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, cæteris 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.
I have not as yet made any attempts of that kind, though I know two or three wayes, which, as far as I have yet considered, seem very probable, and may invite me to make a tryal as soon as I have an opportunity, of which I may hereafter perhaps acquaint the world. In the Interim, I shall describe the Instrument I even now mention'd, by which the refraction of all kinds of Liquors may be most exactly measur'd, thereby to give the curious an opportunity of making what further tryals of that kind they shall think requisite to any of their intended tryals; and to let them see that the laws of Refraction are not only notional.
Schem. 1. Fig. 2.
The Instrument consisted of five Rulers, or long pieces placed together, after the manner exprest in the second Figure of the first Scheme, where AB denotes a straight piece of wood about six foot and two inches long, about three inches over, and an inch and half thick, on the back side of which was hung a small plummet by a line stretcht from top to bottom, by which this piece was set exactly upright, and so very firmly fixt; in the middle of this was made a hole or center, into which one end of a hollow cylindrical brass Box CC, fashion'd as I shall by and by describe, was plac'd, and could very easily and truly be mov'd to and fro; the other end of this Box being put into, and moving in, a hole made in a small arm DD; into this box was fastned the long Ruler EF, about three foot and three or four inches long, and at three foot from the above mention'd Centers PP was a hole E, cut through, and cross'd with two small threads, and at the end of it was fixt a small sight G, and on the back side of it was fixt a small Arm H, with a Screw to fix it in any place on the Ruler LM; this Ruler LM was mov'd on the Center B (which was exactly three foot distance from the middle Center P) and a line drawn through the middle of it LM, was divided by a Line of cords into some sixty degrees, and each degree was subdivided into minutes, so that putting the cross of the threads in E upon any part of this divided line, I presently knew what Angle the two Rules AB and EF made with each other, and by turning the Screw in H, I could fix them in any position. The other Ruler also RS was made much after the same manner, only it was not fixt to the hollow cylindrical Box, but, by means of two small brass Armes or Ears, it mov'd on the Centers of it; this also, by means of the cross threads in the hole S, and by a Screw in K, could be fastned on any division of another line of cords of the same radius drawn on NO. And so by that means, the Angle made by the two Rulers, AB and RS, was also known. The Brass box CC in the middle was shap'd very much like the Figure X, that is, it was a cylindrical Box stopp'd close at either end, off of which a part both of the sides and bottomes was cut out, so that the Box, when the Pipe and that was joyned to it, would contain the Water when fill'd half full, and would likewise, without running over, indure to be inclin'd to an Angle, equal to that of the greatest refraction of Water, and no more, without running over. The Ruler EF was fixt very fast to the Pipe V, so that the Pipe V directed the length of the Ruler EF, and the Box and Ruler were mov'd on the Pin TT, so as to make any
