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 desirable Angle with the Ruler AB. The bottom of this Pipe V was stop'd with a small piece of exactly plain Glass, which was plac'd exactly perpendicular to the Line of direction, or Axis of the Ruler EF. The Pins also TT were drill'd with small holes through the Axis, and through those holes was stretcht and fastned a small Wire. There was likewise a small Pipe of Tin loosly put on upon the end of V, and reaching down to the sight G; the use of which was only to keep any false Rayes of light from passing through the bottom of V, and only admitting such to pass as pierced through the sight G: All things being placed together in the manner describ'd in the Figure; that is, the Ruler AB being fixt perpendicular, I fill'd the Box CC with Water, or any other Liquor, whose refraction I intended to try, till the Wire passing through the middle of it were just covered: then I moved and fixt the Ruler FE at any assignable Angle, and placed the flame of a Candle just against the sight G; and looking through the sight I, I moved the Ruler RS to and fro, till I perceived the light passing through G to be covered, as 'twere, or divided by the dark Wire passing through PP: then turning the Screw in K, I fixt it in that posture: And through the hole S, I observed what degree and part of it was cut by the cross threads in S. And this gave me the Angle of Inclination, APS answering to the Angle of Refraction BPE: for the surface of the Liquor in the Box will be alwayes horizontal, and consequently AB will be a perpendicular to it; the Angle therefore APS will measure, or be the Angle of Inclination in the Liquor; next EPB must be the Angle of Refraction, for the Ray that passes through the sight G, passes also perpendicularly through the Glass Diaphragme at F, and consequently also perpendicularly through the lower surface of the Liquor contiguous to the Glass, and therefore suffers no refraction till it meet with the horizontal surface of the Liquor in CC, which is determined by the two Angles.
By means of this Instrument I can with little trouble, and a very small quantity of any Liquor, examine, most accurately, the refraction of it not only for one inclination, but for all; and thereby am inabled to make very accurate Tables; several of which I have also experimentally made, and find, that Oyl of Turpentine has a much greater Refraction then Spirit of Wine, though it be lighter; and that Spirit of Wine has a greater Refraction then Water, though it be lighter also; but that salt Water also has a greater Refraction then fresh, though it be heavier: but Allum water has a less refraction then common Water, though heavier also. So that it seems, as to the refraction made in a Liquor, the specifick gravity is of no efficacy. By this I have also found that look what proportion the Sine of the Angle of one Inclination has to the Sine of the Angle of Refraction, correspondent to it, the same proportion have all the Sines of other Inclinations to the Sines of their appropriate Refractions.
My way for measuring how much a Glass magnifies an Object, plac'd at a convenient distance from my eye, is this. Having rectifi'd the Microscope, to see the desir'd Object through it very distinctly, at the same time that I look upon the Object through the Glass with one eye, I look upon other Objects at the same distance with my other bare eye; by which means I am able, by the help of a Ruler divided into inches and small parts, and laid on the Pedestal of the Microscope, to cast, as it were, the magnifi'd appearance of the Object upon the Ruler, and thereby exactly to measure the Diameter it appears of through the Glass, which being compar'd with the Diameter it appears of to the naked eye, will easily afford the quantity of its magnifying.
Schem. 1. Fig. 3.
The