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(126 [[left margin]] Fig. [[blank space]] is a draught of an Engine to turn screws. Gents Magaz. for Feb[[superscript]] y [[/superscript]]. 1753. p. 77. N.B. If the piece X moves or slides upon the slider GHIK, at the bottom by means of a screw like the poppets of a Watchmaker's Lathe, then may any length [[strikeout]] between [[/strikeout]] be turned between P and E, provided GHIK be of a sufficient length. Moreover, if R, O, and E be short, especially in a small machine, I see no necessity for more of the poppets A, and D than up to the slider GHIK; if they may not be entirely remove with the poppet C. [[/left margin]] Let ABCD represent four poppets fixed on their frame: suppose in three, [[underline]] viz. [[/underline]] ACD there are fixed brass Sockets for the centers RM and EF, and the hollow mandril PO to move in; the center RM is fixed to the upright bar I, and the center EF moves by a screw in the upright bar X, and may be turned by the winch F; these bars are fixed to a sliding piece GHIK, which passes thro' the poppets, and moves on brass rolls the mandril PO, which passes thro' the poppet B, and turns in the center M, has a screw cut in it at S, which runs in a box fixed in the poppet B. As the string wrapped round the mandril at N, by means of the foot, causes the mandril to turn round, it is plain, it must move forwards towards the center E; but the wood or iron, to be turned being fixed between the the mandril P and the center at E, the wood, or iron, must move in that direction, and the center E be pushed back [[strikethrough]] wards [[/strikethrough]] in its socket, and as the center E recedes, the center M must follow. When the foot is taken off then the mandril and wood, or iron, moves back again, and so on alternately. Let then a tool be applied on [[strikethrough]] the [[/strikethrough]] ^[[insertion]] a [[/insertion]] rest to the wood, or iron, to be turned; it's evident it must be turned in the form of a screw: when you have turned it to your mind in one place, it is only moving the tool forward on the rest to another part: So by this method a screw maybe turned of any length, and by alteration of the mandril, of any size. Yours &c. I.B.N. [[left margin]] FOCUS of Glass found by a Theorem, which corrects an error among Opticians. [[/left margin]] There is an error, which I believe all your opticians in town fall into, with regard to the focus of glasses; I have been disappointed several times, the glasses I wrote for always proving a shorter focus than what I ordered; the reason of which I take to be this: They do not attend to the radius of convexity, or concavity of the tool they grind on, but depend on receiving the image of objects in the street before the shop, or the windows, &c. of the room on a piece of white paper, the distance of which from the glass they call the focus, or radius of convexity, but the radius of convexity is found by this equation [[numerator]] df [[/numerator]] / [[denominator]] d+f [[/denominator]] = r, where f=distance of the image from the glass, d=distance of the object from the glass, and r= true focus; the nearer the object made use of, the more the difference of their focus from the truth. [[left margin]] Trajeclorium Lunare, a description & use of it, by its inventor [[/left margin]] Description of an instrument called the TRAJECTORIUM LUNARE, invented by [[underline]] James Ferguson [[/underline]] Limner in [[underline]] London [[/underline]], for delineating the path of the Earth and of the Moon; shewing that the line of the moon's motion in the heavens is concave to the sun in every part of her Orbit. In Fig [[blank space]] , AB represents a wooden bar about 84 inches long, to be turned by hand round the axis of the wheel CC, at A; the wheel being kept kept fixed by its spikes I, K, L, when softly pressed down on the floor of a room. The index D, fixt to the said bar, points
