<cb/> valve C, and prevents the return of the water downwards, which opens the valve D, by which the water ascends above it. And thus, by repeating the strokes of the Pump-rod handle, the valves alternately open and shut, and the water is drawn up at every stroke, and runs out at the nozle or spout near the top.

<hi rend="italics">The Lifting</hi> <hi rend="smallcaps">Pump</hi> differs from the sucking Pump only in the disposition of its valves and the form of its piston frame. This kind of Pump is represented in fig. 2, pl. 23; where the lower valve D is moveable, being worked up and down with the Pump rod, which lifts the water up, and so opens the upper valve C, which is fixed, and permits the water to issue through it, and run out at top. Then as the piston D descends, the weight of the water above C shuts that valve C, and so prevents its return, till that valve be opened again by another lift of the piston D. And so alternately.

<hi rend="italics">The Forcing</hi> <hi rend="smallcaps">Pump</hi> raises the water through the sucker, or lower valve C (fig. 3, pl. 23), in the same manner as the sucking Pump; but as the piston or plunger D has no valve in it, the water cannot get above it when this is pushed down again; instead of which, a side pipe is inserted between C and D, having a fixed valve at E opening upwards, through which the water is forced out of the Pump by pushing down the plunger D.

<hi rend="italics">Observations on Pumps.</hi>—The force required to work a Pump, is equal to the weight of water raised at each stroke, or equal to the weight of water filling the cavity of the pipe, and its height equal to the length of the stroke made by the piston. Hence if <hi rend="italics">d</hi> denote the diameter of the pipe, and <hi rend="italics">l</hi> the length of the stroke, both in inches; then is .7854<hi rend="italics">d</hi><hi rend="sup">2</hi><hi rend="italics">l</hi> the content of the water raised at a stroke, in inches, or .0028<hi rend="italics">d</hi><hi rend="sup">2</hi><hi rend="italics">l</hi> in ale gallons; and the weight of it is (<hi rend="italics">d</hi><hi rend="sup">2</hi><hi rend="italics">l</hi>)/220 ounces or ((<hi rend="italics">d</hi><hi rend="sup">2</hi><hi rend="italics">l</hi>)/3520)lb. But if the handle of the pump be a lever which gains in the power of <hi rend="italics">p</hi> to 1, the force of the hand to work the Pump will be only ((<hi rend="italics">d</hi><hi rend="sup">2</hi><hi rend="italics">l</hi>)/(3520<hi rend="italics">p</hi>))lb, or, when <hi rend="italics">p</hi> is 5 for instance, it will be ((<hi rend="italics">d</hi><hi rend="sup">2</hi><hi rend="italics">l</hi>)/17600)lb. And all these over and above the friction of the moving parts of the Pump.

To the forcing Pump is sometimes adapted an air vessel, which, being compressed by the water, by its elasticity acts upon the water again, and forces it out to a great distance, and in a continued stream, instead of by jerks or jets. So, Mr. Newsham's water engine, for extinguishing fire, consists of two forcing Pumps, which alternately drive water into a close vessel of air, by which means the air in it is condensed, and compresses the water so strongly, that it rushes out with great impetuosity and force through a pipe that comes down into it, making a continued uniform stream.

By means of forcing Pumps, water may be raised to any height whatever above the level of a river or spring; and machines may be contrived to work these Pumps, either by a running stream, a fall of water, or by horses.

<hi rend="italics">Ctesebes</hi>'s <hi rend="smallcaps">Pump</hi>, acts both by suction and by pression. Thus, a brass cylinder ABCD (fig. 5, pl. 23) furnished with a valve at L, is placed in the water. In this is fitted the piston KM, made of green wood, which will not swell in the water, and is adjusted to the <cb/> aperture of the cylinder with a covering of leather, but without any valve. Another tube NH is fitted on at H, with a valve I opening upwards.—Now the piston being raised, the water opens the valve L, and rises into the cavity of the cylinder. When the piston is depressed again, the valve I is opened, and the water is driven up through the tube HN.

This was the Pump used among the Ancients, and that from which both the others have been deduced. Sir Samuel Morland has endeavoured to increase its force by lessening the friction; which he has done to good effect, so as to make it work with very little.

There are various kinds of Pumps used in ships, for throwing the water out of the hold, and upon other occasions, as the Chain Pump, &c.

<hi rend="italics">Air</hi>-<hi rend="smallcaps">Pump</hi>, in Pneumatics, is a machine, by means of which the air is emptied out of vessels, and a kind of vacuum produced in them. For the particulars of which, see <hi rend="smallcaps">Air</hi>-<hi rend="italics">Pump.</hi>

</div1><div1 part="N" n="PUNCHEON" org="uniform" sample="complete" type="entry"><head>PUNCHEON</head>, a measure for liquids, containing 1/3 of a tun, or a hogshead and 1/3, or 84 gallons.

</div1><div1 part="N" n="PUNCHINS" org="uniform" sample="complete" type="entry"><head>PUNCHINS</head>, or <hi rend="smallcaps">Punchions</hi>, in Building, short pieces of timber placed to support some considerable weight.

PUNCTATED <hi rend="italics">Hyperbola,</hi> in the higher geometry, an hyperbola whose conjugate oval is infinitely small, that is, a point.

PUNCTUM <hi rend="italics">ex Comparatione,</hi> is either focus, in the ellipse or hyperbola; so called by Apollonius, because the rectangle under two abscisses made at the focus, is equal to one fourth part of what he calls the figure, which is the square of the conjugate axis, or the rectangle under the transverse and the parameter.

</div1><div1 part="N" n="PURBACH" org="uniform" sample="complete" type="entry"><head><persName><surname full="yes">PURBACH</surname> (<foreName full="yes"><hi rend="smallcaps">George</hi></foreName>)</persName></head>, a very eminent mathematician and astronomer, was born at Purbach, a town upon the confines of Bavaria and Austria, in 1423, and educated at Vienna. He afterwards visited the most celebrated universities in Germany, France, and Italy; and found a particular friend and patron in cardinal Cusa at Rome. Returning to Vienna, he was appointed mathematical professor, in which office he continued till his death, which happened in 1461, in the 39th year of his age only, to the great loss of the learned world.

Purbach composed a great number of pieces, upon mathematical and astronomical subjects; and his fame brought many students to Vienna, and among them, the celebrated Regiomontanus, between whom and Purbach there subsisted the strictest friendship and union of studies till the death of the latter. These two laboured together to improve every branch of learning, by all the means in their power, though astronomy seems to have been the favourite of both; and had not the immature death of Purbach prevented his further pursuits, there is no doubt but that, by their joint industry, astronomy would have been carried to very great perfection. That this is not merely surmise, may be learnt from those improvements which Purbach actually did make, to render the study of it more easy and practicable. His first essay was, to amend the Latin translation of Ptolomy's Almagest, which had been made from the Arabic version: this he did, not by the help of the Greek text, for he was unacquainted with that language, but by drawing the most probable conjectures from a strict attention to the sense of the author.