The science of Hydrostatics treats of the nature gravity, pressure, and motion of fluids in general; and of weighing solids in them.

A fluid is a body that yields to the least pressure or difference of pressures. Its particles are so exceedingly small, that they cannot be discerned by the best of microscopes; they are hard, since no fluid, except air or steam, can be pressed into a less space than it naturally possesses; and they are round and smooth, since they are so easily moved among one another.

All bodies, both fluid and solid, press downwards by the force of gravity; but fluids have this wonderful property, that their pressure upwards and sidewise is equal to their pressure downwards; and this is always in proportion to their perpendicular height, without any regard to their quantity; for, as each particle is quite free to move, it will move towards that part or side on which the pressure is least. And hence, no particle or quantity of a fluid can be at rest, till it is every way equally pressed.

(Plate XCIX. fig. 2.) To show by experiment that fluids press upward as well as downward, let AB be a long upright tube filled with water near to its top; and CD a small tube open at both ends, and immersed into the water in the large one: if the immersion be quick, you will see the water rise in the small tube to the same height that it stands in the great one, or until the surfaces of the water in both are on the same level: which shows that the water is pressed upward into the small tube by the weight of what is in the great one; otherwise it could never rise therein contrary to its natural gravity; unless the diameter of the bore were so small, that the attraction of the tube would raise the water; which will never happen, if the tube be as wide as that in a common barometer. And as the water rises no higher in the small tube than till its surface be on a level with the surface of the water in the great one, this shows that the pressure is not in proportion to the quantity of water in the great tube, but in proportion to its perpendicular height therein: for there is much more water in the great tube all around the small one, than what is raised to the same height in the small one, as it stands in the great.

Take out the small tube, and let the water run out of it; then it will be filled with air. Stop its upper end with the cork C, and it will be full of air all below the cork: this done, plunge it again to the bottom of the water in the great tube, and you will see the water rise up in it to the height E; which shows that the air is a body, otherwise it could not hinder the water from rising up to the same height as it did before, namely, to A; and in so doing, it drove the air out at the top; but now the air is confined by the cork C: and it also shows that the air is a compressible body; for if it were not so, a drop of water could not enter into the tube.

The pressure of fluids being equal in all directions, it follows, that the sides of a vessel are as much pressed by a fluid in it, all around in any given ring of points, as the fluid below that ring is pressed by the weight of all that stands above it. Hence the pressure upon every point in the sides, immediately above the bottom, is equal to the pressure upon every point of the bottom. To show this by experiment, let a hole be made at E (fig. 3.) in the side of the tube AB close by the bottom; and another hole of the same size in the bottom, at C; then pour water into the tube, keeping it full as long as you choose the holes should run, and have two basins ready to receive the water that runs through the two holes, until you think there is enough in each basin; and you will find, by measuring the quantities, that they are equal; which shows that the water runs with equal speed through both holes; which it could not have done, if it had not been equally pressed through them both: for if a hole of the same size be made in the side of the tube, as about f, and if all three are permitted to run together, you will find that the quantity run through the hole at f is much less than what has run in the same time through either of the holes C or e. In the same figure, let the tube be re-curved from the bottom at O into the shape DE, and the hole at C be stopp'd with a cork. Then pour water into the tube to any height, as Ag, and it will spout up in a jet EFG, nearly as high as it is kept in the tube AB, by continuing to pour in as much there as runs through the hole E; which will be the case whilst the surface Ag keeps at the same height. And if a little ball of cork G be laid upon the top of the jet, it will be supported thereby, and dance upon it. The reason why the jet rises not quite so high as the surface of the water Ag, is owing to the resistance it meets with in the open air: for if a tube, either great or small, was screwed upon the pipe at E, the water would rise in it until the surfaces of the water in both tubes were on the same level; as will be shewn by the next experiment.

The hydrostatic paradox.

Any quantity of a fluid, how small soever, may be made to balance and support any quantity, how great soever. This is deservedly termed the hydrostatical paradox, which we shall first shew by an experiment, and then account for it upon the principle above-mentioned, namely, that the pressure of fluids is directly as their perpendicular heights, without any regard to their quantities.

Let a small glass tube DCG, (fig. 4.) open at both ends, and bended at B, be joined to the end of a great one AI at cd, where the great one is also open; so that these tubes in their openings may freely communicate with each other. Then pour water through a small-necked funnel into the small tube at H; this water will run through the joining of the tubes at cd, and rise up into the great tube; and if you continue pouring until the surface of the water comes to any part, as A, in the great tube, and then leave off, you will see that the surface of the water in the small tube will be just as high at D; so that the perpendicular altitude of the water will be the same in both tubes, however small the one be in proportion to the other. This shews, that the small column DCG balances and supports the great column Acd; which it could not do if their pressures were not equal against one another in the recurved bottom at B.—If the small tube be made longer, and inclined in the situation GEF, the surface of the water in it will stand at F, on the same level with the surface A in the great tube; that is, the water will have the same perpendicular height in both tubes, although the column in the small tube is longer than that in the great one; the former being oblique, and the latter perpendicular.

Since then the pressure of fluids is directly as their perpendicular heights, without any regard to their quantities, it appears that whatever the figure or size of vessels be, if they are of equal heights, and if the areas of their bottoms are equal, the pressures of equal heights of water are equal upon the bottoms of these vessels; even though the one should hold a thousand or ten thousand times as much water as would fill the other. To confirm this part of the hydrostatical paradox by an experiment, let two vessels be prepared of equal heights, but very unequal contents, such as AB in fig. 5. and AB in fig. 6.

Let each vessel be open at both ends, and their bottoms Dd Dd be of equal widths. Let a brass bottom CC be exactly fitted to each vessel, not to go into it, but for it to stand upon; and let a piece of wet leather be put between each vessel and its brass bottom, for the sake of closeness. Join each bottom to its vessel by a hinge D, so that it may open like the lid of a box; and let each bottom be kept up to its vessel by equal weights E and E, hung to lines which go over the pulleys F and F (whose blocks are fixed to the sides of the vessels at f) and the lines tied to hooks at d and d, fixed in the brass bottoms opposite to the hinges D and D. Things being thus prepared and fitted, hold the vessel AB (fig. 5.) upright in your hands over a basin on a table, and cause water to be poured into the vessel slowly, till the pressure of the water bears down its bottom at the side d, and raises the weight E; and then part of the water will run out at d. Mark the height at which the surface H of the water stood in the vessel, when the bottom began to give way at d; and then, holding up the other vessel AB (fig. 4.) in the same manner, cause water to be poured into it at H; and you will see that when the water rises to A in this vessel, just as high as it did in the former, its bottom will also give way at d, and it will lose part of the water.

The natural reason of this surprising phenomenon is, that since all parts of a fluid at equal depths below the surface are equally pressed in all manner of directions, the water immediately below the fixed part Bf (fig. 4.) will be pressed as much upward against its lower surface within the vessel, by the action of the column Ag, as it would be by a column of the same height, and of any diameter whatever; (as was evident by the experiment with the tube, fig. 3.) and therefore, since action and reaction are equal and contrary to each other, the water immediately below the surface Bf will be pressed as much downward by it, as if it was immediately touched and pressed by a column of the height gA, and of the diameter Bf; and therefore, the water in the cavity BDdf will be pressed as much downward upon its bottom CC, as the bottom of the other vessel (fig. 5.) is pressed by all the water above it.

To illustrate this a little farther, let a hole be made at f (fig. 5.) in the fixed top Bf, and let a tube G be put into it; then, if water be poured into the tube A, it will (after filling the cavity BD) rise up into the tube G, until it comes to a level with that in the tube A; which is manifestly owing to the pressure of the water in the tube A, upon that in the cavity of the vessel below it. Consequently, that part of the top Bf, in which the hole is now made, would, if corked up, be pressed upward with a force equal to the weight of all the water which is supported in the tube G: and the same thing would hold at g, if a hole were made there. And so if the whole cover or top Bf were full of holes, and had tubes as high as the middle one Ag put into them, the water in each tube would rise to the same height as it is kept into the tube A, by pouring more into it, to make up the deficiency that it sustains by supplying the others, until they were all full; and then the water in the tube A would support equal heights of water in all the rest of the tubes, Or, if all the tubes except A, or any other one, were taken away, and a large tube equal in diameter to the whole top B' were placed upon it, and cemented to it; and then if water were poured into the tube that was left in either of the holes, it would ascend through all the rest of the holes, until it filled the large tube to the same height that it stands in the small one, after a sufficient quantity had been poured into it: which shews, that the top B' was pressed upward by the water under it, and before any hole was made in it, with a force equal to that wherewith it is now pressed downward by the weight of all the water above it in the great tube. And therefore, the reaction of the fixed top B' must be as great, in pressing the water downward upon the bottom CC, as the whole pressure of the water in the great tube would have been, if the top had been taken away, and the water in that tube left to press directly upon the water in the cavity BD'.

The hydrostatic bellows.

Perhaps the best machine in the world for demonstrating the upward pressure of fluids, is the hydrostatic bellows A (fig. 7.) which consists of two thick oval boards, each about 16 inches broad, and 18 inches long, covered with leather, to open and shut like a common bellows, but without valves; only a pipe B, about three feet high, is fixed into the bellows at e. Let some water be poured into the pipe at c, which will run into the bellows, and separate the boards a little. Then lay three weights b, c, d, each weighing 100 pounds, upon the upper board; and pour more water into the pipe B, which will run into the bellows, and raise up the board with all the weights upon it; and if the pipe be kept full, until the weights are raised as high as the leather which covers the bellows will allow them, the water will remain in the pipe, and support all the weights, even though it should weigh no more than a quarter of a pound, and they 300 pounds: nor will all their force be able to cause them to descend and force the water out at the top of the pipe.

The reason of this will be made evident, by considering what has been already said of the result of the pressure of fluids of equal heights without any regard to their quantity. For, if a hole be made in the upper board, and a tube be put into it, the water will rise in the tube to the same height that it does in the pipe; and would rise as high (by supplying the pipe) in as many tubes as the board could contain holes. Now, suppose only one hole to be made in any part of the board, of an equal diameter with the bore of the pipe B; and that the pipe holds just a quarter of a pound of water; if a person claps his finger upon the hole, and the pipe be filled with water, he will find his finger to be pressed upward with a force equal to a quarter of a pound. And as the same pressure is equal upon all equal parts of the board, each part, whose area is equal to the area of the whole, will be pressed upward with a force equal to that of a quarter of a pound: the sum of all which pressures against the under side of an oval board 16 inches broad, and 18 inches long, will amount to 300 pounds; and therefore so much weight will be raised up and supported by a quarter of a pound of water in the pipe.

Hence, if a man stands upon the upper board, and blows into the bellows through the pipe B, he will raise himself upward upon the board: and the smaller the bore of the pipe is, the easier he will be able to raise himself. And then, by clapping his finger upon the top of the pipe, he can support himself as long as he pleases; provided the bellows be air-tight, so as not to lose what is blown into it.

Upon this principle of the upward pressure of fluids, a piece of lead may be made to swim in water, by immersing it to a proper depth, and keeping the water from getting above it. Let CD (fig. 8.) be a glass tube, open at both ends, and EFG a flat piece of lead, exactly fitted to the lower end of the tube, not to go within it, but for it to stand upon; with a wet leather between the lead and tube to make close work. Let this leaden bottom be half an inch thick, and held close to the tube by pulling the packthread IHL upward at L with one hand, whilst the tube is held in the other by the upper end C. In this situation, let the tube be immersed in water in the glass vessel AB, to the depth of six inches below the surface of the water at K; and then, the leaden bottom EFG will be plunged to the depth of somewhat more than eleven times its own thickness: holding the tube at that depth, you may let go the thread at L; and the lead will not fall from the tube, but will be kept to it by the upward pressure of the water below it, occasioned by the height of the water at K above the level of the lead. For as lead is 11.33 times as heavy as its bulk of water, and is in this experiment immersed to a depth somewhat more than 11.33 times its thickness, and no water getting into the tube between it and the lead, the column of water EabcG below the lead is pressed upward against it by the water KDEGL all around the tube; which water being a little more than 11.33 times as high as the lead is thick, is sufficient to balance and support the lead at the depth KE. If a little water be poured into the tube upon the lead, it will increase the weight upon the column of water under the lead, and cause the lead to fall from the tube to the bottom of the glass vessel, where it will lie in the situation bd. Or, if the tube be raised a little in the water, the lead will fall by its own weight, which will then be too great for the pressure of the water around the tube upon the column of water below it.

Let two pieces of wood be planed quite flat, so as no water may get in between them when they are put together: let one of the pieces, as bd, be cemented to the bottom of the vessel AB. (fig. 8.) and the other piece be laid flat and close upon it, and held down to it by a stick, whilst water is poured into the vessel; then remove the stick, and the upper piece of wood will not rise from the lower one: for, as the upper one is pressed down both by its own weight and the weight of all the water over it, whilst the contrary pressure of the water is kept off by the wood under it, it will lie as still as a stone would do in its place. But if it be raised ever so little at any edge, some water will then get under it; which being acted upon by the water above, will immediately press it upward; and as it is lighter than its bulk of water, it will rise, and float upon the surface of the water.

All fluids weigh just as much in their own element as they. they do in open air. To prove this by experiment, let as much shot be put into a phial, as, when corked, will make it sink in water; and being thus charged, let it be weighed, first in air, and then in water, and the weights in both both cases wrote down. Then, as the phial hangs suspended in water, and counterpoised, pull out the cork, that water may run into it, and it will descend, and pull down that end of the beam. This done, put as much weight into the opposite scale as will restore the equipoise; which weight will be found to answer exactly to the additional weight of the phial when it is again weighed in air, with the water in it.

The velocity with which water spouts out at a hole in the side or bottom of a vessel, is as the square root of the depth or distance of the hole below the surface of the water. For, in order to make double the quantity of a fluid run through one hole as through another of the same size, it will require four times the pressure of the other, and therefore must be four times the depth of the other below the surface of the water: and for the same reason, three times the quantity running in an equal time through the same sort of hole, must run with three times the velocity, which will require nine times the pressure; and consequently must be nine times as deep below the surface of the fluid: and so on.—To prove this by an experiment, let two pipes, as C and g (fig. 9.) of equal sized bores, be fixed into the side of the vessel AB; the pipe g being four times as deep below the surface of the water at b in the vessel as the pipe C is: and whilst these pipes run, let water be constantly poured into the vessel, to keep the surface still at the same height. Then, if a cup that holds a pint be so placed as to receive the water that spouts from the pipe C, and at the same moment a cup that holds a quart be so placed as to receive the water that spouts from the pipe g, both cups will be filled at the same time by their respective pipes.

The horizontal distance, to which a fluid will spout from a horizontal pipe, in any part of the side of an upright vessel below the surface of the fluid, is equal to twice the length of a perpendicular to the side of the vessel, drawn from the mouth of the pipe to a semicircle described upon the altitude of the fluid: and therefore, the fluid will spout to the greatest distance possible from a pipe whose mouth is at the centre of the semicircle; because a perpendicular to its diameter (supposed parallel to the side of the vessel) drawn from that point, is the longest that can possibly be drawn from any part of the diameter to the circumference of the semicircle. Thus, if the vessel AB (fig. 9.) be full of water, the horizontal pipe D be in the middle of its side, and the semicircle Nedeb be described upon D as a centre, with the radius or semidiameter DgN, or Df/b, the perpendicular Dd to the diameter NDf, is the longest that can be drawn from any part of the diameter to the circumference Nedeb. And if the vessel be kept full, the jet G will spout from the pipe D, to the horizontal distance NM, which is double the length of the perpendicular Dd. If two other pipes as C and E, be fixed into the side of the vessel at equal distances above and below the pipe D, the perpendiculars Cc and Ee, from these pipe to the semicircle, will be equal; and the jets F and H spouting from them will each go to the horizontal distance NK; which is double the length of the equal perpendiculars Cc or Dd.

Fluids by their pressure may be conveyed over hills and valleys in bended pipes, to any height not greater than the level of the springs from whence they flow. But when they are designed to be raised higher than the springs, forcing engines must be used; which shall be described when we come to treat of pumps.

A syphon, generally used for decanting liquors, is a bended pipe, whose legs are of unequal lengths; and the shortest leg must always be put into the liquor intended to be decanted, that the perpendicular altitude of the column of liquor in the other leg may be longer than the column in the immersed leg, especially above the surface of the water. For, if both columns were equally high in that respect, the atmosphere, which presses as much upward as downward, and therefore acts as much upward against the column in the leg that hangs without the vessel, as it acts downward upon the surface of the liquor in the vessel, would hinder the running of the liquor through the syphon, even though it were brought over the bended part by suction. So that there is nothing left to cause the motion of the liquor, but the superior weight of the column in the longer leg, on account of its having the greater perpendicular height.

Let D (fig. 10.) be a cup filled with water to C, and ABC a syphon, whose shorter leg BCF is immersed in the water from C to F. If the end of the other leg were no lower than the line AC, which is level with the surface of the water, the syphon would not run, even though the air should be drawn out of it at the mouth A. For although the suction would draw some water at first, yet the water would stop at the moment the suction ceased; because the air would act as much upward against the water at A, as it acted downward for it by pressing on the surface at C. But if the leg AB comes down to G, and the air be drawn out at G by suction, the water will immediately follow, and continue to run, until the surface of the water in the cup comes down to F; because, till then, the perpendicular height of the column BAG will be greater than that of the column CB; and consequently, its weight will be greater, until the surface comes down to F; and then the syphon will stop, though the leg CF should reach to the bottom of the cup. For which reason, the leg that hangs without the cup is always made long enough to reach below the level of its bottom; as from d to E: and then, when the syphon is emptied of air by suction at E, the water immediately follows, and by its continuity brings away the whole from the cup; just as pulling one end of a thread will make the whole clue follow.

If the perpendicular height of a syphon, from the surface of the water to its bended top at B, be more than 33 feet, it will draw no water, even though the other leg were much longer, and the syphon quite emptied of air, because the weight of a column of water 33 feet high is equal to the weight of as thick a column of air, reaching from the surface of the earth to the top of the atmosphere; so that there will then be an equilibrium; and consequently, though there would be weight enough of air upon the surface C to make the water ascend in the leg; leg CB almost to the height B, if the syphon were emptied of air, yet the weight would not be sufficient to force the water over the bend; and therefore, it could never be brought into the leg BAC.

Tantalus's cup.

Let a hole be made quite through the bottom of the cup A (fig. 11.) and the longer leg of the bended syphon BCED be cemented into the hole, so that the end D of the shorter leg DE may almost touch the bottom of the cup within. Then, if water be poured into this cup, it will rise in the shorter leg by its upward pressure, extruding the air all the way before it through the longer leg: and when the cup is filled above the bend of the syphon at F, the pressure of the water in the cup will force it over the bend of the syphon: and it will descend in the longer leg CBG, and run through the bottom, until the cup be emptied.

This is generally called Tantalus's cup, and the legs of the syphon in it are almost close together; and a little hollow statue, or figure of a man, is sometimes put over the syphon to conceal it; the bend E being with the neck of the figure as high as the chin. So that poor thirsty Tantalus stands up to the chin in water, imagining it will rise a little higher, and he may drink; but instead of that, when the water comes up to his chin, it immediately begins to descend; and so, as he cannot stoop to follow it, he is left as much pained with thirst as ever.

The fountain at command.

This device called the fountain at command acts upon the same principle with the syphon in the cup. Let two vessels A and B (Plate C. fig. 1.) be joined together by the pipe C which opens into them both. Let A be open at top, B close both at top and bottom (save only a small hole at b to let the air get out of the vessel B) and A be of such a size as to hold about six times as much water as B. Let a syphon DEF be soldered to the vessel B, so that the part DE may be within the vessel, and F without it; the end D almost touching the bottom of the vessel, and the end F below the level of D: the vessel B hanging at A by the pipe C (soldered into both) and the whole supported by the pillars G and H upon the stand I. The bore of the pipe must be considerably less than the bore of the syphon.

The whole being thus constructed, let the vessel A be filled with water, which will run through the pipe C, and fill the vessel B. When B is filled above the top of the syphon at E, the water will run through the syphon, and be discharged at F. But since the bore of the syphon is larger than the bore of the pipe, the syphon will run faster than the pipe, and will soon empty the vessel B; upon which the water will cease from running through the syphon at F, until the pipe C re-fills the vessel B, and then it will begin to run as before. And thus the syphon will continue to run and stop alternately, until all the water in the vessel A has run through the pipe C.—So that after a few trials, one may easily guess about what time the syphon will stop, and when it will begin to run: and then to amuse others, he may call out stop, or run, accordingly.

Upon this principle, we may easily account for intermitting or reciprocating springs. Let AA (fig. 2.) be part of a hill, within which there is a cavity BB; and from this cavity a vein or channel running in the direction BCDE. The rain that falls upon the side of the hill will sink and strain through the small pores and crannies G, G, G, G; and fill the cavity H with water. When the water rises to the level HHC, the vein BCDE will be filled to C, and the water will run through CDF as through a syphon; which running will continue until the cavity be emptied, and then it will stop until the cavity be filled again.

The common pump.

The common sucking pump, with which we draw water out of wells, is an engine both pneumatic and hydraulic. It consists of a pipe open at both ends, in which is a moveable piston, bucket, or sucker, as big as the bore of the pipe in that part wherein it works; and is leathered round, so as to fit the bore exactly; and may be moved up and down, without suffering any air to come between it and the pipe or pump-barrel.

We shall explain the construction both of this and the forcing pump by pictures of glass models, in which both the action of the pistons and motion of the valves are seen.

Hold the model DCBL (fig. 3.) upright in the vessel of water K, the water being deep enough to rise at least as high as from A to L. The valve a on the moveable bucket G, and the valve b on the fixed box H, (which box quite fills the bore of the pipe or barrel at H) will each lie close, by its own weight, upon the hole in the bucket and box, until the engine begins to work. The valves are made of brass, and covered underneath with leather for closing the holes the more exactly: and the bucket G is raised and depressed alternately by the handle E and rod D d, the bucket being supposed at B before the working begins.

Take hold of the handle E, and thereby draw up the bucket from B to C, which will make room for the air in the pump all the way below the bucket to dilate itself, by which its spring is weakened, and then its force is not equivalent to the weight or pressure of the outward air upon the water in the vessel K: and therefore, at the first stroke, the outward air will press up the water through the notched foot A, into the lower pipe, about as far as e: this will condense the rarefied air in the pipe between e and C to the same state it was in before; and then, its spring within the pipe is equal to the force or pressure of the outward air, the water will rise no higher by the first stroke; and the valve b, which was raised a little by the dilatation of the air in the pipe, will fall, and stop the hole in the box H; and the surface of the water will stand at e. Then, depress the piston or bucket from C to B, and as the air in the part B cannot get back again through the valve b, it will (as the bucket descends) raise the valve a, and so make its way through the upper part of the barrel d into the open air. But upon raising the bucket bucket G a second time, the air between it and the water in the lower pipe at e will be again left at liberty to fill a larger space; and so its spring being again weakened, the pressure of the outward air on the water in the vessel K will force more water up into the lower pipe from e to f; and when the bucket is at its greatest height C, the lower valve b will fall, and stop the hole in the box H as before. At the next stroke of the bucket or piston, the water will rise through the box H towards B, and then the valve b, which was raised by it, will fall when the bucket G is at its greatest height. Upon depressing the bucket again, the water cannot be pushed back through the valve b, which keeps close upon the hole whilst the piston descends. And upon raising the piston again, the outward pressure of the air will force the water up through H, where it will raise the valve, and follow the bucket to C. Upon the next depression of the bucket G, it will go down into the water in the barrel B; and as the water cannot be driven back through the now close valve b, it will raise the valve a as the bucket descends, and will be lifted up by the bucket when it is next raised. Now, the whole space below the bucket being full, the water above it cannot sink when it is next depressed; but upon its depression, the valve a will rise to let the bucket go down; and when it is quite down, the valve a will fall by its weight, and stop the hole in the bucket. When the bucket is next raised, all the water above it will be lifted up, and begin to run off by the pipe F. And thus, by raising and depressing the bucket alternately, there is still more water raised by it; which getting above the pipe F, into the wide top I, will supply the pipe, and make it run with a continued stream.

So, at every time the bucket is raised, the valve b rises, and the valve a falls; and at every time the bucket is depressed, the valve b falls, and a rises.

As it is the pressure of the air or atmosphere which causes the water to rise and follow the piston or bucket G as it is drawn up; and since a column of water 33 feet high is of equal weight with as thick a column of the atmosphere from the earth to the very top of the air; therefore, the perpendicular height of the piston or bucket from the surface of the water in the well must always be less than 33 feet; otherwise the water will never get above the bucket. But, when the height is less, the pressure of the atmosphere will be greater than the weight of the water in the pump, and will therefore raise it above the bucket; and when the water has once got above the bucket, it may be lifted thereby to any height, if the rod D be made long enough, and a sufficient degree of strength be employed, to raise it with the weight of the water above the bucket; without ever lengthening the stroke.

The force required to work a pump, will be as the height to which the water is raised, and as the square of the diameter of the pump-bore, in that part where the piston works. So that, if two pumps be of equal heights, and one of them be twice as wide in the bore as the other, the widest will raise four times as much water as the narrowest; and will therefore require four times as much strength to work it.

The wideness or narrowness of the pump, in any other part besides that in which the piston works, does not make the pump either more or less difficult to work; except what difference may arise from the friction of the bore, which is always greater in a narrow bore than in a wide one, because of the greater velocity of the water.

The pump-rod is never raised directly by such a handle as E at the top, but by means of a lever, whose longer arm (at the end of which the power is applied) generally exceeds the length of the shorter arm five or six times; and, by that means, gives five or six times as much advantage to the power. Upon these principles, it will be easy to find the dimensions of a pump that shall work with a given force, and draw water from any given depth. But, as these calculations have been generally neglected by pump-makers (either for want of skill or industry) the following table was calculated by the late ingenious Mr Booth for their benefit. In this calculation, he supposed the handle of the pump to be a lever increasing the power five times; and had often found that a man can work a pump four inches diameter, and 30 feet high above the bucket, and discharge 27½ gallons of water (English wine measure) in a minute. Now, if it be required to find the diameter of a pump, that shall raise water with the same ease from any other height above the bucket; look for that height in the first column, and over against it in the second you have the diameter or width of the pump; and in the third, you find the quantity of water which a man of ordinary strength can discharge in a minute.

| Height of the pump above the bucket | Diameter of the bore where the bucket works | Water discharged in a minute, English wine-measure | |-------------------------------------|---------------------------------------------|--------------------------------------------------| | Feet | Inches | Gallons | | 10 | 6 .93 | 81 6 | | 15 | 5 .65 | 54 4 | | 20 | 4 .90 | 40 8 | | 25 | 4 .38 | 32 6 | | 30 | 4 .00 | 27 2 | | 35 | 3 .70 | 23 3 | | 40 | 3 .47 | 20 4 | | 45 | 3 .26 | 18 1 | | 50 | 3 .10 | 16 3 | | 55 | 2 .95 | 14 7 | | 60 | 2 .83 | 13 5 | | 65 | 2 .71 | 12 4 | | 70 | 2 .62 | 11 5 | | 75 | 2 .53 | 10 7 | | 80 | 2 .44 | 10 2 |

The forcing-pump.

The forcing-pump raises water through the box H (fig. 4) in the same manner as the sucking-pump does, when the plunger or piston g is lifted up by the rod Dd. But this plunger has no hole through it, to let the water in the barrel barrel BC get above it when it is depressed to B, and the valve b (which rose by the ascent of the water through the box H when the plunger g was drawn up) falls down and stops the hole in H, the moment that the plunger is raised to its greatest height. Therefore, as the water between the plunger g and box H can neither get through the plunger upon its descent, nor back again into the lower part of the pump Lc, but has a free passage by the cavity around H into the pipe MM, which opens into the air-vessel KK at P; the water is forced through the pipe MM by the descent of the plunger, and driven into the air-vessel; and in running up through the pipe at P, it opens the valve a; which shuts at the moment the plunger begins to be raised, because the action of the water against the under side of the valve then ceases.

The water, being thus forced into the air-vessel KK by repeated strokes of the plunger, gets above the lower end of the pipe GHI, and then begins to condense the air in the vessel KK. For, as the pipe GH is fixed air-tight into the vessel below F, and the air has no way to get out of the vessel but through the mouth of the pipe at I, and cannot get out when the mouth I is covered with water, and is more and more condensed as the water rises upon the pipe, the air then begins to act forcibly by its spring against the surface of the water, at H: and this action drives the water up through the pipe IH GF, from whence it spouts in a jet S to a great height; and is supplied by alternately raising and depressing the plunger g, which constantly forces the water that it raises through the valve H, along the pipe MM, into the air-vessel KK.

The higher that the surface of the water H is raised in the air-vessel, the less space will the air be condensed into, which before filled that vessel; and therefore the force of its spring will be so much the stronger upon the water, and will drive it with the greater force through the pipe at F; and as the spring of the air continues whilst the plunger g is rising, the stream or jet S will be uniform, as long as the action of the plunger continues: and when the valve b opens, to let the water follow the plunger upward, the valve a shuts, to hinder the water, which is forced into the air-vessel, from running back by the pipe MM into the barrel of the pump.

If there was no air-vessel to this engine, the pipe GHI would be joined to the pipe MMN at P; and then the jet S would stop every time the plunger is raised, and run only when the plunger is depressed.

Mr Newsham's water-engine, for extinguishing fire, consists of two forcing pumps, which alternately drive water into a close vessel of air; and by forcing the water into that vessel, the air in it is thereby condensed, and compresses the water so strongly, that it rushes out with great impetuosity and force through a pipe that comes down into it; and makes a continued uniform stream by the condensation of the air upon its surface in the vessel.

By means of forcing pumps, water may be raised to any height 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. An instance in each sort will be sufficient to shew the method.

First, by a running stream, or a fall of water. Let AA (fig. 5.) be a wheel turned by the fall of water BB; and have any number of cranks (suppose six) as C, D, E, F, G, H, on its axis, according to the strength of the fall of water, and the height to which the water is intended to be raised by the engine. As the wheel turns round, these cranks move the levers c, d, e, f, g, h, up and down, by the iron rods i, k, l, m, n, o; which alternately raise and depress the pistons by the other iron rods p, q, r, s, t, u, v, w, x, y, in twelve pumps; nine whereof, as L, M, N, O, P, Q, R, S, T, appear in the plate; the other three being hid behind the work at V. And as pipes may go from all these pumps, to convey the water (drawn up by them to a small height) into a close cistern, from which the main pipe proceeds, the water will be forced into this cistern by the descent of the pistons. And as each pipe, going from its respective pump into the cistern, has a valve at its end in the cistern, these valves will hinder the return of the water by the pipes; and therefore, when the cistern is once full, each piston upon its descent will force the water (conveyed into the cistern by a former stroke) up the main pipe, to the height the engine was intended to raise it: which height depends upon the quantity raised, and the power that turns the wheel. When the power upon the wheel is lessened by any defect of the quantity of water turning it, a proportionable number of the pumps may be laid aside, by disengaging their rods from the vibrating levers.

This figure is a representation of the engine erected at Blenheim for the Duke of Marlborough, by the late ingenious Mr Aldersea. The water-wheel is 7 feet diameter, according to Mr Switzer's account in his Hydraulics.

When such a machine is placed in a stream that runs upon a small declivity, the motion of the levers and action of the pumps will be but slow; since the wheel must go once round for each stroke of the pumps. But, when there is a large body of slow running water, a cog or spur-wheel may be placed upon each side of the water-wheel AA, upon its axis, to turn a trundle upon each side; the cranks being upon the axis of the trundle. And by proportioning the cog-wheels to the trundles, the motion of the pumps may be made quicker, according to the quantity and strength of the water upon the first wheel; which may be as great as the workman pleases, according to the length and breadth of the float-boards or wings of the wheel. In this manner, the engine for raising water at London-Bridge is constructed; in which the water-wheel is 20 feet diameter, and the floats 14 feet long.

A quadruple pump-mill for raising water.

The engine is represented in Plate 99, fig. 1. In which ABCD is a wheel, turned by water according to the order of the letters. On the horizontal axis are four small wheels, toothed almost half round; and the parts of their edges on which there are no teeth are cut down so as to be even with the bottoms of the teeth where they stand.

The teeth of these four wheels take alternately into the the teeth of four racks, which hang by two chains over the pulleys Q and L; and to the lower ends of these racks there are four iron rods fixed, which go down into the four forcing pumps, S, R, M, and N. And, as the wheels turn, the racks and pump-rods are alternately moved up and down.

Thus, suppose the wheel G has pulled down the rack I, and drawn up the rack K by the chain: as the last tooth of G just leaves the uppermost tooth of I, the first tooth of H is ready to take into the lowermost tooth of the rack K, and pull it down as far as the teeth go; and then the rack I is pulled upward through the whole space of its teeth, and the wheel G is ready to take hold of it, and pull it down again, and so draw up the other.

In the same manner, the wheels E and F work the racks O and P.

These four wheels are fixed on the axle of the great wheel in such a manner, with respect to the positions of their teeth, that whilst they continue turning round, there is never one instant of time in which one or other of the pump rods is not going down and forcing the water. So that, in this engine, there is no occasion for having a general air-vessel to all the pumps, to procure a constant stream of water flowing from the upper end of the main pipe.

From each of these pumps, near the lowest end, in the water, there goes off a pipe, with a valve on its farthest end from the pump; and these ends of the pipes all enter one close box, into which they deliver the water: and into this box, the lower end of the main conduct-pipe is fixed. So that, as the water is forced or pushed into the box, it is also pushed up the main pipe to the height that it is intended to be raised,

A pump-engine to go by horses.

Where a stream or fall of water cannot be had, and gentlemen want to have water raised, and brought to their houses from a rivulet or spring; this may be effected by a horse engine, working three forcing-pumps which stand in a reservoir filled by the spring or rivulet: the pistons being moved up and down in the pumps by means of a triple crank ABC, which, as it is turned round by the trundle G (Plate 100, fig. 6.) raises and depresses the rods D, E, F. If the wheel has three times as many cogs as the trundle has flaves or rounds, the trundle and cranks will make three revolutions for every one of the wheel: and as each crank will fetch a stroke in the time it goes round, the three cranks will make nine strokes for every turn of the great wheel.

The cranks should be made of cast iron, because that will not bend; and they should each make an angle of 120° with both of the others, as at a, b, c; which is (as it were) a view of their radii, in looking endwise at the axis: and then there will be always one or other of them going downward, which will push the water forward with a continued stream into the main pipe. For, when b is almost at its lowest situation, and is therefore just beginning to lose its action upon the piston which it moves, c is beginning to move downward, which will by its piston continue the propelling force upon the water: and when c is come down to the position of b, a will be in the position of c.

The more perpendicularly the piston rods move up and down in the pumps, the freer and better will their strokes be: but a little deviation from the perpendicular will not be material. Therefore, when the pump-rods D, E, and F go down into a deep well, they may be moved directly by the cranks, as is done in a very good horse-engine of this sort at the late Sir James Creed's at Greenwich, which forces up water about 64 feet from a well under ground, to a reservoir on the top of his house. But when the cranks are only at a small height above the pumps, the pistons must be moved by vibrating levers, as in the above engine at Blenheim: and the longer the levers are, the nearer will the strokes be to a perpendicular.

Let us suppose, that in such an engine as Sir James Creed's, the great wheel is twelve feet diameter, the trundle four feet, and the radius or length of each crank nine inches, working a piston units pump. Let there be three pumps in all, and the bore of each pump be four inches diameter. Then, if the great wheel has three times as many cogs as the trundle has flaves, the trundle and cranks will go three times round for each revolution of the horses and wheel, and the three cranks will make nine strokes of the pumps in that time, each stroke being 18 inches (or double the length of the crank) in a four-inch bore. Let the diameter of the horse-walk be 18 feet, and the perpendicular height to which the water is raised above the surface of the well be 64 feet.

If the horses go at the rate of two miles an hour (which is very moderate walking) they will turn the great wheel 187 times round in an hour.

In each turn of the wheel the pistons make nine strokes in the pumps, which amount to 1683 in an hour.

Each stroke raises a column of water 18 inches long, and four inches thick, in the pump barrels; which column, upon the descent of the piston, is forced into the main pipe, whose perpendicular altitude above the surface of the well is 64 feet.

Now, since a column of water 18 inches long, and four inches thick, contains 226.13 cubic inches, this number multiplied by 1683 (the strokes in an hour) gives 380661 for the number of cubic inches of water raised in an hour.

A gallon, in wine-measure, contains 231 cubic inches, by which divide 380661, and it quotes 1668 in round numbers, for the number of gallons raised in an hour; which, divided by 65, gives 26½ hogsheads ——If the horses go faster, the quantity raised will be so much the greater.

In this calculation it is supposed that no water is wasted by the engine. But as no forcing engine can be supposed to lose less than a fifth part of the calculated quantity of water, between the pistons and barrels, and by the opening and shutting of the valves, the horses ought to walk almost 2½ miles per hour to fetch up this loss.

A column of water four inches thick, and 64 feet high, weighs 3497½ pounds avoirdupois, or 424¾ pounds troy; and this weight, together with the friction of the engine, is the resistance that must be overcome by the strength of the horses. The horse tackle should be so contrived, that the horses may rather push on than drag the levers after them. For if they draw, in going round the walk, the outside leather-traps will rub against their sides and hams; which will hinder them from drawing at right angles to the levers, and so make them pull at a disadvantage. But if they push the levers before their breasts, instead of dragging them, they can always walk at right angles to these levers.

It is no ways material what the diameter of the main or conduct pipe be: for the whole resistance of the water therein, against the horses, will be according to the height to which it is raised, and the diameter of that part of the pump in which the piston works; as we have already observed. So that by the same pump, an equal quantity of water may be raised in (and consequently made to run from) a pipe of a foot diameter, with the same ease as in a pipe of five or six inches; or rather with more ease, because its velocity in a large pipe will be less than in a small one, and therefore its friction against the sides of the pipe will be less also.

And the force required to raise water depends not upon the length of the pipe, but upon the perpendicular height to which it is raised therein above the level of the spring. So that the same force, which would raise water to the height AB (fig. 7.) in the upright pipe AiklmnopqB, will raise it to the same height or level BIH in the oblique pipe AEFGH. For the pressure of the water at the end A of the latter, is no more than its pressure against the end A of the former.

The weight or pressure of water at the lower end of a pipe, is always as the sine of the angle to which the pipe is elevated above the level parallel to the horizon. For, although the water in the upright pipe AB would require a force applied immediately to the lower end A, equal to the weight of all the water in it, to support the water, and a little more to drive it up and out of the pipe; yet if that pipe be inclined from its upright position to an angle of 80 degrees (as in A 80), the force required to support or to raise the same cylinder of water will then be as much less as the sine 80 b is less than the radius AB; or as the sine of 80 degrees is less than the sine of 90. And so, decreasing as the sign of the angle of elevation lessens, until it arrives at its level AC or place of rest, where the force of the water is nothing at either end of the pipe. For, although the absolute weight of the water is the same in all positions, yet its pressure at the lower end decreases, as the sine of the angle of elevation decreases; as will appear plainly by a farther consideration of the figure.

Let two pipes, AB and BC, of equal lengths and bores, join each other at A; and let the pipe AB be divided into 100 equal parts, as the scale S is; whose length is equal to the length of the pipe.—Upon this length, as a radius, describe the quadrant BCD, and divide it into 90 equal parts or degrees.

Let the pipe AC be elevated to 10 degrees upon the quadrant, and then filled with water; then, part of the water that is in it will rise in the pipe AB, and if it be kept full of water, it will raise the water in the pipe AB from A to i; that is, to a level i 10 with the mouth of the pipe at A; and the upright line a 10, equal to Ai, will be the sine of 10 degrees elevation; which being measured upon the scale S, will be about 17.4 of such parts as the pipe contains 100 in length: and therefore, the force or pressure of the water at A, in the pipe A 10, will be to the force or pressure at A in the pipe AB as 17.3 to 100.

Let the same pipe be elevated to 20 degrees in the quadrant, and if it be kept full of water, part of that water will run into the pipe AB, and rise therein to the height Ak, which is equal to the length of the upright line b 20, or to the sine of 20 degrees elevation; which, being measured upon the scale S, will be 34.2 of such parts as the pipe contains 100 in length; and therefore the pressure of the water at A, in the full pipe A 20, will be to its pressure, if that pipe were raised to the perpendicular situation AB, as 34.2 to 100.

| Sine of | Parts | Sine of | Parts | Sine of | Parts | Sine of | Parts | |--------|-------|--------|-------|--------|-------|--------|-------| | D. 1 | 17 | D. 19 | 325 | D. 37 | 602 | D. 55 | 819 | | 2 | 35 | 20 | 342 | 38 | 616 | 56 | 829 | | 3 | 52 | 21 | 358 | 39 | 629 | 57 | 839 | | 4 | 70 | 22 | 375 | 40 | 643 | 58 | 848 | | 5 | 87 | 23 | 391 | 41 | 656 | 59 | 857 | | 6 | 104 | 24 | 407 | 42 | 669 | 60 | 866 | | 7 | 122 | 25 | 423 | 43 | 682 | 61 | 875 | | 8 | 139 | 26 | 438 | 44 | 695 | 62 | 883 | | 9 | 156 | 27 | 454 | 45 | 707 | 63 | 891 | | 10 | 174 | 28 | 469 | 46 | 719 | 64 | 899 | | 11 | 191 | 29 | 485 | 47 | 731 | 65 | 906 | | 12 | 208 | 30 | 500 | 48 | 743 | 66 | 913 | | 13 | 225 | 31 | 515 | 49 | 755 | 67 | 920 | | 14 | 242 | 32 | 530 | 50 | 766 | 68 | 927 | | 15 | 259 | 33 | 545 | 51 | 777 | 69 | 934 | | 16 | 276 | 34 | 559 | 52 | 788 | 70 | 940 | | 17 | 292 | 35 | 573 | 53 | 799 | 71 | 945 | | 18 | 309 | 36 | 588 | 54 | 809 | 72 | 951 |

Elevate Elevate the pipe to the position A 30 on the quadrant; and if it be supplied with water, the water will rise from it into the pipe AB, to the height A1, or to the same level with the mouth of the pipe at 30. The sine of this elevation, or of the angle of 30 degrees, is c 30; which is just equal to half the length of the pipe, or to 50 of such parts of the scale as the length of the pipe contains 100. Therefore, the pressure of the water at A, in a pipe elevated 30 degrees above the horizontal level, will be equal to one half of what it would be, if the same pipe stood upright in the situation AB.

And thus, by elevating the pipe to 40, 50, 60, 70, and 80 degrees on the quadrant, the sines of these elevations will be d 40, e 50, f 60, g 70, and h 80; which will be equal to the heights Am, An, Ao, Ap, and Aq; and these heights measured upon the scale 8 will be 64.3, 76.6, 86.6, 94.0, and 98.5; which expresses the pressures at A in all these elevations, considering the pressure in the upright pipe AB as 100.

Because it may be of use to have the lengths of all the sines of a quadrant from 0 degrees to 90, we have given the foregoing table, shewing the length of the sine of every degree in such parts as the whole pipe (equal to the radius of the quadrant) contains 1000. Then the sines will be integral or whole parts in length. But if you suppose the length of the pipe to be divided only into 100 equal parts, the last figure of each part or sine must be cut off as a decimal; and then those which remain at the left hand of this separation will be integral or whole parts.

Thus, if the radius of the quadrant (supposed to be equal to the length of the pipe AC) be divided into 1000 equal parts, and the elevation be 45 degrees, the sine of that elevation will be equal to 707 of these parts; but if the radius be divided into 100 equal parts, the same sine will be only 70 or 70.7 of these parts. For, as 1000 is to 707, so is 100 to 70.7.

As it is of great importance to all engine-makers, to know what quantity and weight of water will be contained in an upright round pipe of a given diameter and height, so as, by knowing what weight is to be raised, they may proportion their engines to the force which they can afford to work them; we shall subjoin tables shewing the number of cubic inches of water contained in an upright pipe of a round bore, of any diameter from one inch to six and a half; and of any height from one foot to two hundred; together with the weight of the said number of cubic inches, both in troy and avoirdupois ounces. The number of cubic inches divided by 231, will reduce the water to gallons in wine measure; and divided by 382, will reduce it to the measure of ale-gallons. Also, the troy ounces divided by 12, will reduce the weight to troy pounds; and the avoirdupois ounces divided by 16, will reduce the weight to avoirdupois pounds.

And here we must repeat it again, that the weight or pressure of the water acting against the power that works the engine must always be estimated according to the perpendicular height to which it is to be raised, without any regard to the length of the conduct pipe, when it has an oblique position; and as if the diameter of that pipe were just equal to the diameter of that part of the pump in which the piston works. Thus by the tables on the two following pages, the pressure of the water against an engine whose pump is of a 4½ inch bore, and the perpendicular height of the water in the conduct pipe is 80 feet, will be equal to 8057.5 troy ounces, and to 8848.2 avoirdupois ounces; which makes 671.4 troy pounds, and 553 avoirdupois.

**Example.** Required the number of cubic inches, and the weight of the water, in an upright pipe 278 feet high, and 1½ inch diameter?

| Feet | Cubic inches | Troy oz. | Avoir. oz. | |------|--------------|----------|-----------| | 200 | 4241.1 | 2238.2 | 2457.8 | | 70 | 1484.1 | 783.3 | 860.2 | | 8 | 169.6 | 89.5 | 98.3 |

Answ. 278 5895.1 3111.0 3416.3

Here the nearest single decimal figure is only taken into the account; and the whole, being reduced by division, amounts to 25¾ wine-gallons in measure, to 259¾ pounds troy, and 213¾ pounds avoirdupois.

These tables were at first calculated to six decimal places for the sake of exactness; but in transcribing them there are no more than two decimal figures taken into the account, and sometimes but one; because there is no necessity for computing to hundredth parts of an inch or of an ounce in practice.

**The fire engine.**

The fire-engine comes next in order to be explained; but as it would be difficult, even by the best plates, to give a particular description of its several parts, so as to make the whole intelligible, we shall only explain the principles upon which it is constructed.

1. Whatever weight of water is to be raised, the pump rod must be loaded with weights sufficient for that purpose, if it be done by a forcing pump, as is generally the case; and the power of the engine must be sufficient for the weight of the rod, in order to bring it up.

2. It is known, that the atmosphere presses upon the surface of the earth with a force equal to 15 pounds upon every square inch.

3. When water is heated to a certain degree, the particles thereof repel one another, and constitute an elastic fluid, which is generally called steam or vapour.

4. Hot steam is very elastic; and when it is cooled by any means, particularly by its being mixed with cold water, its elasticity is destroyed immediately, and it is reduced to water again.

5. If a vessel be filled with hot steam, and then closed so as to keep out the external air and all other fluids; when that steam is by any means condensed, cooled, or reduced to water, that water will fall to the bottom of the vessel; and the cavity of the vessel will be almost a perfect vacuum.

6. Whenever a vacuum is made in any vessel the air by its weight will endeavour to rush into the vessel, or to drive in any other body that will give way to its pressure; as may be easily seen by a common syringe. For, if you stop the bottom of a syringe, and then draw up the piston, if it be so tight as to drive out all the air before it, and leave a vacuum within the syringe, the piston being let go will be driven down with a great force.

7. The force with which the piston is drove down, when there is a vacuum under it, will be as the square of the diameter of the bore in the syringe. That is to say, it will be driven down with four times as much force in a syringe of a two-inch bore, as in a syringe of one inch: for the areas of circles are always as the squares of their diameters.

8. The pressure of the atmosphere being to 15 pounds upon every square inch, it will be equal to about 12 pounds upon every circular inch. So that if the bore of the syringe be round, and one inch in diameter, the piston will be pressed down into it by a force nearly equal to 12 pounds: but if the bore be two inches diameter, the piston will be pressed down with four times that force.

And hence it is easy to find with what force the atmosphere presses upon any given number either of square or circular inches.

These being the principles upon which this engine is constructed, we shall next describe the chief working parts of it: which are, 1. A boiler. 2. A cylinder and piston. 3. A beam or lever.

The boiler is a large vessel made of iron or copper; and commonly so big as to contain about 2000 gallons.

The cylinder is about 40 inches diameter, bored so smooth, and its leathered piston fitting so close, that little or no water can get between the piston and sides of the cylinder.

Things being thus prepared, the cylinder is placed upright, and the shank of the piston is fixed to one end of the beam, which turns on a centre like a common balance.

The boiler is placed under the cylinder, with a communication between them, which can be opened and shut occasionally.

The boiler is filled about half full of water, and a strong fire is made under it; then, if the communication between the boiler and the cylinder be opened, the cylinder will be filled with hot steam; which would drive the piston quite out at the top of it. But there is a contrivance by which the piston, when it is near the top of the cylinder, shuts the communication at the top of the boiler within.

This is no sooner shut, than another is opened, by which a little cold water is thrown upwards in a jet into the cylinder, which mixing with the hot steam, condenses it immediately; by which means a vacuum is made in the cylinder, and the piston is pressed down by the weight of the atmosphere; and so lifts up the loaded pump-rod at the other end of the beam.

### HYDROSTATIC TABLES

| 1 Inch diameter | 1½ Inches diameter | |-----------------|--------------------| | Feet high | Solidity in cubic inches | Weight in Troy ounces | In avoir dupoise ounces | | 1 | 9.42 | 4.97 | 5.46 | | 2 | 18.85 | 9.95 | 10.92 | | 3 | 28.27 | 14.92 | 16.38 | | 4 | 37.70 | 19.89 | 21.85 | | 5 | 47.12 | 24.87 | 27.31 | | 6 | 56.55 | 29.84 | 32.77 | | 7 | 65.97 | 34.82 | 38.23 | | 8 | 75.40 | 39.79 | 43.69 | | 9 | 84.82 | 44.76 | 49.16 | | 10 | 94.25 | 49.74 | 54.62 | | 20 | 188.49 | 99.48 | 109.24 | | 30 | 282.74 | 149.21 | 163.86 | | 40 | 376.99 | 198.95 | 218.47 | | 50 | 471.24 | 248.69 | 273.09 | | 60 | 565.49 | 298.43 | 327.71 | | 70 | 659.73 | 348.17 | 382.33 | | 80 | 753.98 | 397.90 | 436.95 | | 90 | 843.23 | 447.64 | 491.57 | | 100 | 942.48 | 497.38 | 546.19 | | 200 | 1884.96 | 994.76 | 1092.38 |

| 2 Inches diameter | 2½ Inches diameter | |-------------------|--------------------| | Feet high | Solidity in cubic inches | Weight in Troy ounces | In avoir dupoise ounces | | 1 | 37.70 | 19.89 | 21.85 | | 2 | 75.40 | 39.79 | 43.69 | | 3 | 113.10 | 59.68 | 65.54 | | 4 | 150.80 | 79.58 | 87.29 | | 5 | 188.50 | 99.47 | 109.24 | | 6 | 226.10 | 119.37 | 131.08 | | 7 | 263.89 | 139.26 | 152.93 | | 8 | 301.59 | 159.16 | 174.78 | | 9 | 339.29 | 179.06 | 196.63 | | 10 | 376.99 | 198.95 | 218.47 | | 20 | 753.98 | 397.90 | 436.95 | | 30 | 1130.97 | 596.85 | 665.42 | | 40 | 1507.97 | 795.80 | 873.90 | | 50 | 1884.96 | 994.75 | 1092.37 | | 60 | 2261.95 | 1193.70 | 1310.85 | | 70 | 2638.94 | 1392.65 | 1529.32 | | 80 | 3015.93 | 1591.60 | 1747.80 | | 90 | 3392.92 | 1790.56 | 1966.27 | | 100 | 3769.91 | 1989.51 | 2184.75 | | 200 | 7539.82 | 3979.00 | 4369.50 |

| Feet high | Solidity in cubic inches | Weight in Troy ounces | In avoir dupoise ounces | |-------------------|--------------------------|-----------------------|------------------------| | 1 | 58.90 | 31.08 | 34.14 | | 2 | 117.81 | 62.17 | 68.27 | | 3 | 176.71 | 93.26 | 102.41 | | 4 | 235.62 | 124.34 | 136.55 | | 5 | 294.52 | 155.43 | 170.68 | | 6 | 353.43 | 186.52 | 204.82 | | 7 | 412.33 | 217.60 | 238.96 | | 8 | 471.24 | 248.69 | 273.09 | | 9 | 530.14 | 279.77 | 307.23 | | 10 | 589.05 | 310.86 | 341.37 | | 20 | 1178.10 | 621.72 | 682.73 | | 30 | 1767.15 | 932.58 | 1024.10 | | 40 | 2356.20 | 1243.44 | 1365.47 | | 50 | 2945.25 | 1554.30 | 1706.83 | | 60 | 3534.29 | 1865.16 | 2048.20 | | 70 | 4123.34 | 2176.02 | 2389.27 | | 80 | 4712.39 | 2486.88 | 2730.94 | | 90 | 5301.44 | 2797.74 | 3072.30 | | 100 | 5890.49 | 3108.60 | 3413.67 | | 200 | 11780.98 | 6217.20 | 6827.34 | | 3 Inches diameter | 3¼ Inches diameter | 5 Inches diameter | 5¼ Inches diameter | |------------------------------|-----------------------|-----------------------|------------------------| | Feet high | Solidity in cubic inches | Weight in Troy ounces | In avoirdupois ounces | |-------------------------------|------------------------|-----------------------|------------------------| | 1 84.8 | 115.4 | 235.6 | | | 2 169.6 | 230.9 | 471.2 | | | 3 254.5 | 346.4 | 706.8 | | | 4 339.3 | 461.8 | 942.5 | | | 5 424.1 | 577.3 | 1178.1 | | | 6 508.9 | 692.7 | 1413.7 | | | 7 593.7 | 808.2 | 1643.9 | | | 8 686.8 | 923.6 | 1884.9 | | | 9 770.4 | 1039.1 | 2120.6 | | | 10 843.2 | 1154.5 | 2356.2 | | | 20 1696.5 | 3049.1 | 4712.4 | | | 30 2244.7 | 3429.2 | 5706.8 | | | 40 3392.9 | 4618.1 | 6927.2 | | | 50 4424.1 | 5772.7 | 8143.2 | | | 60 5089.4 | 6927.2 | 9358.1 | | | 70 5971.7 | 8081.7 | 10643.5 | | | 80 6795.8 | 9256.3 | 11949.5 | | | 90 7541.4 | 10391.1 | 13256.2 | | | 100 8482.3 | 11545.4 | 14712.4 | | | 200 16964.6 | 2090.7 | 24125.0 | | | 4 Inches diameter | 4½ Inches diameter | 6 Inches diameter | 6½ Inches diameter | | Feet high | Solidity in cubic inches | Weight in Troy ounces | In avoirdupois ounces | |-------------------------------|------------------------|-----------------------|------------------------| | 1 150.8 | 190.8 | 332.5 | | | 2 301.6 | 381.7 | 678.6 | | | 3 452.4 | 572.6 | 1017.9 | | | 4 603.2 | 763.6 | 1527.2 | | | 5 754.9 | 954.3 | 1908.5 | | | 6 904.8 | 1145.4 | 2317.1 | | | 7 1055.5 | 1337.9 | 2735.2 | | | 8 1206.4 | 1526.8 | 3171.7 | | | 9 1357.2 | 1717.7 | 3604.5 | | | 10 1508.0 | 1906.5 | 4038.7 | | | 20 3115.9 | 2014.6 | 4424.1 | | | 30 4523.9 | 3021.5 | 5035.9 | | | 40 6031.9 | 4037.5 | 5553.9 | | | 50 7539.8 | 4936.5 | 6072.9 | | | 60 9047.8 | 5343.4 | 6600.5 | | | 70 10555.5 | 6117.3 | 7106.5 | | | 80 12063.7 | 6901.7 | 7656.5 | | | 90 13571.7 | 8739.1 | 9067.9 | | | 100 15079.7 | 7958.0 | 10107.1 | | | 200 30159.3 | 14782.8 | 12210.6 | | If the cylinder be 42 inches in diameter, the piston will be pressed down with a force greater than 20000 pounds, and will consequently lift up that weight at the opposite end of the beam: and as the pump-rod with its plunger is fixed to that end, if the bore where the plunger works were 10 inches diameter, the water would be forced up through a pipe of 180 yards perpendicular height.

But, as the parts of this engine have a good deal of friction, and must work with a considerable velocity, and there is no such thing as making a perfect vacuum in the cylinder, it is found that no more than 8 pounds of pressure must be allowed for, on every circular inch of the piston in the cylinder, that it may make about 16 strokes in a minute, about 6 feet each.

Where the boiler is very large, the piston will make between 20 and 25 strokes in a minute, and each stroke 7 or 8 feet; which, in a pump of 9 inches bore, will raise upwards of 300 hogsheads of water in an hour.

It is found by experience, that a cylinder 40 inches diameter will work a pump 10 inches diameter and 100 yards long: and hence we can find the diameter and length of a pump that can be worked by any other cylinder.

For the conveniency of those who would make use of this engine for raising water, we shall subjoin part of a table calculated by Mr. Beighton, shewing how any given quantity of water may be raised in an hour, from 48 to 440 hogsheads; at any given depth, from 15 to 100 yards; the machine working at the rate of 16 strokes per minute, and each stroke being 6 feet long.

One example of the use of this table, will make the whole plain. Suppose it were required to draw 150 hogsheads per hour, at 90 yards depth; in the second column from the right hand, I find the nearest number, viz. 149 hogsheads 40 gallons; against which, on the right hand, I find the diameter of the bore of the pump must be 7 inches; and in the same collateral line, under the given depth 90, I find 27 inches, the diameter of the cylinder fit for that purpose.—And so for any other.

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**A Table shewing the Power of the Engine for raising Water by Fire; Calculated to the Measure of Ale-gallons, at 282 cubic Inches per Gallon.**

| Diameter of the Cylinder in Inches | The depth to be drawn in yards | In one hour | Diam. of pump | |-----------------------------------|-------------------------------|-------------|---------------| | | | Hogsh. Gal. | Inches | | 15 | 20 | | | | 18½ | 21½ | | | | 17 | 19½ | | | | 15½ | 18 | | | | 14 | 16½ | | | | 13½ | 15½ | | | | 12½ | 14½ | | | | 12 | 14 | | | | 11 | 13½ | | | | 10½ | 13 | | | | 10 | 12 | | | | 9½ | 11 | | | | 10 | 11 | | | | 10 | 11 | | | | 9 | 10 | | |

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**The Persian wheel.**

Water may be raised by means of a stream AB (Plate 100, fig. 8.) turning a wheel CDE, according to the order of the letters, with buckets a, a, a, &c., hung upon the wheel by strong pins b, b, b, &c., fixed in the side of the rim: but the wheel must be made as high as the water is intended to be raised above the level of that part of the stream in which the wheel is placed. As the wheel turns, the buckets on the right hand go down into the water, and are thereby filled; and go up full on the left hand, until they come to the top at K; where they strike against the end n of the fixed trough M, and are thereby overset, and empty the water into the trough; from which it may be conveyed in pipes to the place which it is designed for: and as each bucket gets over the trough, it falls into a perpendicular position again, and goes down empty, until it comes to the water at A, where it is filled as before. On each bucket is a spring r, which going over the top or crown of the bar m (fixed to the trough M) raises the bottom of the bucket above above the level of of its mouth, and so causes it to empty all its water into the trough.

Sometimes this wheel is made to raise water no higher than its axis; and then, instead of buckets hung upon it, its spokes C, d, e, f, g, h are made of a bent form, and hollow within; these hollows opening into the holes C, D, E, F, in the outside of the wheel, and also into those at O in the box N upon the axis. So that, as the holes C, D, &c., dip into the water, it runs into them; and as the wheel turns, the water rises in the hollow spokes, c, d, &c., and runs out in a stream P from the holes at O, and falls into the trough Q, from whence it is conveyed by pipes. And this is a very easy way of raising water, because the engine requires neither men nor horses to turn it.

Of the specific gravities of bodies.

The art of weighing different bodies in water, and thereby finding their specific gravities, or weights, bulk for bulk, was invented by Archimedes.

The specific gravities of bodies are as their weights, bulk for bulk; thus a body is said to have two or three times the specific gravity of another, when it contains two or three times as much matter in the same space.

A body immersed in a fluid will sink to the bottom, if it be heavier than its bulk of the fluid. If it be suspended therein, it will lose as much of what it weighed in air, as its bulk of the fluid weighs. Hence, all bodies of equal bulk, which would sink in fluids, lose equal weights when suspended therein. And unequal bodies lose in proportion to their bulks.

The hydrostatic balance.

The hydrostatic balance differs very little from a common balance that is nicely made; only it has a hook at the bottom of each scale, on which small weights may be hung by horse-hairs, or by silk threads. So that a body, suspended by the hair or thread, may be immersed in water without wetting the scale from which it hangs.

If the body thus suspended under the scale, at one end of the balance, be first counterpoised in air by weights in the opposite scale, and then immersed in water, the equilibrium will be immediately destroyed. Then, if as much weight be put into the scale from which the body hangs as will restore the equilibrium (without altering the weights in the opposite scale) that weight which restores the equilibrium will be equal to the weight of a quantity of water as big as the immersed body. And if the weight of the body in air be divided by what it loses in water, the quotient will shew how much that body is heavier than its bulk of water. Thus, if a guinea suspended in air be counterbalanced by 129 grains in the opposite scale of the balance; and then, upon its being immersed in water, it becomes so much lighter as to require 7\(\frac{1}{4}\) grains put into the scale over it, to restore the equilibrium; it shews that a quantity of water, of equal bulk with the guinea, weighs 7\(\frac{1}{4}\) grains, or 7.25; by which divide 129 (the weight of the guinea in air) and the quotient will be 17.793; which shews that the guinea is 17.793 times as heavy as its bulk of bulk of water. And thus any piece of gold may be tried, by weighing it first in air, and then in water; and if, upon dividing the weight in air by the loss in water, the quotient comes out to be 17.793, the gold is good; if the quotient be 18, or between 18 and 19, the gold is very fine; but if it be less than 17\(\frac{1}{4}\), the gold is too much alloyed, by being mixed with some other metal.

If silver be tried in this manner, and found to be 11 times as heavy as water, it is very fine; if it be 10\(\frac{1}{2}\) times as heavy, it is standard; but if it be of any less weight compared with water, it is mixed with some lighter metal, such as tin.

By this method the specific gravities of all bodies that will sink in water may be found. But as to those which are lighter than water, as most sorts of wood are, the following method may be taken, to shew how much lighter they are than their respective bulks of water.

Let an upright stud be fixed into a thick flat piece of brass, and in this stud let a small lever, whose arms are equally long, turn upon a fine pin as an axis. Let the thread which hangs from the scale of the balance be tied to one end of the lever, and a thread from the body to be weighed tied to the other end. This done, put the brass and lever into a vessel; then pour water into the vessel, and the body will rise and float upon it, and draw down the end of the balance from which it hangs; then, put as much weight in the opposite scale as will raise that end of the balance, so as to pull the body down into the water by means of the lever; and this weight in the scale will shew how much the body is lighter than its bulk of water.

There are some things which cannot be weighed in this manner, such as quicksilver, fragments of diamonds, &c., because they cannot be suspended in threads; and must therefore be put into a glass bucket, hanging by a thread from the hook of one scale, and counterpoised by weights put into the opposite scale. Thus, suppose you want to know the specific gravity of quicksilver, with respect to that of water; let the empty bucket be first counterpoised in air, and then the quicksilver put into it and weighed. Write down the weight of the bucket, and also of the quicksilver; which done, empty the bucket, and let it be immersed in water as it hangs by the thread, and counterpoised therein by weights in the opposite scale; then, pour the quicksilver into the bucket in the water, which will cause it to preponderate; and put as much weight into the opposite scale as will restore the balance to an equipoise; and this weight will be the weight of a quantity of water equal in bulk to the quicksilver. Lastly, divide the weight of the quicksilver in air, by the weight of its bulk of water, and the quotient will shew how much the quicksilver is heavier than its bulk of water.

If a piece of brass, glass, lead, or silver, be immersed and suspended in different sorts of fluids, its different losses of weight therein will shew how much it is heavier than its bulk of the fluid; the fluid being lightest, in which the immersed body loses least of its aerial weight. A solid bubble of glass is generally used for finding the specific gravities of fluids.

Hence we have an easy method of finding the specific gravities both of solids and fluids, with regard to the respective specific bulks of common pump water, which is generally made a standard for comparing all the others by.

In constructing tables of specific gravities with accuracy, the gravity of water must be represented by unity or 1,000, where three cyphers are added, to give room for expressing the ratios of other gravities in decimal parts, as in the following table.

Take away the decimal point from the numbers in the right hand column, or (which is the same) multiply them by 1,000, and they will show how many ounces avoirdupois are contained in a cubic foot of each body.

How to find out the quantity of adulteration in metals.

The use of the table of specific gravities will best appear by an example. Suppose a body to be compounded of gold and silver, and it is required to find the quantity of each metal in the compound.

First find the specific gravity of the compound, by weighing it in air and in water, and dividing its aerial weight by what it loses thereof in water, the quotient will show its specific gravity, or how many times it is heavier than its bulk of water. Then, subtract the specific gravity of silver (found in the table) from that of the compound, and the specific gravity of the compound from that of gold; the first remainder shows the bulk of gold, and the latter the bulk of silver, in the whole compound: and if these remainders be multiplied by the respective specific gravities, the products will show the proportion of weights of each metal in the body. Example,

Suppose the specific gravity of the compounded body to be 13; that of standard silver (by the table) is 10.5, and that of gold 19.63; therefore 10.5 from 13, remains 2.5, the proportional bulk of the gold; and 13 from 19.63, remains 6.63, the proportional bulk of silver in the compound. Then, the first remainder 2.5, multiplied by 19.63, the specific gravity of gold, produces 49.075 for the proportional weight of gold; and the last remainder 6.63 multiplied by 10.5, the specific gravity of silver, produces 69.615 for the proportional weight of silver in the whole body. So that, for every 49.07 ounces or pounds of gold, there are 69.6 pounds or ounces of silver in the body.

Hence it is easy to know whether any suspected metal be genuine, or alloyed, or counterfeit; by finding how much it is heavier than its bulk of water, and comparing the same with the table: if they agree, the metal is good; if they differ, it is alloyed or counterfeited.

How to try spirituous liquors.

A cubic inch of good brandy, rum, or other proof spirits, weighs 235.7 grains; therefore, if a true inch cube of any metal weighs 235.7 grains less in spirits than in air, it shows the spirits are proof. If it loses less of its aerial weight in spirits, they are above proof: if it loses more, they are under. For, the better the spirits are, they are the lighter; and the worse, the heavier.

The hydrometer is one of the most useful instruments of the philosophic kind; for though the hydrostical balance be the most general instrument for finding the

| A cubic inch of | Troy weight | Avoirdup. | Comparative weight | |----------------|-------------|-----------|--------------------| | | oz. pw. gr. | oz. drams | | | Very fine gold | 10 7 3.83 | 1 5 80 | 19.637 | | Standard gold | 9 19 6.44 | 10 14 90 | 18.888 | | Guinea gold | 9 7 17 18 | 10 4 76 | 17.793 | | Moidore gold | 9 0 19.84 | 9 14.71 | 17.140 | | Quicksilver | 7 7 11.61 | 8 1.45 | 14.019 | | Lead | 5 19 17.55 | 6 9.08 | 11.325 | | Fine silver | 5 16 23.23 | 6 6.66 | 11.087 | | Standard silver| 5 11 3.36 | 6 1.54 | 10.535 | | Copper | 4 13 7.04 | 5 1.89 | 8.843 | | Plate brass | 4 4 9.60 | 4 10.09 | 8.000 | | Steel | 4 2 20.12 | 4 8.70 | 7.852 | | Iron | 4 0 15.20 | 4 6.77 | 7.645 | | Block tin | 3 17 5.68 | 4 3.79 | 7.321 | | Spelter | 3 14 12.86 | 4 1.42 | 7.065 | | Lead ore | 3 11 17.76 | 3 14.96 | 6.800 | | Glass of antimony | 2 15 16.80 | 3 0.89 | 5.280 | | German antimony| 2 2 4.80 | 2 5.04 | 4.000 | | Copper ore | 2 1 11.83 | 2 4.43 | 3.775 | | Diamond | 1 15 20.88 | 1 15.48 | 3.400 | | Clear glass | 1 13 5.58 | 1 13.16 | 3.150 | | Lapis lazuli | 1 12 5.27 | 1 12.27 | 3.054 | | Welch asbestos | 1 10 17.57 | 1 10.97 | 2.913 | ### HYDROSTATICS

**The Table concluded.**

| A cubic inch of | Troy weight | Avoirdup | Comparative weight | |-----------------|------------|----------|--------------------| | | oz. pw. gr.| oz. drams| | | White marble | 1 8 13.41 | 1 9.06 | 2.707 | | Black ditto | 1 8 12.65 | 1 9.02 | 2.704 | | Rock crystal | 1 8 1.00 | 1 8.61 | 2.658 | | Green glass | 1 7 15.38 | 1 8.26 | 2.620 | | Cornelian stone | 1 7 1.21 | 1 7.73 | 2.568 | | Flint | 1 6 19.63 | 1 7.53 | 2.542 | | Hard paving stone | 1 5 22.87 | 1 6.77 | 2.460 | | Live sulphur | 1 1 2.40 | 1 2.52 | 2.000 | | Nitre | 1 0 1.08 | 1 1.59 | 1.900 | | Alabaster | 0 19 18.74 | 1 1.35 | 1.875 | | Dry ivory | 0 19 6.09 | 1 0.89 | 1.825 | | Brimstone | 0 18 23.76 | 1 0.66 | 1.800 | | Alum | 0 17 21.92 | 0 15.72 | 1.714 | | Ebony | 0 11 18.82 | 0 10.34 | 1.117 | | Human blood | 0 11 2.89 | 0 9.76 | 1.054 | | Amber | 0 10 20.79 | 0 9.54 | 1.030 | | Cow's milk | 0 10 20.79 | 0 9.54 | 1.030 | | Sea water | 0 10 20.79 | 0 9.54 | 1.030 | | Pump water | 0 10 13.30 | 0 9.26 | 1.000 | | Spring water | 0 10 12.94 | 0 9.25 | 0.999 | | Distilled water | 0 10 11.42 | 0 9.20 | 0.993 | | Red wine | 0 10 11.42 | 0 9.20 | 0.993 | | Oil of amber | 0 10 7.63 | 0 9.06 | 0.978 | | Proof spirits | 0 9 19.73 | 0 8.62 | 0.931 | | Dry oak | 0 9 18.00 | 0 8.56 | 0.925 | | Olive oil | 0 9 15.17 | 0 8.45 | 0.913 | | Pure spirits | 0 9 3.27 | 0 8.02 | 0.866 | | Spirit of Turpentine | 0 9 2.76 | 0 7.99 | 0.864 | | Oil of Turpentine | 0 8 8.53 | 0 7.33 | 0.772 | | Dry Crabtree | 0 8 1.69 | 0 7.08 | 0.765 | | Sassafras wood | 0 5 2.04 | 0 4.46 | 0.482 | | Cork | 0 2 12.77 | 0 2.21 | 0.240 |

Specific gravities of all sorts of bodies, yet the hydrometer is best suited to find those of fluids in particular, both as to ease and expedition.

This instrument should be made of copper, since ivory imbibes spirituous liquors, and thereby alters its gravity; and glass is apt to break. The most simple kind, used for finding the strength of spirits, consists of a copper-ball Bb Plate 101. (fig. 1. n° 1.) with a brass wire, AB, ¼ of an inch thick, soldered into it. The upper part of this wire being filed flat on one side, is marked proof at m, because it sinks exactly to this mark in proof-spirits. There are other two marks at A and B, to show whether the liquor be above or below proof, according as the hydrometer sinks to A or emerges to B, when a brass weight as C or K has been screwed on at the bottom c. There are also weights to be screwed on, for showing the specific gravities of fluids quite to common water. The round part of the wire above the ball, may be marked so as to represent river water when it sinks to RW,

(ibid. n° 2) the weight which fits the instrument for river water being screwed on at c: also when put into spring-water, mineral water, sea-water, and water of salt springs, it will emerge or rise gradually to the marks SP, MI, SE, SA; and, on the contrary, when put into Bristol-water, rain-water, port-wine, and mountain wine, it will successively sink to the marks, br, ra, po, mo.

Another kind, which serves to distinguish the specific differences of fluids to great nicety, consists of a large hollow ball B, (ibid. n° 3) with a smaller ball b under it, partly filled with quicksilver or small shot, and screwed on to the lower part of the former, in order to render it but little specifically lighter than water: it has also a small short neck at C, into which is screwed the graduated brass-wire AC, which by its weight causes the body of the instrument to descend in the fluid, with part of the stem.

When this instrument is swimming in the liquor contained in the jar LLMK, the part of the fluid displaced placed by it will be equal in bulk to the part of the instrument under water, and equal in weight to that of the whole instrument. Suppose the weight of the whole were 4000 grains, then it is evident we can by this means compare together the different bulks of 4000 grains of various sorts of fluids. For if the weight A be such as shall cause the aræometer to sink in rain-water, till its surface comes to the middle point of the stem 20; and if, after this, it be immersed in common spring water, and the surface is observed to stand \( \frac{1}{5} \) of an inch below the middle point 20; it is evident that the same weight of each water differs in bulk only by the magnitude of \( \frac{1}{5} \) of an inch in the stem.

Now suppose the stem were ten inches long, and weighed 100 grains, then every tenth of an inch would be one grain weight; and since the stem is of brass, and brass is about eight times heavier than water, the same bulk of water will be equal to \( \frac{1}{8} \) of a grain; and consequently to the \( \frac{1}{8} \) of \( \frac{1}{8} \) part, that is, a 3200th part of the whole bulk, which is a degree of exactness as great as can be desired. Yet the instrument is capable of still greater exactness, by making the stem or neck consist of a flat thin slip of brass, instead of one that is round or cylindrical: by this means we increase the surface, which is the most requisite thing; and diminish the solidity, by which the instrument is rendered more exact.

In order to adapt this instrument to all sorts of uses, there ought to be two different stems to screw on and off in a small hole at a. One stem should be such a nice thin slip of brass, or rather of steel, like a watch-spring set straight, as we have just mentioned, on one side of which ought to be the several marks or divisions to which it will sink in various sorts of waters, as rain-water, river-water, spring-water, sea-water, salt spring-water, &c. And on the other side you mark the division to which it sinks in various lighter fluids, as hot bath-water, Bristol water, Lincomb water, Chelten water, port-wine, mountain, madeira, and various other sorts of wine. But in this case the weight A on the top must be a little less than before, when it was used for the heavier waters.

But, in case of trying the strength of spirituous liquors, a common cylindric stem will do best, because of its strength and steadiness; and this ought to be so contrived, that, when immersed in what is called proof-spirit, the surface of the spirit may be upon the middle point 20; which is easily done by duly adjusting the small weight A on the top, and making the stem of such a length, that, when immersed in water, it may just cover the ball, and rise to a; but, when immersed in pure spirit, it may arise to the top at A; then by dividing the upper and lower parts a 20, A 20, into ten equal parts each, when the instrument is immersed in any sort of spirituous liquor, it will immediately show how much it is above or below proof.

This proof-spirit consists of half water and half alcohol or pure spirit; that is, such as when poured upon gunpowder, and set on fire, will burn all away, and permit the powder to take fire, which it will, and flash as in the open air. But if the spirit be not so highly rectified, there will remain some phlegm or water, which will make the powder wet, and unfit to take fire. This proof-spirit of any kind weighs seven pounds twelve ounces per gallon.

The common method of shaking the spirits in a vial, and, by raising a crown of bubbles, to judge by the manner of their rising or breaking away whether the spirit be proof or near it, is very precarious, and capable of great fallacy. There is no way so easy, quick, certain, and philosophical, as this by the aræometer, which will demonstrate infallibly the difference of bulks, and consequently specific gravities, in equal weights of spirits, to the 30, 40, or 50 thousandth part of the whole, which is a degree of accuracy beyond which nothing can be desired.

All bodies expand with heat, and contract with cold; but some more and some less than others: and therefore the specific gravities of bodies are not precisely the same in summer as in winter. It has been found, that a cubic inch of good brandy is 10 grains heavier in winter than in summer; as much spirit of nitre, 20 grains; vinegar 6 grains, and spring water 3. Hence it is most profitable to buy spirits in winter, and sell them in summer, since they are always bought and sold by measure. It has been found, that 32 gallons of spirits in winter will make 33 in summer.

The expansion of all fluids is proportionable to the degree of heat; that is, with a double or triple heat a fluid will expand two or three times as much.

Upon these principles depends the construction of the thermometer, in which the globe or bulb, and part of the tube, are filled with a fluid, which, when joined to the barometer, is spirits of wine tinged, that it may be the more easily seen in the tube. But when thermometers are made by themselves, quicksilver is generally used.

In the thermometer, a scale is fitted to the tube, to show the expansion of the quicksilver, and consequently the degree of heat. And, as Fahrenheit's scale is most in esteem at present, we shall explain the construction and graduation of thermometers according to that scale.

First, let the globe or bulb, and part of the tube, be filled with a fluid; then immerse the bulb in water just freezing, or snow just thawing; and even with that part in the scale where the fluid then stands in the tube, place the number 32, to denote the freezing point: then put the bulb under your arm pit, when your body is of a moderate degree of heat, so that it may acquire the same degree of heat with your skin; and when the fluid has risen as far as it can by that heat, there place the number 97: then divide the space between these numbers into 65 equal parts, and continue those divisions both above 97 and below 32, and number them accordingly.

This may be done in any part of the world; for it is found that the freezing point is always the same in all places, and the heat of the human body differs but very little: so that the thermometers made in this manner will will agree with one another; and the heat of several bodies will be shewn by them, and expressed by the number upon the scale, thus:

Air, in severe cold weather, in our climate, from 15 to 25. Air in winter, from 26 to 42. Air in spring and autumn, from 43 to 53. Air at midsummer, from 65 to 68. Extreme heat of the summer sun, from 86 to 100. Butter just melting, 95. Alcohol boils with 174 or 175. Brandy with 190. Water 212. Oil of turpentine 550. Tin melts with 498, and lead with 540. Milk freezes about 30, vinegar 28, and blood 27.

A body specifically lighter than a fluid will swim upon its surface, in such a manner, that a quantity of the fluid equal in bulk with the immersed part of the body, will be as heavy as the whole body. Hence, the lighter a fluid is, the deeper a body will sink in it; upon which depends the construction of the hydrometer or water-poise.

From this we can easily find the weight of a ship, or any other body that swims in water. For, if we multiply the number of cubic feet which are under the surface, by 62.5, the number of pounds in one foot of fresh water; or by 63, the number of pounds in a foot of salt water; the product will be the weight of the ship, and all that is in it. For, since it is the weight of the ship that displaces the water, it must continue to sink until it has removed as much water as is equal to it in weight; and therefore the part immersed must be equal in bulk to such a portion of the water as is equal to the weight of the whole ship.

To prove this by experiment, let a ball of some light wood, such as fir or pear-tree, be put into water contained in a glass vessel; and let the vessel be put into a scale at one end of a balance, and counterpoised by weights in the opposite scale: then, marking the height of the water in the vessel, take out the ball; and fill up the vessel with water to the same height that it stood at when the ball was in it; and the same weight will counterpoise it as before.

From the vessel's being filled up to the same height at which the water stood when the ball was in it, it is evident that the quantity poured in is equal in magnitude to the immersed part of the ball; and from the same weight counterpoising, it is plain that the water poured in is equal in weight to the whole ball.

In troy weight, 24 grains make a pennyweight, 20 pennyweights make an ounce, and 12 ounces a pound. In avoirdupois weight, 16 drams make an ounce, and 16 ounces a pound. The troy pound contains 5760 grains, and the avoirdupois pound 7000; and hence, the avoirdupois dram weighs 27.34375 grains, and the avoirdupois ounce 437.5.