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VOL. IX.

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ENCYCLOPÆDIA BRITANNICA.

HYDROSTATICS;

A SCIENCE which treats of the weight, motion, and equilibria of liquid bodies. Under this head, not only accounts of the nature and properties of fluids in general are introduced, and the laws by which they act; but also the art of weighing solid bodies in fluids, in order to discover their specific gravities.

SECT. I. Of FLUIDS in general.

Sir Isaac Newton's definition of a fluid is, That it is a body yielding to any force impressed, and which hath its parts very easily moved one among another. See FLUIDITY.

This definition supposes the motion spoken of produced by a partial pressure; for in the case of an incompressible fluid, it is demonstrated by Dr Keil, that under a total or an equal pressure, it would be impossible that the yielding body should move.

The original and constituent parts of fluids are by the moderns conceived to be particles small, smooth, hard, and spherical: according to which opinion, every particle is of itself a solid or a fixed body; and, when considered singly, is no fluid, but becomes so only by being joined with other particles of the same kind. From this definition, it hath been concluded by some philosophers, that some substances, such as mercury, are essentially fluid, on account of the particular configuration of their particles; but later discoveries have evinced the fallacy of this opinion, and that fluidity is truly to be reckoned an effect of heat. See FLUIDITY.

That fluids have vacuities, will appear upon mixing salt with water, a certain quantity whereof will be dissolved, and thereby imbibed, without enlarging the dimensions. A fluid's becoming more buoyant, is a certain proof that its specific gravity is increased, and of consequence that many of its vacuities are thereby filled: after which it may still receive a certain quantity of other dissolvable bodies, the particles whereof are adapted to the vacancies remaining, without adding any thing to its bulk, though the absolute weight of the whole fluid be thereby increased.

This might be demonstrated, by weighing a phial of rain-water critically, with a nice balance: pour this water into a cup, and add salt to it; refund of the clear liquor what will again fill the phial; an increase of weight will be found under the same dimensions, from a repletion, as has been said, of the vacuities of the fresh water with saline particles.

VOL. IX. Part I.

And as fluids have vacuities, or are not perfectly dense; it is also probable, that they are compounded of small spheres of different diameters, whose interstices may be successively filled with apt materials for that purpose: and the smaller these interstices are, the greater will be the gravity of the fluid always be.

For instance, suppose a barrel be filled with bullets in the most compact manner, a great many small shots may afterwards be placed in the interstices of those balls, the vacuities of the shot may then be replenished with a certain quantity of sea-sand; the interstices of the grains of the sand may again be filled with water; and thus may the weight of the barrel be greatly augmented, without increasing the general bulk.— Now this being true with regard to solids, is applicable also to fluids. For instance, river-water will dissolve a certain quantity of salt; after which it will receive a certain quantity of sugar; and after that, a certain quantity of alum, and perhaps other dissolvable bodies, and not increase its first dimensions.

The more perfect a fluid is, the more easily will it yield to all impressions, and the more easily will the parts unite and coalesce when separated. A perfect fluid is that whose parts are put into motion by the least force imaginable: an imperfect one is that whose parts yield to a small force, not the least. It is probable, that in nature there is no perfect fluid, the element of fire perhaps excepted; since we see that the mutual attraction of the parts of all the fluids, subject to our experiments, renders them cohesive in some degree; and the more they cling together, the less perfect their fluidity is. If, for instance, a glass be filled with water above the brim, it will visibly rise to a convex surface, which, was it a perfect fluid, free from either tenacity or cohesion, would be impossible.

Mercury, the most perfect fluid we know, is not exempt from this attraction; for should the bottom of a flat glass, having a gentle rising toward the middle, be covered thin with quicksilver, a little motion of the machine will cause the fluid soon to separate from the middle, and lie round it like a ring, having edges of a considerable thickness.

But if a like quantity thereof be poured into a golden cup, it will, on the contrary, appear higher considerably on the sides than in the middle. Which may proceed in part, perhaps, from the gold's being of great density, and therefore capable of exerting thereon a greater degree of attraction than other metals. Probably too it may happen from its having pores of

an apter disposition and magnitude to receive the minute mercurial particles, than those of iron and some other metals; and therefore the attraction of cohesion in this experiment may obtain also: and every one knows how easily these two bodies incorporate, and make a perfect amalgama. But the reason commonly given for the two phenomena is, that mercury, in the first case, attracts itself more than it does glass; and, in the last case, mercury attracts gold more than it does itself.

Sir Isaac Newton held all matter to be originally homogeneous; and that from the different modifications and texture of it alone, all bodies receive their various structure, composition, and form. In his definition of a fluid, he seems to imply, that he thought fluids to be composed of primary solids; and, in the beginning of his Principia, he speaks of sand and powders as of imperfect fluids.

Borelli has demonstrated, that the constituent parts of fluids are not fluid, but consistent bodies; and that the elements of all bodies are perfectly firm and hard. The incompressibility of water, proved by the Florentine experiment, is a sufficient evidence also, that each primary particle or spherule thereof is a perfect and impenetrable solid. Mr Locke too, in his Essay on Human Understanding, admits this to be so.

This famous experiment was first attempted by the great lord Verulam, who inclosed a quantity of water in lead, and found that it inclined rather to make its way through the pores of the metal, than be reduced into less compass by any force that could be applied. The academics of Florence made this experiment afterwards more accurately with a globe of silver, as being a metal less yielding and ductile than gold. This being filled with water, and well closed, they found, by hammering gently thereon, that the sphericity of the globe was altered to a less capacious figure (as might geometrically be proved); but a part of the water always like dew came through its sides before this could be obtained. This has been attempted by Sir Isaac Newton, and so many competent judges, on gold and several other metals since, with equal success, that we do not hold any fluid in its natural state, except the air, to be either compressible or elastic.— In some experiments by Mr Canton, it hath been observed, that water is more or less compressed according to the different constitution of the atmosphere; whence it hath been concluded that the Florentine experiment was erroneous: but it will not follow, that water can be compressed by any artificial force, because nature hath a method of compressing it; any more than that solid metal can be compressed artificially, though we know that very slight degrees of heat and cold will expand or contract its dimensions. See WATER.

SECT. II. Of the Gravity and Pressure of Fluids.

All bodies, both fluid and solid, press downwards by the force of gravity: but fluids have this wonderful property, that their pressure upwards and sideways 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 in 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.

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 your 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 run 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 C into the shape DE, and the hole at

Pressure of Fluids. C be flopt 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 shown by the next experiment.

The hydrostatic paradox. 5 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 show by an experiment, and then account for it upon the principle above mentioned, namely, that the pressure of fluids is directly as their perpendicular height, without any regard to their quantity.

Plate CCCCXIX. Fig. 4. Let a small glass tube $DCG$, 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 shows, that the small column $DCG$ balances and supports the great column $Aed$; 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 $AB$ 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 lie 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 brass bottoms opposite to the hinges $D$ and $D$. Things being thus prepared and fitted, hold the vessel $AB$ (fig. 6.) 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. 5.) 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. 5.) 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. 4.) 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. 6.) is pressed by all the water above it.

To illustrate this a little farther, let a hole be made at $f$ 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 whole 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 in the tube $A$, by pouring more into it, to make up the deficiency that it sustains by supplying the others, until they are 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 $Bf$ 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

4. Pressure of Fluids. same height that it stands in the small one, after a sufficient quantity had been poured into it: which shows, that the top Bf was pressed upward by the water under it, and before any hole was made in it, with a force equal 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 Bf 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 df.

6. The hydrostatic bellows, fig. 7. Perhaps the best machine in the world for demonstrating the upward pressure of fluids, is the hydrostatic bellows, which consists of two thick oval boards AB, EF, each about 16 inches broad, and 18 inches long: the sides are of leather, joined very close to the top and bottom by strong nails. CD is a pipe screwed into a piece of brass on the top-board at C. Let some water be poured into the pipe at D, which will run into the bellows, and separate the boards a little. Then lay three weights, each weighing 100 pounds, upon the upper board; and pour more water into the pipe, 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.

7. How a man may raise himself upward by his breath. 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, 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 hole, will be pressed upward with a force equal to that of a quarter of a pound: the sum of all which pressures against the underside of an oval board 16 inches broad, and 18 inches long, will amount to 300lb.; 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, 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 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 may be it, but for it to stand upon; with a wet leather between the lead and the 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 EabG 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. But the following method of making an extremely heavy body float upon water is more elegant. Take a long glass tube, open at both ends; stopping the lower end with a finger, pour in some quicksilver at the other end, so as to take up about half an inch in the tube below. Immerse this tube, with the finger still at the bottom, in a deep glass vessel filled with water; and when the lower end of the tube is about seven inches below the surface, take away the finger from it, and then you will see the quicksilver not sink into the vessel, but remain suspended upon the tube, and floating, if we may so express it, upon the water in the glass vessel.

In the same manner as an heavy body was made to swim on water, by taking away the upward pressure; so may a light body, like wood, be made to remain so sunk at the bottom, by depriving it of all pressure from below: for if two equal pieces of wood be planed, surface to surface, so that no water can get between them, and then one of them (cd) be cemented to the inside of the vessel's bottom; then the other being placed upon this, and, while the vessel is filling, being kept down by a stick; when the stick is removed and the vessel full, the upper piece of wood will not rise from the lower one, but continue sunk under water, though it is actually much lighter than water; for as there is no resistance to its under surface to drive it upward, while its upper surface is strongly pressed down, it must necessarily remain at the bottom.

HYDROSTATICS.

Plate CCXXXIX.

Fig. 1.

Fig. 13.

Fig. 2.

Fig. 14.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 8.

Fig. 7.

Fig. 10. Fig. 11. Fig. 12.

Fig. 9.

WHEN an unspongy or solid body sinks in a vessel of water, it removes a body of water equal to its own bulk, out of the place to which it descends. If, for instance, a copper ball is let drop into a glass of water, we well know, that if it sinks, it will take up as much room as a globe of water equal to itself in size took up before.

Let us suppose, that this watery globe removed by the ball were frozen into a solid substance, and weighed in a scale against the copper ball: now the copper ball being more in weight than the globe, it is evident that it will sink its own scale, and drive up the opposite, as all heavier bodies do when weighed against lighter; if, on the contrary, the copper ball be lighter than the water globe, the ball will rise. Again, then let us suppose the copper ball going to be immersed in water; and that, in order to descend, it must displace a globe of water equal to itself in bulk. If the copper ball be heavier than the globe, its pressure will overcome the other's resistance, and it will sink to the bottom; but if the watery globe be heavier, its pressure upwards will be greater than that of the ball downward, and the ball will rise or swim. In a word, in proportion as the ball is heavier than the similar bulk of water, it will descend with greater force; in proportion as it is lighter, it will be raised more to the surface.

From all this we may deduce one general rule, which will measure the force with which any solid body tends to swim or sink in water; namely, Every body immersed in water, loses just as much of its weight as equals the weight of an equal bulk of water. Thus, for instance, if the body be two ounces, and an equal bulk of water be one ounce, the body when plunged, will sink towards the bottom of the water with a weight of one ounce. If, on the contrary, the solid body be but one ounce, and the weight of an equal bulk of water be two ounces; the solid, when plunged, will remove but one ounce, that is half as much water as is equal to its own bulk: so that, consequently, it cannot descend; for to do that, it must remove a quantity of water equal to its own bulk. Again, if the solid be two ounces, and the equal bulk of water two ounces, the solid, wherever it is plunged, will neither rise nor sink, but remain suspended at any depth.

Thus we see the reason why some bodies swim in water, and others sink. Bodies of large bulk and little weight, like cork or feathers, must necessarily swim, because an equal bulk of water is heavier than they; bodies of little bulk but great weight, like lead or gold, must sink, because they are heavier than an equal bulk of water. The bulk and the weight of any body considered together, is called its specific gravity; and the proportion of both in any body is easily found by water. A body of little bulk and great weight, readily sinks in water, and it is said to have specific gravity; a body of great bulk and little weight, loses almost all its weight in water, and therefore is said to have but little specific gravity. A woolpack has actually greater real gravity, or weighs more in air, than a cannon ball; but for all that, a cannon ball may have more specific gravity, and weigh more than the woolpack, in water.

Density is a general term that means the same thing; Specific gravity is only a relative term, used when solids are weighed in fluids, or fluids in fluids.

As every solid sinks more readily in water, in proportion as its specific gravity is great, or as it contains greater weight under a smaller bulk, it will follow, that the same body may very often have different specific gravities, and that it will sink at one time and swim at another. Thus a man, when he happens to fall alive into the water, sinks to the bottom; for the specific gravity of his body is then greater than that of water: but if, by being drowned, he lies at the bottom for some days, his body swells by putrefaction, which disunites its parts; thus its specific gravity becomes less than that of water, and he floats upon the surface.

Several more important uses are the result of our being able exactly to determine the specific gravities of bodies. We can, by weighing metals in water, discover their adulterations or mixtures with greater exactness than by any other means whatsoever. By this means, the counterfeit coin, which may be offered us as gold, will be very easily distinguished, and known to be a base metal. For instance, if we are offered a brass counter for a guinea, and we suspect it; suppose, to clear our suspicions, we weigh it in the usual manner against a real guinea in the opposite scale, and it is of the exact weight, yet still we suspect it; What is to be done? To melt or destroy the figure of the coin would be inconvenient and improper: a much better and more accurate method remains. We have only to weigh a real guinea in water, and we shall thus find that it loses but a nineteenth part of its weight in the balance: We then weigh the brass counter in water, and we actually find it loses an eighth part of its weight by being weighed in this manner. This at once demonstrates, that the coin is made of a base metal, and not gold; for as gold is the heaviest of all metals, it will lose less of its weight by being weighed in water than any other.

This method Archimedes first made use of to detect a fraud with regard to the crown of Hiero king of Syracuse. Hiero had employed a goldsmith to make him a crown, and furnished him with a certain weight of gold for that purpose; the crown was made, the weight was the same as before, but still the king suspected that there was an adulteration in the metal. Archimedes was applied to; who, as the story goes, was for some time unable to detect the imposition. It happened, however, one day as the philosopher was stepping into a bath, that he took notice the water rose in the bath in proportion to the part of his body immersed. From this accident he received a hint; wherewith he was so transported, that he jumped out of the bath, and ran naked about the streets of Syracuse, crying in a wild manner, I have found it! I have found it!—In consequence of this speculation, he procured a ball of gold and another of silver, exactly of the weight of the crown, considering, that if the crown were altogether of gold, the ball of gold would be of the same bulk as the crown, and when immersed in water, would raise the water just as high as the crown immersed; but if it were wholly of silver, the ball of silver being immersed, would raise the water no higher than the crown immersed; and if the crown was of gold

gold and silver mixed in a certain proportion, this proportion would be discovered by the height to which the crown would raise the water higher than the gold and lower than the silver. Accordingly, let AMLB be a vessel filled with water to the height DC, and let the mass of gold, equal in weight to the crown, on being immersed into the water, raise the surface of it to E, and the mass of silver raise it to G; then if the height of the vessel above DC be divided into equal parts, and $DF=1$, and $DG=19$, it is plain the bulks of gold and silver will be as $DF$ to $DG$, and the specific gravities in the inverse proportion of these quantities, or as $DG$ to $DF$. If the crown be immersed, it will raise the surface of water to E; whence the proportion of the bulks of the gold and silver in the crown may be determined. For since the difference of the specific gravities of the gold and silver is $DG-DF=FG=8$, if the bulk of the crown is divided into eight equal parts, it is evident, that since the specific gravities of the debased and pure gold crowns will be as the bulks inversely, that is, as $DF$ to $DE$, we can easily find the point H, which will express the specific gravity of the former; for $DE:DF::DG:DH$. This point H always divides the difference $FG$ into two parts $GH$, $HE$, which have the same proportion as the parts of silver in the crown to the parts of gold; for as the point E ascends, the point H descends, and when E coincides with G, H falls upon E, and the crown becomes wholly silver; on the contrary, when E descends to F, and H ascends to G, the crown becomes wholly gold; therefore FH will be every where to HG as the parts of gold to the parts of silver in the crown. Consequently, in the present case, because the crown, when immersed, raises the water to the height DE, and H is three divisions below G, it shows that three of the eight parts of the crown are silver, and the other five parts gold, as H is five of the divisions above F. Hence the bulk of the gold in the crown is to that of the silver as 5 to 3. In some such method as this Archimedes deduced his proposition, viz. that the difference of the specific gravities of the compound and lighter ingredient, i. e. 5 (supposing the specific gravity of gold to silver as 19 to 11, and the specific gravity of the king's crown to be 16), is to the difference of the specific gravities of the heavier ingredient and the compound, i. e. 3, as the bulk of gold to that of silver made up of: so that if the whole crown were divided into eight parts, the gold would consist of five, and the silver of three; and the magnitudes 5 and 3, multiplied by the specific gravities 19 and 11 respectively, will give the numbers 95 and 33, expressing the proportion of the weight of the gold to that of the silver.

This proposition of Archimedes may be demonstrated analytically in the following manner: let the magnitudes of the gold and silver in the crown be A and B, and their specific gravities as $a$ and $b$; then, since the absolute gravity of any body is compounded of its magnitude and specific gravity, the weight of the gold is $aA$, of the silver $bB$, and of the crown $aA+bB=cA+B$, supposing $c$ to be the specific gravity of the mixture. Hence $aA-cA=cB-bB$; and consequently $c-b:a-c::A:B$, as before.

Upon this difference in the weight of bodies in open air and water, the hydrostatic balance has been formed; which differs very little from a common balance, but that it hath an hook at the bottom of one scale, on which the weight we want to try may be hung by an horse-hair, and thus suspended in water, without wetting the scale from whence it hangs. First, the weight of the body we want to try is balanced against the parcel or weight in open air; then the body is suspended by the hook and horse-hair at the bottom of the scale in water, which we well know will make it lighter, and destroy the balance. We then can know how much lighter it will be, by the quantity of the weights we take from the scale to make it equipoise; and of consequence we thus precisely can find out its specific gravity compared to water (A). This is the most exact and infallible method of knowing the genuineness of metals, and the different mixtures with which they may be adulterated, and it will answer for all such bodies as can be weighed in water. As for those things that cannot be thus weighed, such as quicksilver, small sparks of diamond, and such like, as they cannot be suspended by an horse-hair, they must be put into a glass bucket, the weight of which is already known: this, with the quicksilver, must be balanced by weights in the opposite scale, as before, then immersed, and the quantity of weights to be taken from the opposite scale will show the specific gravity of the bucket and the quicksilver together: the specific gravity of the bucket is already known; and of consequence the specific gravity of the quicksilver, or any other similar substance, will be what remains.

As we can thus discover the specific gravity of different solids by plunging them in the same fluid, so we can discover the specific gravity of different fluids, by plunging the same solid body into them; for in proportion as the fluid is light, so much will it diminish the weight of the body weighed in it. Thus we may know that spirit of wine has less specific gravity than water, because a solid that will swim in water will sink in spirit; on the contrary, we may know that spirit of nitre has greater specific gravity than water, because a solid that will sink in water will swim upon the spirit of nitre. Upon this principle is made that simple instrument called an hydrometer, which serves to measure the lightness or weight of different fluids. For that liquors weigh very differently from each other is found by experience. Suppose we take a glass vessel which is divided into two parts, communicating with each other by a small opening of a line and an half diameter. Let the lower part be filled up to the division with red-wine, then let the upper part be filled with water. As the red-wine is lighter than water, we shall see it in a short time rising like a small thread up through the water, and diffusing itself upon the surface, till at length we shall find the wine and water have changed their places; the water will be seen in the lower half, and the wine in the upper half, of the vessel. Or take a small bottle AB, the neck of which must be very narrow, the mouth not more than $\backslash frac\{1\}\{8\}$ of an inch wide; and have a glass vessel CD, whose height exceeds that of the bottle about two inches. With

(A) This is the common hydrostatic balance. The reader will see an improved apparatus at Hydrostatic Balance, in order of the alphabet.

With a small funnel fill the bottle quite full of red-wine, and place it in the vessel CD, which is to be full of water. The wine will presently come out of the bottle, and rise in form of a small column to the surface of the water; and at the same time the water, entering the bottle, will supply the place of the wine; for water being specifically heavier than wine, must hold the lowest place, while the other naturally rises to the top. A similar effect will be produced if the bottle be filled with water, and the vessel with wine: for the bottle being placed in the vessel in an inverted position, the water will descend to the bottom of the vessel, and the wine will mount into the bottle.

In the same manner we may pour four different liquors, of different weights, into any glass vessel, and they shall all stand separate and unmixed with each other. Thus, if we take mercury, oil of tartar, spirit of wine, and spirit of turpentine, shake them together in a glass, and then let them settle a few minutes, each shall stand in its proper place, mercury at the bottom, oil of tartar next, spirit of wine, and then spirit of turpentine above all. Thus we see liquors are of very different densities; and this difference it is that the hydrometer is adapted to compare. In general, all vinous spirits are lighter than water; and the less they contain of water, the lighter they are. The hydrometer, therefore, will inform us how far they are genuine, by showing us their lightness; for in pure spirit of wine it sinks less than in that which is mixed with a small quantity of water.

The hydrometer should be made of copper: for ivory imbibes spirituous liquors, and thereby alters their gravity; and glass requires an attention that is incompatible with expedition. The most simple hydrometer consists of a copper ball B, to which is soldered a brass wire AB, one quarter of an inch thick. The upper part of this wire being filed flat, is marked proof, at p, fig. 4. because it sinks exactly to that mark in proof-spirits. There are two other marks at A and B, fig. 3, to show whether the liquor be one-tenth above or below proof, according as the hydrometer sinks to A, or emerges to B, when a brass weight, as C or K, is screwed to its bottom c. There are other weights to screw on, which show the specific gravity of different fluids, quite down 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, fig. 4. the weight which answers to that water being then screwed on; and when put into spring-water, mineral-water, sea-water, and water of salt springs, it will gradually rise to the marks SP, MI, SE, SA. On the contrary, when it is put into Bristol water, rain-water, port-wine, and mountain-wine, it will successively sink to the marks br, ra, po, mo. Instruments of this kind are sometimes called areometers.

There is another sort of hydrometer that is calculated to ascertain the specific gravity of fluids to the greatest precision possible, and which consists of a large hollow ball B, fig. 5, with a smaller ball b screwed on to its bottom, partly filled with mercury or small shot, in order to render it but little specifically lighter than water. The larger ball has also a short neck at C, into which is screwed the graduated brass-wire AC, which, by a small weight at A, 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 ILMK, the part of the fluid displaced by it will be equal in bulk to the part of the instrument under water, and equal in weight to the whole instrument. Now, suppose the weight of the whole to be four thousand grains, it is then evident we can by this means compare the different dimensions of four thousand grains of several sorts of fluids. For if the weight at A be such as will cause the ball to sink in rain-water till its surface come to the middle point of the stem 20; and after that, if it be immersed in common spring-water, and the surface be observed to stand at one-tenth of an inch below the middle point 20; it is apparent, that the same weight of each water differs only in bulk by the magnitude of one-tenth of an inch in the stem.

Now, suppose the stem to be ten inches long, and to weigh a hundred grains, then every tenth of an inch will weigh one grain: and as the stem is of brass, which is about eight times heavier than water, the same bulk of water will be equal to one-eighth of a grain, and consequently to the one-eighth of one four-thousandth part, that is, one thirty-two thousandth part of the whole bulk. This instrument is capable of still greater precision, by making the stem or neck consist of a flat thin slip of brass, instead of one that is cylindrical: for by this means we increase the surface, which is the most requisite circumstance, and diminish the solidity, which necessarily renders the instrument still more accurate.

To adapt this instrument to all purposes, there should be two stems, to screw on and off, in a small hole at a. One stem should be a smooth thin slip of brass, or rather steel, like a watch-spring set straight, similar to that we have just now mentioned; on one side of which is to be the several marks or divisions to which it will sink in different sorts of water, as rain, river, spring, sea, and salt-spring waters, &c.; and on the other side you may mark the divisions to which it sinks in various lighter fluids, as hot Bath water, Bristol water, Lincomb water, Cheltenham water, port-wine, mountain, madeira, and other sorts of wines. But here the weight at A on the top must be a little less than before when it was used for heavier waters.

But in trying the strength of the 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 rise to the top A. Then, by dividing the upper and lower parts a 20 and A 20, into ten equal parts each, when the instrument is immersed into any sort of spirituous liquor, it will immediately show how much it is above or below proof.

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

The common method of shaking the spirits in a phial, and raising a head of bubbles, to judge by their manner of rising or breaking whether the spirit be proof, or near it, is very fallacious. There is no way for certain, and at the same time so easy and expeditious, as this by the hydrometer.

A variety of different constructions of the hydrometer have recently been made with a particular view of improving the instrument, so as to ascertain the strengths of spirits, and worts in brewing, in the most easy and accurate manner. As it would be unnecessary to describe all of them here, we shall conclude this section with descriptions of those only which have been most approved and are now in general use. The Customs have for a long time adopted an hydrometer of an old construction, by the late Mr Clarke. It differs very little from the one above described (fig. 3. 4.); and has belonging to it a great variety of weights, which are occasionally secured on to the bottom of the stem: This renders the instrument troublesome and complicated in its use, and where dispatch in business and accuracy are wanted, not so commodious as such an instrument should be.

An hydrometer upon a very simple construction, easy in its application, and sufficiently accurate for the common purposes it is wanted to answer, by distillers and others concerned in the sale and state of spirits, is made by Mr Wm. Jones mathematical instrument maker in Holborn. It requires only three weights, to discover the strengths of spirits from alcohol down to water. This hydrometer, like others, is adjusted to a temperate state of the air, or $60^\{\backslash circ\}$ of the thermometer with Fahrenheit's scale; but as an alteration of this temperature very materially affects the gravity of spirits, causing them by the instrument to appear stronger when the weather is hotter, and the contrary, it has been found indispensably necessary to place a thermometer in the spirits previous to the immersing of the instrument, and make a just allowance for the several degrees that the mercury may be above or below the temperature above mentioned. This has been usually, though inaccurately, estimated at the rate of one gallon allowance for every three degrees of the thermometer above or below $60^\{\backslash circ\}$; viz. for every three degrees warmer, reckoning the spirit one gallon in the 100 weaker than what is shown by the hydrometer; and for every three degrees colder than $60^\{\backslash circ\}$, allowing one gallon in the 100 stronger. In this hydrometer, the thermometer is united with the instrument; and from experiment its divisions are adjusted to the different degrees above or below the temperate state. The concentration is also considered in this instrument, which is the mutual penetration of spirit and water when mixed together; which in strong spirits is so considerable as to cause a diminution of 4 gallons in the 100: for example, if to 100 gallons of spirit of wine, found by the instrument to be 66 gallons in the 100 over proof, you add 66 gallons of water in order to reduce it to a proof state; the mixture, instead of producing 166 gallons, will produce 162 gallons only of proof spirits, and therefore 4 gallons will be lost in the mutual penetration of the particles of the water and spirit.

Fig. 6. is a representation of the whole instrument, with the thermometer united. Its length A B is about $9\backslash frac\{1\}\{2\}$ inches; its ball C, is of the shape nearly of an egg, and made of hard brass, and about $1\backslash frac\{1\}\{2\}$ inch e
N^o 161.

in its horizontal diameter. It has a square stem A D, on the four sides of which are graduated the different strengths of the spirit. The other three sides not shown in this figure are represented in fig. 7. with the three weights belonging to them, marked n^o 1. 2. and 3. corresponding to the sides similarly marked at the top. When the instrument is placed in the spirit to be tried, if it sinks to the divisions on the stem without a weight, the strength will be shown on the side marked O on the top; and it will indicate any strength from 74 gallons in the 100, to 47 to the 100 above proof. The small figures, as 4 at 66, $3\backslash frac\{1\}\{2\}$ at 61, $2\backslash frac\{1\}\{2\}$ at 48, &c. show the concentration by mixture above mentioned, viz. the rate of diminutions that will take place, by making a mixture with water, to reduce the spirit at those strengths to proof. If the hydrometer does not sink to the stem without a weight, it must be made to do so by applying either of the three weights requisite. The side n^o 1. with the weight n^o 1. shows the strength of spirits from 46 to 13 gallons to the 100 above proof, as before. The concentration figures are 2, $1\backslash frac\{1\}\{2\}$, &c. the use as before. The side n^o 2. with the weight n^o 2. shows the remainder of the over-proof to proof, the division of which is marked P on the instrument, and every gallon in 100 under proof down to 29. The side n^o 3. with its weight, shows the remainder from 30 gallons in the 100 under proof down to water, marked W, which may be considered 100 in 160. The application of the thermometer (F) now appears easy and expeditious; for as it is immersed in the spirits with the hydrometer, they both may be observed at one experiment or trial. The scale of the thermometer is divided into four columns; two on one side, as shown in the figure, and two on the other. At the top of the columns are marks O. 1. 2. 3. agreeing with the weights, or no weight, in use; and that column of divisions of the thermometer is to be observed which corresponds with the weights in use; if no weight is used, then the column marked O is observed. The divisions of the thermometer commence from the middle of each column at the temperate point, which is marked O: then for as many divisions as the quicksilver in the tube appears above O, so many gallons in the 100 must the spirit be reckoned weaker; and for so many divisions as the quicksilver may appear below O, as many gallons in the 100 must be reckoned stronger.

Hydrometers of a similar construction, and with no more weights, Mr Jones makes for discovering to great exactness the different strengths or specific gravity of worts in brewing, of different minerals, sea waters, &c. For these purposes the thermometer is not united with the instrument; but is found to be more useful separately, and of a larger dimension. Notwithstanding the above hydrometer answering the general purposes in an accurate and easy manner, yet the industry of several ingenious persons interested in the sale of spirits has been exerted to construct an instrument of the greatest possible exactness. The effects of heat and cold upon different strengths of spirits not being so uniform as generally understood, and every different degree of strength of spirit between water and alcohol having its peculiar degree of contraction and dilatation, errors of some importance must be found in the hydrometers constructed upon the usual principle of temperature. With a view to obviate this defect, Mr Dicas of Liverpool constructed some years back an hydrometer of the form
ge-

Fig. 1.

Fig. 3.

Fig. 6.

Specific Gravity. generally used, with 36 weights, which were valued from 0 to 370, including the divisions on the stem; but the improvement consists solely in an ivory sliding rule which accompanies the instrument. In the graduation of this rule, is considered the different effects of heat and cold above-mentioned on the spirits. Every degree of strength included by the hydrometer between 0 and 370, has the same series of numbers placed on the sliding part of the rule; opposite to which, on the fixed rule, are marked the different strengths, and which are thus determined by immediate inspection. They proceed on one side from water to proof, and on the other from proof to alcohol, and divided in such a manner, as to show how many gallons in the 100 the spirits are above or below proof. There is also a line, containing the concentration for every degree of strength; and, what is the chief advantage of the rule, at one end of the side is placed a scale, containing the degree of heat from 30 to 80 of Fahrenheit's scale, with a flower de luce opposite, as an index, to fix it to the temperature of the spirits. By the assistance of this sliding rule, the exact state of the spirits is correctly obtained. A perfect comprehension of this rule can only be had by an inspection of it, and it always accompanies the hydrometer on sale. Mr Dicas has obtained a patent for his improvement.

18 Mr Quin's universal hydrometer. An hydrometer of a more universal construction has been made by Mr Quin, who for many years has been accustomed to construct hydrometers of various kinds. This hydrometer is made of hard brass; and therefore not so liable to be injured as fine copper, of which hydrometers are usually made: it is constructed so as to ascertain, in a plain and expeditious manner, the strength of any spirit from alcohol to water, with the concentration and specific gravity of each different strength; and discovers also the weight of worts, &c. with four weights only; which, according to the old construction of hydrometers, would require a far greater number of weights. Fig. 8. is a representation of the instrument, with its four sides of the stem graduated and figured at top, to correspond with the weights below. The side of the square-stem engraved A, B, C, D, &c. to Z, shows the strength of any spirit from alcohol to water; and the three other sides, numbered 1, 2, 3, are adapted for worts, &c. The heat and cold altering the density of spirits, and giving to every degree of strength a peculiar degree of contraction and dilatation; this circumstance is considered in dividing the sliding rule belonging to and sold with the hydrometer. This sliding rule is nearly similar to that of Mr Dicas's above-mentioned, and differs but very little from it. Some directions for the use of this hydrometer may further exemplify its simplicity and accuracy.

Find the heat of the spirit by a thermometer, and bring the star on the sliding rule to the degree of heat on the thermometer scale, and against the number of the weight and letter on the stem you have the strength of the spirit pointed out on the sliding rule, which is lettered and numbered as the instrument and weights are.

The weights apply on the under stem at C. Example. Suppose the heat of the spirit 65° by the thermometer, and of such strength as to sink the hydrometer to D on the stem, without any weight; then put the star (on the rule) to 65° of the thermometer, Vol. IX. Part I.

and against D you have 75 gallons to the 100 over proof; at this strength the concentration is 5 gallons (marked above 75); and the specific gravity is nearly 811, as marked below D: so that if 75 gallons of water are added to 100 gallons of this spirit, the mixture will be hydrometer proof; but will only produce in measure 170 gallons. Again, let the heat be 50°, and the spirit require the weight n° 1. to sink the instrument to I on the stem; then put the star to 50° of heat, and against I on the sliding rule you have 52½ gallons to 100 over proof, concentration 2½ gallons, and the specific gravity 854.

If the instrument with the weight n° 2. should sink to Q on the stem, and the heat 41°, it shows the strength 19 gallons to the 100 over proof, concentration ¼, specific gravity 905.

If the spirit be at 32° of heat, and the weight n° 3. sinks the instrument to letter S on the stem on the sliding rule, it shows the liquor to be 13 gallons in the 100 under proof, concentration ¼, specific gravity 945. So of the rest. In ascertaining the strength or gravity of worts, the weight n° 4. is always to continue on the hydrometer; and the weights n° 1, 2, 3, are adapted to the sides n° 1, 2, 3, of the square stem; which discovers the exact gravity of the worts.

The instrument is adjusted so as to sink in rain water at 60° of the thermometer with the weight n° 1. to W, on the side of the stem n° 1. and shows to 26° heavier than water. The side n° 2. with its corresponding weight n° 2. shows from 26° to 53°, and the side n° 3. ascertains from 53° to 81°, or 40½ pounds per barrel heavier than water; two degrees on the stem being a pound per barrel.

To use the hydrometer in ascertaining the gravity of two or more worts.

Rule. Multiply the gravity of each wort by its respective number of barrels or gallons; divide the sum of the products by the number of gallons or barrels; the quotient will be the mean gravity required.

When the heat of the worts cannot be conveniently tried at 60° of the thermometer, the following small table shows the number of divisions to be added for the heat:

This table is not philosophically true; yet the error from it will not exceed a quarter of a pound per barrel in any gravity, and for fermentation; but for more accuracy in this particular Mr Quin completes a scale which may be applied to any particular degree of heat.

Mr Nicholson has lately improved the construction of the hydrometer, and made it a new instrument for measuring the specific gravity of bodies; and for that purpose it appears the most accurate of any yet constructed. See fig. 9. where AA represents a small scale, which may be taken off at D; diameter $1\backslash frac\{1\}\{2\}$ inch, weight 44 grains. B a stem of hardened steel wire; diameter $\backslash frac\{1\}\{16\}$ inch. E a hollow copper globe; diameter $2\backslash frac\{1\}\{8\}$ inches, weight with stem 369 grains. FF a stirrup of wire screwed to the globe at C. G a small scale serving likewise as a counterpoise; diameter $1\backslash frac\{1\}\{2\}$ inch, weight with stirrup 1634 grains. The other dimensions may be had from the figure, which is $\backslash frac\{1\}\{2\}$ of the linear magnitude of the instrument itself.

In the construction, it is assumed, that the upper scale shall constantly carry 1000 grains when the lower scale is empty, and the instrument sunk in distilled water at the temperature of $60^\backslash circ$ Fahrenheit to the middle of the wire or stem. The length of the stem is arbitrary, as is likewise the distance of the lower scale from the surface of the globe. But the length of the stem being settled, the lower scale may be made lighter, and consequently the globe less, the greater its distance is taken from the surface of the globe; and the contrary. It is to be noted that the diameter of each scale must not be less than the side of a cube of water weighing 1000 grains.

The distances of the upper and lower scales respectively from the nearest surface of the globe being settled, add half the side of a cube of water weighing 1000 grains to the distance of the upper scale. This increased distance, and the said distance of the lower scale, may be considered as the two arms of a lever; and, by the property of that mechanical power,

As the number expressing the lower distance,

Is to the whole weight above; namely 1000 grains added to the weight of the upper scale;

So is the number expressing the upper distance,

To the lower weight, when the instrument has no tendency to any one position.

This last found weight must be considerably increased, in order that the instruments may acquire and preserve a perpendicular position.

Add together into one sum the weight of the lower scale thus found, the weight of the upper scale and its load, and the estimate weight of the ball and wires. Find the solid content of an equal weight of water; and thence, by the common rules of mensuration the diameter of an equal sphere. This will be the diameter, from outside to outside, of the globe that will float the whole.

As this process, and every other part of the present description, may be easily deduced from the well known laws of hydrostatics, it is unnecessary to enlarge here on the demonstrative part.

To measure the specific gravities and thermometrical expansions of fluids. If the extreme length or height of the instrument be moderate, its weight, when loaded, will be about 3100 grains. It is, however, necessary in practice, that its weight should be accurately found by experiment. This whole weight is equal to that of a quantity of distilled water at the temperature of $60^\backslash circ$, whose bulk is equal to that part of the instrument which is below the middle of the stem. If, therefore, the instrument be immersed to the middle of the stem in any other fluid at the same temperature

(which may be done by altering the load), the difference between this last load and 1000 grains will be the difference between equal bulks of water and of the other fluid, the weight or the mass of water being known to be 3100 grains. If the said difference be excess above 1000 grains it must be added, or if it be defect subtracted from 3100 grains: the sum or remainder will be a number whose ratio to 3100 will express the ratio of the specific gravity of the assumed fluid to that of water. And this ratio will be expressed with considerable accuracy; for the instrument having a cylindrical stem of no more than $\backslash frac\{1\}\{16\}$ of an inch diameter, will be raised or depressed near one inch by the subtraction or addition of $\backslash frac\{1\}\{16\}$ of a grain, and will therefore indicate with ease such mutations of weight as do not fall short of $\backslash frac\{1\}\{16\}$ of a grain, or $\backslash frac\{1\}\{3100\}$th part of the whole. Consequently, the specific gravities of all fluids, in which this instrument can be immersed, will be found to five places of figures.

It is evident, that this instrument is a kind of thermometer, perhaps better adapted than the common one for measuring the expansions of fluids by heat. As the fluid, in the common thermometer, rises by the excess of expansion of the fluid beyond the expansion of the glass vessel; so this instrument will fall by the excess of the same expansion beyond the proper expansion of the materials it is composed of.

To measure the specific gravities of solid bodies. The solid bodies to be tried by this instrument must not exceed 1000 grains in weight. Place the instrument in distilled water, and load the upper scale or dish till the surface of the water intersects the middle of the stem. If the weights required to effect this be exactly 1000 grains, the temperature of the water answers to $60^\backslash circ$ of Fahrenheit's scale; if they be more or less than 1000 grains, it follows, that the water is colder or warmer. Having taken a note of this weight, unload the scale, and place therein the body whose specific gravity is required. Add more weight, till the surface of the water again bisects the stem. The difference between the added weight and the former load is the weight of the body in air. Place now the body in the lower scale or dish under water, and add weights on the upper scale till the surface of the water once more bisects the stem. This last added weight will be the difference between 1000 grains and the weight of the body in water. To illustrate this by an example.

N. B. The specific gravity of lead and tin, and (probably other metals) will vary in the third figure when the same piece of metal is melted and cooled a second time. This difference probably arises from the arrangement of the parts in cooling more or less suddenly.

When

Specific Gravities. When the instrument is once adjusted in distilled water, common water may be afterwards used. For the ratio of the specific gravity of the water made use of to that of distilled water being known ($=\backslash frac\{b\}\{a\}$), and the ratio of the specific gravity of the solid to the water made use of being also known ($=\backslash frac\{c\}\{b\}$), the ratio of the specific gravity of the solid to that of distilled water will be compounded of both (that is, $\backslash frac\{cb\}\{ab\}$).

There is reason to conclude from the experiments of various authors, that they have not paid much attention either to the temperature or specific gravity of the water they made use of. They who are inclined to be contented with a less degree of precision than is intended in the construction here described, may change the stem, which for that purpose may be made to take out for a larger.

One of the greatest difficulties that attends hydrostatical experiments, arises from the attraction or repulsion that obtains at the surface of the water. After trying many expedients to obviate the irregularities arising from this cause, Mr Nicholson finds reason to prefer the simple one, of carefully wiping the whole instrument, and especially the stem, with a clean cloth. The weights in the dish must not be esteemed accurate while there is either a cumulus or a cavity in the water round the stem.

Yet, after all, we cannot with great geometrical certainty rely upon either the hydrometer or the hydrostatic balance; for there are some natural inconveniences that disturb the exactness with which they discover the specific gravities of different bodies. Thus, if the weather be hotter at one time than another, all fluids will swell, and consequently they will be lighter than when the weather is cold: the air itself is at one time heavier than at another, and will buoy up bodies weighed in it; they will therefore appear lighter, and will of consequence seem heavier in water. In short, there are many causes that would prevent us from making tables of the specific gravities of bodies, if rigorous exactness were only expected; for the individuals of every kind of substance differ from each other, gold from gold, and water from water. In such tables, therefore, all that is expected is to come as near the exact weight as we can; and from an inspection into several, we may make an average near the truth. Thus, Muschenbroek's table makes the specific gravity of rain-water to be nearly eighteen times and an half less than that of a guinea; whereas our English tables make it to be but seventeen times and an half, nearly, less than the same. But though there may be some minute variation in all our tables, yet they in general may serve to conduct us with sufficient accuracy.

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.

A TABLE of the SPECIFIC GRAVITIES of several Solid and Fluid Bodies.

Take away the decimal point from the numbers in the right-hand column, or (which is the same) multiply them by 1000, and they will show how many

Hydraulics. ounces avoirdupois are contained in a cubic foot of each body.

²⁰ 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.

Suppose the specific gravity of the compounded body 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.

²¹ How to try spirituous liquors. A cubical 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.

SECT. IV. Hydraulics.

HYDRAULICS is that part of hydrostatics, which reaches to estimate the swiftness or the force of fluids in motion.

It has been always thought an inquiry of great curiosity, and still greater advantage, to know the causes by which water spouts from vessels to different heights and distances. We have observed, for instance, an open vessel of liquor upon its stand, pierced at the bottom: the liquor, when the opening is first made, spouts out with great force; but as it continues to run, becomes less violent, and the liquor flows more feebly. A knowledge of hydraulics will instruct us in the cause of this diminution of its strength; it will show precisely how far the liquor will spout from any vessel, and how fast or in what quantities it will flow. Upon the principles of this science, many machines worked

by water are entirely constructed; several different engines used in the mechanic arts, various kinds of mills, pumps, and fountains, are the result of this theory, judiciously applied.

And what is thus demonstrated of the bottom of the vessel, is equally true at every other depth whatsoever. Let us then reduce this into a theorem: 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, 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.

²² 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 be full of water, the horizontal pipe D be in the middle of its side, and the semicircle N e d e b be described upon D as a centre, with the radius or semidiameter D g N, or D f b, the perpendicular D d to the diameter N D b is the longest that can be drawn from any part of the diameter to the circumference N e d e b. And if the vessel be kept full, the jet C will spout from the pipe D, to the horizontal distance N M, which is double the length of the perpendicular D d. 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 C e and E e, from these pipes to the semicircle, will be equal: and the jets F and H spouting from them will each go to the horizontal distance N K; which is double the length of either of the equal perpendiculars C e or D d.

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. This is what the ancients were ignorant of; and therefore they left them to be conveyed over hills and valleys.

Hydraulics. they usually built Aqueducts (vast rows of arches one above another, between two hills, at a vast expence of money, time, and labour), in order to convey water over them, cross the valley, in a common channel. This is now done to equal advantage, and at much less expence, by a range of pipes laid down one hill and up the other. An instance whereof may be given by a bent tube or crane; into one of the equal legs whereof if water be poured, it will rise to the same level exactly in the other. The reason is obvious: In the leg A, (fig. 14.) there are, suppose, two ounces of water endeavouring by the power of gravity to descend with the force of 2; these will thrust forward, buoy up, and support an equal quantity of a like fluid in B; and the bottom of the machine C, against which both sides equally bear, will of consequence sustain a double pressure, or that of four ounces; and in the present case will pretty well represent the prop or fixed point of a balance-beam; as the equal fluid-columns AC, and BC, may be admitted to denote equal weights, suspended on the balance arms, counterpoising each other. So that the rise of fluids to their first level, thus considered, is a case truly statical; and all their other motions proceed only from weight added.

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 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 else follow. Hydraulics.

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 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 BAG.

Mercury may be drawn through a syphon in the same manner as water; but then the utmost height of the syphon must always be less than 30 inches, as mercury is near 14 times heavier than water. That fluids are forced through the syphon by the pressure of the atmosphere, is proved experimentally by the air-pump; for, if a syphon immersed in a vessel of water be placed when running in the receiver, and the air extracted, the running will immediately cease. It is however certain, that a syphon of a particular kind, once set a running, will persist in its motion, though removed into the most perfect vacuum our air-pumps will make: or, if the lower orifice of a full syphon be shut, and the whole be thus placed in a receiver, with a contrivance for opening the orifice when the air is exhausted; the water will be all emptied out of the vessel, as if it had been in open air.

This fact has been sufficiently ascertained by many approved hydrostatical writers. Desaguliers informs us, that he made the experiment both with water and mercury; for having filled a syphon, recurved at the extremities of its legs, successively with those liquors, and suspended it by a slip-wire in the receiver of an air-pump, over two small jars containing mercury to unequal heights (and water, when water was used in the syphon), he exhausted the air out of the receiver, and then letting down the syphon, so that its two ends went into the liquor in the jars, the liquor ran from the higher into the lower vessel. He also made an experiment in the open air, where the mercury ran through a syphon, whose bend was more than 31 inches above the lower orifice of the short leg of the syphon. But neither of these experiments afford a just objection against the preceding doctrine, viz. that the air is the cause of the discharge of liquors from one vessel into another, by means of syphons; for its running in vacuo was only owing to the attraction of cohesion, which acts for a small height; because the experiment will not succeed in vacuo, if the syphon used for mercury has its bend six inches higher than the orifice of the short leg, and if the bend for the syphon of water be two or three feet high; neither will the last mentioned with mercury in the open air answer, if the bend of the syphon be forty inches high; and in all the experiments the bores of the syphons must be very small.

The figure of the syphon may be varied at pleasure, (see fig. 1. 2. 3.) provided only the orifice C be below the level of the surface of the water to be drawn up; but still the farther it is distant from it, the faster will the fluid be carried off. And if, in the course of the flux, the orifice A be drawn out of the fluid, all the liquor in the syphon will go out at the lower orifice C; that in the leg CB dragging, as it were, that in the shorter leg AB after it. If a filled syphon be so disposed, as that both orifices A and C be in the same horizontal line; the fluid will remain pendant in each leg, how unequal soever the length of the legs may be. Fluids, therefore, in syphons, seem as if were to form one continued body; so that the heavier part descending like a chain, pulls the lighter after it.

Upon the principle of the syphon depend the experiments of Tantalus's cup, n^o 44; the Fountain at command, n^o 45; and the inverted drinking-glass, n^o 58. As to the last of these, it may be here observed, that if the paper was put dry on such a vessel empty, it would sink in the air, and fall away even by its own gravity; and if put on wet, it were to be doubted whether a very small weight added thereto would not separate it from the glass, so inconsiderable would the tenacity of the water be in this case. The paper therefore cannot be supposed to support the incumbent weight of water; and the true cause thereof must be this: The bottom and sides of the inverted glass-vessel being rigid, keep off the pressure of the air from the fluid above, whereas it hath liberty of access and freely acts thereon below: and that it does so, will in part appear to an observer by the concavity of the paper underneath. Could the air's pressure in this case be any how admitted through the foot of the vessel inverted, without doubt the whole column would descend together. And the like would happen should the paper be removed; but for a different reason, viz. the large column of water in the mug, being composed of many collateral ones, which, being disposed as in a bundle, rest on the paper wherewith the vessel is covered, as on a common base; and these being all equally dense, and equally fluid, are all retained, and continued of the same length, by the general and uniform pressure of the air against the paper below; and so long as this continues, none of them getting the least advantage over the rest, they are all sustained in a body compact together. But when the paper is removed, it being scarce possible to hold the vessel so exactly level, but that some one or other of these smaller fluid columns will become longer, consequently heavier, than those adjacent, and, over-balancing the rest, will descend, and give the lighter fluid, the air, leave to rise in its place, even to the top of the glass: the general pressure whereof being there admitted, will soon cause the rest of them to move, and the whole quantity will then descend, seemingly together.

Again, should a vessel be but part filled with water, the same effect will follow to a certain degree. For instance, suppose we fill a long glass half with water, cover it with paper, and turn it down as before. Six inches suppose of water, endeavouring to descend, will by its weight rarefy the air in the glass above it, perhaps a 60th part or more. The denser air without will then overpoise the air rarefied within; and there-

fore a certain quantity of water, equal to the difference of the two pressures, will in this case be thereby buoyed up and supported. But the air within the glass being dilated as aforesaid, the water suspended must be expected to hang something below the mouth of it; though not enough, perhaps, to overcome the tenacity of the water, and make it all descend.

Upon the principle of the syphon also we may easily account for intermitting or reciprocating springs. Let the springs AA be part of a hill, within which there is a cavity BB; and from this cavity a vein or channel running in the direction of 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 K 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.

We have seen that fluids led in pipes will always rise to the level of the reservoir whence they are supplied; the rising column being pushed forward, and raised by another equally heavy, at the same time endeavouring to descend. A like effect might be expected from jets of water thus impelled, did not friction against the sides of the machines, and the resistance of the air, both lateral and perpendicular, generally prove an abatement, and prevent its rising so high as the head.

Where jets are executed in the best manner, and the friction spoken of is as much as possible removed, the impediment of the air only, through which they needs must beat in their rise, will cause them, according to experiment, to fall short of the height of the reservoirs, in the following proportions, viz.

Whence in general it may be observed:
That as often as a five-feet jet (to be taken in these matters as a standard,) shall

Hydraulics. Shall be contained in the height of any jet proposed;
By so many inches multiplied into themselves, or squared,

The surface of the water in the reservoir which supplies it, ought to exceed that jet in height.

Thus, to obtain a jet of 30 feet, which contains five feet six times, the reservoir ought to be 36 inches or a yard higher; and a jet of 60 feet may be had from a head higher by four times that difference, 144 inches, or four yards. So that jets done in the best manner fall short of the heights of their reservoirs, in a kind of sub-duplicate ratio of the heights to which they rise.

This great disproportion in the rise of jets must in general be owing to the resistance of the air they are made to move through; which has been shown to be in proportion to the squares of their celerities respectively: nor can the acceleration of the falling water in the pipe, or the retardment of the rising stream by the action of gravity, be concerned at all in it; since these are probably adequate, and counterbalance each other every where in the same level.

Their air's resistance being thus considerable, it will always be found necessary to increase the bore of the adjutage or spouting-pipe with the height of the reservoir: for if it be too small, the rising stream will want sufficient weight and power to divide the air; which being densest near the earth, a small stream of water, endeavouring to mount to a great height, will be dashed against it with so great violence, as to fall away in a mist and be wholly lost. And it may be observed, that the weightier any body is, the greater force it will have when in motion: since an ounce-ball fired from a musket, will go much farther, and do greater execution, than will an equal weight of shot; and these again may be projected farther than so much lead rased into powder and fired off. A charge of water fired from a pistol would scarce wet a paper at the distance of six feet. Accordingly, should a cask of water be any where pierced with holes of two, four, six, eight, and twelve lines over, all in the same level, the larger bore will always be found to throw the water farthest.

It may be of use here to add Mr Mariotte's proportions of the bores of the adjutages and pipes of conduct, who was very conversant in these things, and hath written very well on this subject.

N. B. The French divide their inch into 12 equal parts, which they call lines.

Hence it may be remarked, that there is a certain and fit proportion to be observed between the adjutage

whereby the jet is delivered, and the pipe conducting it from the head. In general, About five times the diameter of the adjutage for jets under half an inch, and six or seven times for all above, will seize the pipes of conduct pretty well: not but it will always be an error on the right side, to have them rather larger than in strictness they ought to be, that the jet may always be freely supplied with water, and in due time.

For a like reason, if there be occasion for a cock to be placed in any part of the pipe of conduct, particular care must be taken that it should be there bigger in proportion, that the water-way may not be pinched; but that the cavity be left at least equal to the bore of the rest of the pipe.

The bore of an adjutage cannot be too smooth or true. Those that are cylindrical are best; those that are bored conical worst, because of the reflections of the water from the inclined sides of the machine, which in the hurry of the issuing stream will in them unavoidably be made.

When fluids are designed to be raised higher than the springs from whence they flow, forcing engines must be used; of which and other hydraulic machines, we come now to give a particular account.

SECT. V. Hydraulic Engines.

THE pump is at once the most common and most useful of all the hydraulic instruments. It was first invented by Ctesibes, a mathematician of Alexandria, 120 B. C.; when the air's pressure came afterwards to be known, it was much improved, and it is now brought to a great degree of perfection.

Ctesibes's pump acted both by suction and pulsion; and its structure and action are as follow:—A brass cylinder ABCD, furnished with a valve in L, is placed in the water. 2. In this is fitted the embulus MK, made of green wood, which will not swell in the water, and adjusted to the aperture of the cylinder with a covering of leather, but without any valve. In II is fitted on another tube NH, with a valve that opens upwards in I. Now, the embulus EK being raised, the water opens the valve in L, and rises into the cavity of the cylinder:—and when the same embulus is again depressed, the valve I is opened, and the water driven up through the tube HN. This is the pump used among the ancients, and that from which the others afterwards are deduced. Sir S. Morland has endeavoured to increase its force by lessening the friction; which he has done to good effect, inasmuch as to make it work without almost any friction at all.

Of this pump as now used there are simply three kinds, viz. the sucking, the forcing, and the lifting-pump. By the two last, water may be raised to any height, with an adequate apparatus and sufficient power: by the former it may, by the general pressure of the atmosphere on the surface of the well-water, be raised no more than 33 feet, as was before hinted, though in practice it is seldom applied to the raising it much above 28; because from the variations observed on the barometer, it is apprehended that the air may, on certain occasions, be something lighter than 33 feet of water; and whenever that shall happen, for want of the due counterpoise, this pump may fail in its performance.

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 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 upright in the vessel of water K, the water being deep enough to rise at least as high as from A to I. 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, 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, as 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 dilation 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 G a second time, the air between it and the water in the lower pipe at a 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. And 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.

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 water in 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, it 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

Hydraulic
Engines.

inches diameter and 30 feet high, and discharge 27 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 surface of the well; 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.

The forcing-pump raises water through the box H 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 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 GHI

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 IHGF, from whence it spouts in a jet S to a great height; and is supplied by alternately raising and depressing of 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.

Of lifting-pumps there are several sorts; the most common is thus constructed. AB is the barrel, fixed in the frame KILM; which is also fixed immovable, with the lower part in the water that is to be pumped up. GEQHO is a frame with two strong iron rods, moveable through holes in the upper and lower parts of the pump, IK and LM. In the bottom of this frame is fixed an inverted piston BD, with its bucket and valve uppermost at D. From the top of the barrel there goes off a part KH, either fixed to the barrel, or moveable by a ball and socket (as here represented at F); but in either case so very exact and tight, that no water or air can possibly get into the barrel, as that would prevent the effect of the pump. In this part, at C, is fixed a valve opening upward.

When the piston frame is thrust down into the water, the piston D will descend, and the water beneath it rush up through the valve at D, and get above the piston; where, upon the frame's being lifted up, the piston will force the water through the valve C, into the cistern P, there to run off by the spout. It is to be remembered, that this sort of pump must be set so far in the water, that the piston may play below its surface. It appears by the above description, that this is only a different manner of constructing a forcing-pump.

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 show the method.

1. By a running stream, or a fall of water. Let Plate AA be a wheel, turned by the fall of water BB; and CCXI. have fig. 5.

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, w, x, y, in 12 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 Alderslea. The water-wheel is 7½ feet in 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 flow 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 the same manner the engine for raising water at London-Bridge is constructed.

The wheels of the London-bridge water-works are placed under the arches of the bridge, and moved by the common stream of the tide-water of the river. A B the axle-tree of the water-wheel is nineteen feet long, and three feet in diameter; in which C, D, E, F, are four sets of arms, eight in each place, on which are fixed G G G G, four sets or rings of felloes twenty feet in diameter, and the floats H H H fourteen feet long, and eighteen inches deep, being about twenty-six in number. The wheel lies with its two gudgeons, or centre pins, A, B, upon two brasses in the pieces M N, which are two great levers, whose fulcrum or prop is an arched piece of timber L; the levers being made circular on their lower sides to an arch of the radius M O, and kept in their places by two arching studs fixed in the felloe L, through two mortises in the lever M N. The wheel is by these levers made to rise and fall with the tide in the following

manner. The levers M N are sixteen feet long; from the fulcrum of the lever to O the gudgeon of the water-wheel, six feet; and from O to the arch at N, ten feet. To the bottom of the arch N is fixed a strong triple chain P, made after the fashion of a watch-chain, but the links arched to a circle of one foot diameter, having notches or teeth to take hold of the leaves of a pinion of cast iron Q, ten inches diameter, with eight teeth in it moving on an axis. The other loose end of this chain has a large weight hanging at it to help to counterpoise the wheel, and preserve the chain from sliding on the pinion. On the same axis is fixed a cog-wheel R, six feet diameter, with forty-eight cogs. To this is applied a trundle, or pinion S of six rounds or teeth; and upon the same axis is fixed T, a cog-wheel of fifty-one cogs, into which the trundle V of six rounds works, on whose axis is a winch or windlass W, by which one man with the two windlasses raises or lets down the wheel as there is occasion. And because the fulcrums of these levers M N are in the axis of the trundle K, viz. at M or X, in what situation soever the wheel is raised or let down, the cog-wheel I, I, is always equidistant from M, and works or gears truly. By means of this machine the strength of an ordinary man will raise about fifty ton weight.

I, I, is a cog-wheel fixed near the end of the great axis eight feet diameter, and forty-four cogs working into a trundle K, of four feet and an half diameter, and twenty rounds, whose axis or spindle is of cast iron four inches in diameter, lying in brasses at each end as at X. ZZ is a quadruple crank of cast iron, the metal being six inches square, each of the necks being turned one foot from the centre, which is fixed in brasses at each end in two headstocks fastened down by caps. One end of this crank at Y is placed close abutting to the end of the axle-tree X, where they are at those ends six inches diameter, each having a slit in the ends where an iron wedge is put one half into the end X, the other half into Y, by means of which the axis X turns about the crank ZZ. The four necks of the crank have each an iron spear or rod fixed at their upper ends to the respective libra or lever, a 1, 2, 3, 4, within three feet at the end. These levers are twenty-four feet long, moving on centres in the frame b b b b; at the end of which, at c 1, 2, 3, 4, are jointed four rods with their forcing plugs working into d 1, 2, 3, 4, four cast iron cylinders four feet three quarters long, seven inches bore above and nine below where the valves lie, fastened by screwed flanches over the four holes of a hollow trunk of cast iron, having four valves in it just over e e e e, at the joining on of the bottom of the barrels or cylinders, and at one end a sucking pipe and grate f going into the water, which supplies all the four cylinders alternately.

From the lower part of the cylinders d 1, d 2, d 3, d 4, come out necks turning upward arch-wise, as g g g g, whose upper parts are cast with flanches to screw up to the trunk b b b b; which necks have bores of seven inches diameter, and holes in the trunk above communicating with them, at which joining are placed four valves. The trunk is cast with four bosses or protuberances standing out against the valves to give room for their opening and shutting; and on the upper side are four holes stopped with plugs to take out on occasion to cleanse the valves. One end of this trunk is stopped

Hydraulic Engines. flopped by a plug i. To the other iron pipes are joined as i 2, by flanches, through which the water is forced up to any height or place required.

Besides these four forcers there are four more placed at the other ends of the libra, or levers (not shown here to avoid confusion, but to be seen on the left hand), the rods being fixed at a 1, 2, 3, 4, working in four such cylinders, with their parts d d, &c. e e, f f, g g, and i, as before described, standing near k k.

At the other end of the wheel (at B) is placed all the same sort of work as at the end A is described, viz.

All which work could not be drawn in one perspective view without making it very much confused.

Mr Beighton, who has described the structure and operation of this engine (see Phil. Transl. abr. vol. vi. p. 358.) has calculated the quantity of water raised by it in a given time. In the first arch next the city there is one wheel with double work of sixteen forcers; and in the third arch one wheel with double work at one end and single at the other, having twelve forcers; a second wheel in the middle having eight forcers, and a third wheel with sixteen: so that there are in all fifty-two forcers; one revolution of a wheel produces in every forcer 2$\backslash frac\{1\}\{2\}$ strokes; so that one turn of the four wheels makes 114 strokes. When the river acts with most advantage, the wheels go six times round in a minute, and but 4$\backslash frac\{1\}\{2\}$ at middle water: hence the number of strokes in a minute is 684; and as the stroke is 2$\backslash frac\{1\}\{2\}$ feet in a seven-inch bore, it raises three ale gallons; and all raise per minute 2052 ale gallons; i. e. 123120 gallons = 1954 hogsheds per hour, and at the rate of 46896 hogsheds in a day, to the height of 120 feet. Such is the utmost quantity they can raise, supposing that there were no imperfections or loss at all; but Mr Beighton infers, from experiments performed on engines whose parts were large and excellently constructed, that they will lose one fifth and sometimes one fourth of the calculated quantity. For an estimate of the power by which the wheels are moved, see Phil. Transl. ubi supra.

Mr Beighton observes, that though these water-works may justly be esteemed as good as any in Europe, yet some things might be altered much for the better. If (he says), instead of sixteen forcers, they worked only eight, the stroke might be five feet in each forcer, which would draw much more water with the same power in the wheel; because much water is lost by the two frequent opening and shutting of the valves; and that the bores that carry off the water from the forcers are too small; and that they should be near nine inches in diameter. This objection Dr Desaguliers says is of no force, unless the velocity of the pistons was very great; but here the velocity of the water passing through the bores is much less than two feet in a second. This last writer observes, that a triple crank distributes the power better than a quadruple one. He adds, that forcers made with thin leather tanned, of about the thickness of the upper-leather of a countryman's shoe, would be much better than those

of the stiff leather commonly used. Dr Desaguliers has formed a comparison of the powers of this engine with those of the famous machine at MARLY. Estimating the quantity of water merely raised by these machines, the former raises almost twice and a quarter as much as the latter; but considering that the London bridge water-works raise this water but 120 feet high, and that the Marly engine raises its water 533 feet high, he deduces from a calculation formed on these different heights, and on the difference of the fall of water on both engines, this conclusion, viz. that the effect of the four wheels at London-bridge is three times greater than that of four of the wheels at Marly.

The engine at London-bridge was put up by Mr Sorocold towards the beginning of this century: the contrivance for raising and falling the water-wheel was the invention of Mr Hadley, who put up the first of that kind at Worcester, for which he obtained a patent.

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 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 thro' 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 conduit-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.

2. 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, 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-rod 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 12 feet diameter, the trundle 4 feet, and the radius or length of each crank 9 inches, working a piston in its 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 4 inches thick, contains 226.08 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 1468 in round numbers, for the number of gallons raised in an hour; which, divided by 63, gives 26$\backslash frac\{1\}\{2\}$ hogheads. 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 2$\backslash frac\{1\}\{2\}$ miles per hour to fetch up this loss.

A column of water 4 inches thick and 64 feet high, weighs 349$\backslash frac\{2\}\{3\}$ pounds avoirdupois, or 424$\backslash frac\{1\}\{3\}$ 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-straps 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 in the upright pipe Aiklmnopq B, 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 the 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

Hydraulic Engines. raise the same cylinder of water will then be as much less as the fine 80 b is less than the radius AB; or as the fine of 80 degrees is less than the fine of 90. And so, decreasing as the fine 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 fine of the angle of elevation decreases; as will appear plainly by a farther consideration of the figure.

Let two pipes AB and AC, 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 BDC, and divide it into 90 equal parts or degrees.

Let the pipe AC be elevated to 10 degrees upon the quadrant, and 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 10: and the upright line a 10, equal to A i, will be the fine 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 A k, which is equal to the length of the upright line b 20, or to the fine 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.

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 A l, or to the same level with the mouth of the pipe at 30. The fine of this elevation, or of the angle of 30 degrees, is e 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 fines 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 Ar; and these heights measured upon the scale S 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 fines of a quadrant from 0 degrees to 90, we have given the foregoing Table, showing the length of the fine of every degree in such parts as the whole pipe (equal to the radius of the quadrant) contains 1000. Then the fines 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 fine 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 fine of that elevation will be equal to 707 of these parts: but if the radius be divided only into 100 equal parts, the same fine will be only 70.7 or 707/10 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 showing 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

Hydrostatic Tables. The number of cubic inches divided by 231, will reduce the water to gallons in wine-measure; and, divided by 282, 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 following Tables, the pressure of the water, against an engine whose pump is of a $4\backslash frac\{1\}\{2\}$ 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 $1\backslash frac\{1\}\{2\}$ inch diameter.

Here the nearest single decimal figure is only taken into the account; and the whole being reduced by division, amounts to $25\backslash frac\{1\}\{2\}$ wine-gallons in measure; to $259\backslash frac\{1\}\{2\}$ pounds troy, and to $213\backslash frac\{1\}\{2\}$ pounds avoirdupois.

These tables were at first calculated to fix 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.

HYDROSTATICAL TABLES.

Under the article STEAM-Engine, the reader will find a particular account of that useful invention, with a correct description and plate of it in its improved state.

The multiplying machine, has no dependence on the Steam-
action of the atmosphere; but, by the weight of water-
ter only, and without pump-work of any kind, raises
water sufficient to serve a gentleman's feat, with an
overplus for fountains, fish-ponds, &c.

AB are two copper pans or buckets of unequal
weight and size, suspended to chains, which alternately
wind off and on the multiplying-wheel YZ; whereof
the wheel Y is smaller in diameter, and Z larger, in
proportion to the different lifts each is designed to per-
form.

When the buckets are empty, they are stopped level with the spring at X, whence they are both filled with water in the same time.

The greater of the two, A, being the heavier when full, preponderates and descends ten feet, perhaps from C to D; and the lesser, B, depending on the same axis, is thereby weighed up or raised from E to F, suppose 30 feet.

Here, by particular little contrivances, opening the valves placed at bottom of each of these buckets, they both discharge their water in the same time, through apertures proportionable to their capacities; the smaller into the cistern W, whence it is conveyed for service by the pipe T, and the larger at D, to run waste by the drain below at H. The bucket B being empty, is so adjusted as then to overweigh; and descending steadily as it rose betwixt the guiding rods VV, brings or weighs up A to its former level at X, where both being again replenished from the spring, they thence proceed as before. And thus will they continue constantly moving (merely by their circumstantial difference of water-weight, and without any other assistance than that of sometimes giving the iron-work a little oil) so long as the materials shall last, or the spring supply water.

The steadiness of the motion is in part regulated by a worm turning a jack-fly, and a little simple wheel-work at LM; which communicating with the multiplying wheel axle at M, is thereby moved forward or backward as the buckets either rise or descend. But what principally keeps the whole movement steady, is the equilibrium preserved in the whole operation by a certain weight of lead, at the end of a lever of fit length, and fixed on one of the spindles of the wheel-work, the numbers whereof are so calculated as, during the whole performance up and down, to let it move no more than one-fourth of a circle, from G to K; by which contrivance, as more or less of the chains suspending the buckets come to be wound off their respective wheels Y and Z, this weight gradually falls in as a counterbalance, and so continues the motion equable and easy in all its parts.

The water wasted by this machine is not above the hundredth part of what a water-wheel will expend, to raise an equal quantity. But where a fall, proportionable to the intended rise of water, cannot be had, with a convenient fewer to carry off the waste water over and above, this device cannot be well put in practice.

WATER may also be raised by means of a stream AB The Per-
turning a wheel CDE, according to the order of the
D let-

letters, with buckets $a,\; a,\; a,\; a$, &c. hung upon the wheel by strong pins $b,\; b,\; b,\; b$, &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 overfet, 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 the level 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 $CD$, &c. dip into the water, it runs into them; and as the wheel turns, the water rises in the hollow spokes $e,\; d$, &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.

Engines for extinguishing fire are either forcing or lifting pumps; and being made to raise water with great velocity, their execution in great measure depends upon the length of their levers, and the force wherewith they are wrought.

For example, $AB$ is the common squirting fire-engine. $DC$ is the frame of a lifting-pump, wrought by the levers $E$ and $F$ acting always together. During the stroke, the quantity of water raised by the piston $N$ spouts with force through the pipe $G$, made capable of any degree of elevation by means of the yielding leather-pipe $H$, or by a ball and socket, capable of turning every way, screwed on the top of the pump. Between the strokes on this machine the stream is discontinued. The engine is supplied by water poured in with buckets above; the dirt and filth whereof are kept from choking the pump work by help of the strainer $IK$.

A considerable improvement has since been made to these machines, in order to keep them discharging a continual stream. In doing whereof it is not to be understood that they really throw out more water than do the squirting ones of the same size and dimensions with themselves; but that the velocity of the water, and of course the friction of all the parts, being less violent, the stream is more even and manageable, and may be directed hither or thither with greater ease and certainty than if it came forth only by fits and starts: The machine, thus improved, is therefore generally better adapted to the purpose intended than the former, especially in the beginning of these calamitous accidents.

The stream is made continual from the spring of air confined in a strong metal vessel $CC$, in the fire engine $AB$, fixed between the two forcing-pumps $D$ and $E$, wrought with a common double lever $FG$ moving on the centre $H$. The pistons in $D$ and $E$ both suck and force alternately, and are here represented in their different actions; as are also the respective valves at $IK$ and $LM$.

The water to supply this engine, if there be no opportunity of putting the end of a sucking-pipe, occasionally to be screwed on, into a moat or canal, which would spare much hurry and labour in case of fire, is also poured into the vessel $AB$; and being strained through the wire grate $N$, is, by the pressure of the atmosphere, raised through the valves $K$ and $M$ into the barrels of $D$ or $E$, when either of these forcers ascend; whence again it will be powerfully pushed when they descend into the air-vessel $CC$, through the valves $I$ and $L$ by turns: by the force whereof the common air between the water and the top of the air-vessel $O$ will from time to time be forcibly crowded into less room, and much compressed; and the air being a body naturally endowed with a strong and lively spring, and always endeavouring to dilate itself every way alike in such a circumstance, bears strongly both against the sides of the vessel wherein it is confined, and the surface of the water thus injected; and so makes a constant regular stream to rise through the metal pipe $P$ into the leather one $Q$, screwed thereon; which being flexible, may be led about into rooms and entries, as the case may require.

Should the air contained in this vessel be compressed into half the space it took up in its natural state, the spring thereof will be much about doubled; and as before it equalled and was able to sustain the pressure of a single atmosphere, it having now a double force, by the power of that spring alone will throw water into air, of the common degree of density, about thirty feet high. And should this compression be still augmented, and the quantity of air which at first filled the whole vessel be reduced into one-third of that space, its spring will be then able to resist, and consequently to raise the weight of a treble atmosphere; in which case, it will throw up a jet of water sixty feet high. And should so much water again be forced into the vessel as to fill three parts of the capacity, it will be able to throw it up about ninety feet high: and wherever the service shall require a still greater rise of water, more water must be thrust into this vessel; and the air therein being thus driven by main force into a still narrower compass, at each explosion, the gradual restitution thereof to its first dimensions is what regularly carries on the stream between the strokes, and renders it continual during the operation of the machine.

This experiment, in little, may be either made on the lifting or forcing pump, the nozels of which may be left large, on purpose for the reception of the small pipe $F$, reaching nearly to the valve at $E$, and occasionally to be screwed in. Between this pipe and the sides and top of the nozel $H$, a quantity of air will necessarily be lodged, which, when the forcer acts, will be compressed at every stroke by the rise of the water; more whereof will be pushed through $E$ than can immediately get away, through the pipe $F$, which

Hydraulic Engines. is to be always less in diameter than the opening of the valve at E: the degree of which condensation, and that of the restitution to its natural state of density, may be observed through the glass-machines, to satisfaction.

40 The screw of Archimedes. Plate CCLXII. fig. 1. ARCHIMEDES'S SCREW is a sort of spiral pump, and receives its name from its inventor. It consists of a long cylinder AB with a hollow pipe CD round it; and is placed in an oblique position, with the lower end in the water, the other end being joined to the lower end of the winch IK, supported by the upright piece IR.

When this screw is immersed in the water, it immediately rises in the pipe by the orifice C to a level with the surface of the water EF; and if the point in the spiral, which in the beginning of the motion is coincident with the surface of the water, happen not to be on the lower side of the cylinder, the water, upon the motion of the screw, will move on in the spiral till it come to the point on the other side that is coincident with the water. When it arrives at that point, which we will suppose to be O, it cannot afterwards possess any other part of the spiral than that on the lowest part of the cylinder: for it cannot move from O toward H or G, because they are higher above the horizon; and as this will be constantly the case after the water in the spiral has attained the point O, it is plain it must always be on the under side of the cylinder.

But because the cylinder is in constant motion, every part of the spiral screw, from O to D, will by degrees succeed to the under part of the cylinder. The water therefore must succeed to every part of it, from O to D, as it comes on the lower side; that is, it must ascend on the lower part of the cylinder through all the length of the pipe, till it come to the orifice at D, where it must run out, having nothing further to support it.

41 The balance-pumps. fig. 3, 4. THIS is a simple and easy method of working two pumps at once, by means of the balance AB, having a large iron ball at each end, and placed in equilibrium on the two spindles C, as represented in the 6th figure. On the right and left are two boards I, nailed to two cross pieces, fastened to the axis of the machine. On these boards the person who is to work the pump stands, and supports himself by a cross piece nailed to the two posts ED, fig. 5. At the distance of ten inches on each side the axis are fastened the pistons MN.

The man, by leaning alternately on his right and left foot, puts the balance in motion, by which the pumps OP are worked, and the water thrown into the pipe H, and carried to a height proportional to the diameter of the valves and the force of the balance. There must be placed on each side an iron spring, as F and G, to return the balance, and prevent its acquiring too great velocity.

42 The chain-pump. Plate CCXLII. fig. 4. THE CHAIN-PUMP, AB, is ordinarily made from twelve to twenty-four feet long; and consists of two collateral square barrels, and a chain of pistons of the same form, fixed at proper distances thereon. The chain is moved in these round a coarse kind of wheel-work at either end of the machine, the teeth whereof are so made as to receive one half of the flat pistons, and let them fold in; and they take hold of the links as they rise in one of the barrels, and return by the other. The machine is wrought either by the turning

of one handle or two, according to the labour required, depending on the height to which the water is to be raised. A whole row of the pistons (which go free of the sides of the barrel by perhaps a quarter of an inch) are always lifting when the pump is at work; yet do they, by the general push in the ordinary way of working, as it is pretty brisk, commonly bring up a full bore of water in the pump. This machine is so contrived, that, by the continual folding in of the pistons, stones, dirt, and whatever happens to come in the way, may also be cleared; and therefore it is generally made use of to drain ponds, to empty sewers, and remove foul waters, in which no other pump could work.

43 THE last machine to be described consists of five hydraulic pieces of board, forming a sort of scoop, as B. The handle C is suspended by a rope fastened to three poles, placed in a triangle, and tied together at A. Plate CCXLIII.

The working of this machine consists entirely in balancing the scoop that contains the water, and directing it in such manner that the water may be thrown in any given direction. It is evident that the operation of this machine is so very easy, that it may rather be considered as an agreeable and salutary recreation than hard labour.

With this machine a man of moderate strength, by two strokes in four seconds, can draw half a cubic foot of water, that is, more than four hundred cubic feet in an hour.

This machine is frequently used by the Dutch in emptying the water from their dikes.

SECT. VI. Entertaining Experiments.

44 1. SEVERAL amusing appearances may be produced by disguising or diversifying a syphon. It may, for example, be disguised in a cup, from which no liquor will flow till the fluid is raised therein to a certain height; but when the efflux is once begun, it will continue till the vessel is emptied. Thus, fig. 11. is a cup, in the centre whereof is fixed a glass pipe A, continued through the bottom at B, over which is put another glass tube, made air-tight at top by means of the cork at C; but left so open at foot, by holes made at D, that the water may freely rise between the tubes as the cup is filled. Till the fluid in the cup shall have gained the top of the inner pipe at A, no motion will appear. The air however from between the two pipes being in the mean time extruded, by the rise of the denser fluid, and passing down the inner tube, will get away at bottom; and the water, as soon as the top of the inclosed tube shall be covered thereby, will very soon follow, and continue to rise in this machine, as in the syphon, till the whole is run off.

This is called by some, a Tantalus's cup; and, to humour the thought, a hollow figure is sometimes put over the inner tube, of such a length, that when the fluid is got nearly up to the lips of the man, the syphon may begin to act and empty the cup.

This is in effect no other than if the two legs of the syphon were both within the vessel, as in fig. 12. into which the water poured will rise in the shorter leg of the machine, by its natural pressure upwards, to its own level; and when it shall have gained the bend of the syphon, it will come away by the longer leg, as already

already described. An apple, an orange, or any other solid, may be put into the vessel, to raise the water, when it is near the bend, to set it a-running, by way of amusement.

Again, let the handle of the cup, fig. 11, be hollow; let the tube CD, screwed therein, communicate freely with the water poured into the cup, that it may rise equally in both. Being once above the level ED, it will overflow, and descending through the cavity DB, will empty the cup of its liquor.

2. The device called the fountain at command, acts upon the same principle with the syphon in the cup. Let two vessels A and B be joined together by the pipe C, which opens into them both. Let A be opened 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 folded to the vessel D, 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 to A by the pipe C (folded 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 as 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 E, until the pipe C refills 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.

3. This figure represents a very pretty portable fountain, which, being charged with water, and inverted, will play a jet nearly as high as the reservoir, till the fluid is exhausted; and then turned up on the other end, the same thing will happen, and a real clepsydra, or water-clock, be thereby formed.

This device consists of two hollow vessels, A and B, communicating with each other only by the recurved tubes C and D; at the ends of which, E and F, are placed small adjutages to direct the jet. G and H are two open tubes, folded into the bottom of the basins belonging to A and B, through which the water flows in, and fills those vessels to a certain height, that is, according to their length. They by their disposition also prevent the return of the water the same way, when the machine is turned upside down.

4. Provide a cylindric vessel of glass or china, ABCD, about a foot high, and four inches diameter. Make a hole in its bottom, in which glue a small glass-tube E, of about one-third of an inch diameter, and whose end has been partly closed in the flame of a lamp, so that it will not suffer the water to pass out but by

drops, and that very slowly. Cover the top of the vessel with a circle of wood F, in the centre of which make a round hole about half an inch diameter.

Have a glass tube GH, a foot high, and a quarter of an inch diameter; and at one end let it have a small glass globe I, to which you may hang a weight L, by which it is kept in equilibrio, on or near the surface of the water; or you may pour a small quantity of mercury into the tube, for the same purpose. Fill the vessel with water; put the tube in it, and over it place the cover F, through the hole of which the tube must pass freely up and down. Now, as the water drops gradually out of the vessel, the tube will continue to descend till it come to the bottom.

Therefore, paste on the tube a graduated paper, and put it in the vessel when nearly full of water. Hang a watch by it, set to a certain hour; and as the tube descends, mark the hours, with the half and quarter hours. If the vessel be sufficiently large, with regard to the hole at the bottom, it will go for 12 hours, a day, or as much longer as you please, and requires no other trouble than that of pouring in water to a certain height. Care must be had, however, that the water be clean; for if there be any sediment, it will in time stop the small hole at bottom, or at least render the motion of the water irregular.

The vessel may be of tin, but the pipe at bottom should be glass, that its small aperture may not alter by use. It is to be observed, that the tube of one of these clocks is not to be graduated by another; for though the vessel be of the same diameter at top, it may not be perfectly cylindrical throughout; nor is it easy to make the hole at the bottom of one vessel exactly of the same dimension with that of another.

5. The Hon. Mr Charles Hamilton has described a curious clepsydra or water-clock of new construction. An open canal ee, supplied with a constant and equal stream by the syphon d, has at each end ff, open pipes of exactly equal bores, which deliver the water that runs along the canal e, alternately into the vessels g 1, g 2, in such a quantity as to raise the water from the mouth of the tantalus i, exactly in an hour. The canal ee is equally poised by the two pipes f 1, f 2, upon a centre r, the ends of the canal e are raised alternately, as the cups zz are depressed, to which they are connected by lines running over the pulleys ll. The cups zz are fixed at each end of the balance mm, which moves up and down upon its centre v. n 1, n 2, Are the edges of two wheels or pulleys, moving different ways alternately, and fitted to the cylinder o by oblique teeth both in the cavity of the wheel and upon the cylinder, which, when the wheel n moves one way, that is, in the direction of the minute hand, meet the teeth of the cylinder and carry the cylinder with it, and, when n moves the contrary way, slip over those of the cylinder, the teeth not meeting, but receding from each other. One or other of these wheels nn continually moves o in the same direction, with an equable and uninterrupted motion. A fine chain goes twice round each wheel, having at one end a weight x, always out of water, which equilibrates with y at the other end, when kept floating on the surface of the water in the vessel g, which y must always be; the two cups zz, one at each end of the balance, keep it in equilibrio, till one of them is forced down

HYDROSTATICS.

Plate CCXLII.

Fig. 1.

A U-shaped tube with point A at the top left, B at the top right, and C at the bottom right.

Fig. 2.

An inverted U-shaped tube with point B at the top left, A at the bottom left, and C at the bottom right.

Fig. 3.

A simple U-shaped tube with point A at the top left, B at the top right, and C at the bottom right.

A person stands on a ladder labeled A, pouring water into a tube that leads to point B at the bottom of a pond.

Fig. 5.

A water wheel on wheels with a person operating it. A tube labeled G leads from the wheel to a person. Other points are labeled A, B, C, D, E, F, H, and K.

Fig. 6.

A complex water wheel mechanism on wheels. A person on the left holds a tube labeled T, and another person on the right holds a tube labeled G. The wheel has multiple tubes labeled A, B, C, D, E, F, G, H, I, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, AA, BB, CC, DD, EE, FF, GG, HH, II, JJ, KK, LL, MM, NN, OO, PP, QQ, RR, SS, TT, UU, VV, WW, XX, YY, ZZ.

Fig. 7.

A large, detailed water wheel mechanism with many tubes and gears. The wheel is labeled with letters A through Z and AA through ZZ. It is shown in operation, with water flowing through the tubes.

A. Bell, Print. & Ad. Sculptor, 1761.

down by the weight and impulse of the water, which it receives from the tantalus $t,\; t$: each of these cups $z,\; z$, has likewise a tantalus of its own $b,\; b$, which empties it after the water has done running from $g$, and leaves the two cups again in equilibrio: $q$ is a drain to carry off the water. The dial-plate, &c. needs no description. The motion of the clepsydra is effected thus: As the end of the canal $e,\; e$, fixed to the pipe $f,\; 1$, is, in the figure, the lowest, all the water supplied by the syphon runs through the pipe $f,\; 1$, into the vessel $g,\; 1$, till it runs over the top of the tantalus $t$; when it immediately runs out at $i$ into the cup $z$, at the end of the balance $m$, and forces it down; the balance moving on its centre $v$. When one side of $m$ is brought down, the string which connects it to $f,\; 1$, running over the pulley $l$, raises the end $f,\; 1$, of the canal $e$, which turns upon its centre $r$, higher than $f,\; 2$; consequently, all the water which runs through the syphon $d$ passes through $f,\; 2$ into $g,\; 2$, till the same operation is performed in that vessel, and so on alternately. As the height the water rises in $g$ in an hour, viz. from $s$ to $t$, is equal to the circumference of $n$, the float $y$ rising through that height along with the water, lets the weight $x$ act upon the pulley $n$, which carries with it the cylinder $o$; and this, making a revolution, causes the index $k$ to describe an hour on the dial plate. This revolution is performed by the pulley $n,\; 1$; the next is performed by $n,\; 2$, whilst $n,\; 1$ goes back, as the water in $g,\; 1$ runs out through the tantalus; for $y$ must follow the water, as its weight increases, out of it. The axis $o$ always keeps moving the same way; the index $p$ describes the minutes; each tantalus must be wider than the syphon, that the vessels $g,\; g$ may be emptied as low as $s$, before the water returns to them.

6. To the tube wherein the water is to rise, fit a spherical or lenticular head, $AB$, made of a plate of metal, and perforated at top with a great number of little holes. The water rising with vehemence towards $AB$, will be there divided into innumerable little threads, and afterwards broke, and dispersed into the finest drops.

7. To the tube $AB$, folder two spherical segments $C$ and $D$, almost touching each other; with a screw $E$, to contract or amplify the interface or chink at pleasure. Others choose to make a smooth, even cleft, in a spherical or lenticular head, fitted upon the tube. The water spouting through the chink, or cleft, will expand itself in manner of a cloth.

8. Make a hollow globe $A$, of copper or lead, and of a size adapted to the quantity of water that comes from the pipe to which it is to be placed. Pierce a number of small holes thro' this globe, that all tend towards its centre; observing, however, that the diameters of all these holes, taken together, must not exceed that of the pipe at the part from whence the water flows. Annex to it a pipe $B$, of such height as you think convenient; and let it be screwed at $C$, to the pipe from whence the jet flows. The water that comes from the jet rushing with violence into the globe, will be forced out at the holes, with the direction in which they are made, and will produce a very pleasing sphere of water.

9. Procure a little figure made of cork, as $AB$, which you may paint, or dress in a light stuff, after your own fancy. In this figure you are to place the small hollow cone $C$, made of thin leaf-braze. When

the figure is placed on the jet-d'eau that plays in a perpendicular direction, it will remain suspended on the top of the water, and perform a great variety of motions.

If a hollow ball of copper, of an inch diameter, and very light, be placed on a similar jet, it will, in like manner, remain suspended, revolving on its centre, and spreading the water all round it, in the manner represented by fig. 6. or Plate CCXLIV. fig. 1.—But note, that as it is necessary the ball, &c. when on the descent, should keep the same precise perpendicular wherein it rose (since otherwise it would miss the stream and fall downright), such a fountain should only be played in a place free from wind.

10. Make a hollow leaden cone $A$, whose axis is one-third of the diameter of its base. The circle $C$, that forms its base, must be in proportion to the surface of water that flows from the jet on which it is to be placed, that it may flow from it equally on all sides. To the cone join the pipe $B$, which serves not only as a support, but is to be pierced with a number of holes, that it may supply the cone with a sufficient quantity of water. Screw the tube just mentioned to the top of that from whence the jet proceeds.—The water that rushes into the cone from the pipe, will run over its circumference, and form a hemispherical cascade. If this piece be so constructed that it may be placed in a reversed position, it will produce a fountain in the form of a vase, (see fig. 2); and if there be a sufficient quantity of water, both these pieces may be placed on the same pipe, the fountain at top and the cascade underneath, which by their variety will produce a very pleasing appearance.

11. Let there be two portions of a hollow sphere, that are very shallow: and let them be so joined together, that the circular space between them may be very narrow. Fix them vertically to a pipe from whence a jet proceeds. In that part by which the portions of the sphere are joined, there must be made a number of holes; then the water rushing into the narrow cavity will be forced out from the holes, and produce a regular figure of the sun, as in the plate. This piece requires a large quantity and force of water to make it appear to advantage.

Several pieces of this sort may be placed over each other, in a horizontal direction, and so that the same pipe may supply them all with water (see fig. 6. of plate CCXLV.) It is proper to observe, that the diameter of these pieces must continually diminish, in proportion to their distance from the bottom.

12. Make a hollow circle $A$, the sides of which are to be pierced with 12 or 15 holes, made in an inclined direction: or you may place the like number of small tubes round the circle. Fix this circle on the top of a jet, in such manner that it may turn freely round. The water rushing violently into the hollow circle will keep it in continual motion; and at the same time forcing out of the holes or small tubes, will form a revolving figure with rays in different directions, as in the plate.

13. Provide a strong copper vessel $A$, of such figure as you think convenient; in which folder a pipe $BE$, of the same metal. Let there be a cock at $H$, which must be made so tight that no air can pass by it. The pipe $BE$ must go very near the bottom of the vessel, but

not touch it. There must be another pipe F, at whose extremity G there is a very small hole: this pipe must be screwed into the former.

The vessel being thus disposed, take a good syringe; and placing the end of it in the hole at G, open the cock, and force the air into the vessel; then turn the cock and take out the syringe. Repeat this operation several times, till the air in the vessel be strongly condensed. Then fill the syringe with water, and force it into the vessel, in the same manner as you did the air; and repeat this operation till you can force no more water into the vessel; then shut the cock. This vessel will be always ready to perform an extempore jet d'eau: for, on turning the cock, the spring of the compressed air will force out the water with great violence, and the jet will continue, though constantly decreasing in force, till the water is all exhausted, or the air within the vessel is come to the same density with that without.

14. Let there be made a tin vessel, about six inches high, and three inches in diameter. The mouth of this vessel must be only one quarter of an inch wide; and in its bottom make a great number of small holes about the size of a common sewing needle. Plunge this vessel in water, with its mouth open; and when it is full, cork it up and take it out of the water. So long as the vessel remains corked, no water whatever will come out; but as soon as it is uncorked, the water will issue out from the small holes at its bottom. You must observe, that if the holes at its bottom of the vessel be more than one sixth of an inch diameter, or if they be in too great number, the water will run out though the vessel be corked; for then the pressure of the air against the bottom of the vessel will not be sufficient to confine the water.

An experiment similar to this is made with a glass filled with water, over which a piece of paper is placed. The glass is then inverted; and the water, by the pressure of the air under it, will remain in the glass. That the paper, though the seeming, is not the real, support of the water, will appear from n^o 25.

15. In this fountain, the air being compressed by the concealed fall of water, makes a jet, which, after some continuance, is considered by the ignorant as a perpetual motion; because they imagine that the same water which fell from the jet arises again. The boxes CE and DXY being close, we see only the basin ABW, with a hole at W, into which the water spouting at B falls; but that water does not come up again; for it runs down through the pipe WX into the box DXY, from whence it drives out the air through the ascending pipe YZ, into the cavity of the box CE, where, pressing upon the water that is in it, it forces it out through the spouting pipe OB, as long as there is any water in CE; so that this whole play is only whilst the water contained in CE, having spouted out, falls down through the pipe WX into the cavity DXY. The force of the jet is proportionable to the height of the pipe WX, or of the boxes CE and DY above one another: the height of the water, measured from the basin ABW to the surface of the water in the lower box DXY, is always equal to the height measured from the top of the jet to the surface of the water in the middle cavity at CE. Now, since the surface CE is always falling, and the water in DY always rising,

the height of the jet must continually decrease, till it is shorter by the height of the depth of the cavity CE, which is emptying, added to the depth of the cavity DY, which is always filling; and when the jet is fallen so low, it immediately ceases. The air is represented by the points in this figure. To prepare this fountain for playing, which should be done unobserved, pour in water at W, till the cavity DXY is filled; then invert the fountain, and the water will run from the cavity DXY into the cavity CE, which may be known to be full, when the water runs out at B held down. Set the fountain up again, and, in order to make it play, pour in about a pint of water into the basin ABW; and as soon as it has filled the pipe WX, it will begin to play, and continue as long as there is any water in CE. You may then pour back the water left in the basin ABW, into any vessel, and invert the fountain, which, being set upright again, will be made to play, by putting back the water poured out into ABW; and so on as often as you please.

The fountain fig. 3. is of the same kind; but having double the number of pipes and concealed cavities, it plays as high again. In order to understand its structure, see fig. 7. The basin is A, the four cavities are B, C, D, and E, from which the water through the pipe f G spouts up to double the height of the fountain, the air at E, which drives it, being doubly condensed. The water going down the pipe t (e. gr. three feet long), condenses the air that goes up into the cavity C through the pipe z, so as to make it $\backslash frac\{1\}\{2\}$ stronger than the common air; then the water, which falling in the pipe 3 from C to D, is capable, by the height of its fall, of condensing the air at E, so as to make it $\backslash frac\{1\}\{4\}$ stronger, being pushed at C by air already condensed into $\backslash frac\{1\}\{2\}$ less space, causes the air at E to be condensed twice as much; that is, to be $\backslash frac\{1\}\{4\}$ stronger than common air; and therefore it will make the water at G spout out with twice the force, and rise twice as high as it would do if the fountain had been of the same structure with the former. In playing this fountain turn it upside down, and taking out the plugs g, h, fill the two cavities C and E, and having shut the holes again, set the fountain upright, and pour some water into the basin A, and the jet will play out at G; but the fountain will begin to play too soon, and therefore the best way is to have a cock in the pipe 3, which, being open, whilst the cavities C and E are filled, and shut again before the fountain is set up, will keep the water thrown into the basin from going down the pipe t, and that of the cavity C from going down the pipe 3, by which means the fountain will not play before its time, which will be as soon as the cock is opened.

16. Procure a tin vessel ABC, five inches high and four in diameter; and let it be closed at top. To the cal cascade, bottom of this vessel let there be soldered the pipe DE, fig. 5. of ten inches length, and half an inch in diameter: this pipe must be open at each end, and the upper end must be above the water in the vessel. To the bottom also fix five or six small tubes F, about one-eighth of an inch diameter. By these pipes the water contained in the vessel is to run slowly out.

Place this machine on a sort of tin basin GHI, in the middle of which is a hole of one quarter of an inch diameter.

Entertain-
ing experi-
ments.

diameter. To this tube DE, fix some pieces that may support the vessel over the basin; and observe that the end D, of the tube DE, must be little more than one quarter of an inch from the basin. There must be also another vessel placed under the basin, to receive the water that runs from it.

Now, the small pipes discharging more water into the basin than can run out at the hole in its centre, the water will rise in the basin, above the lower end of the pipe DE, and prevent the air from getting into the vessel AB; and consequently the water will cease to flow from the small pipes. But the water continuing to flow from the basin, the air will have liberty again to enter the vessel AB, by the tube DE, and the water will again flow from the small pipes. Thus they will alternately stop and flow as long as any water remains in the vessel AB.

As you will easily know, by observing the rise of the water, when the pipes will cease to flow, and by the fall of it, when they will begin to run again, you may safely predict the change; or you may command them to run or stop, and they will seem to obey your orders.

62
The illumi-
nated foun-
tain.
Plate
CCXLIII
fig. 9.

17. This fountain begins to play when certain candles placed round it are lighted, and stops when those candles are extinguished. It is constructed as follows. Provide two cylindrical vessels, AB and CD. Connect them by tubes open at both ends, as HL, FB, &c. so that the air may descend out of the higher into the lower vessel. To these tubes fix candlesticks H, &c. and to the hollow cover CF, of the lower vessel, fit a small tube EF, furnished with a cock G, and reaching almost to the bottom of the vessel. In G let there be an aperture with a screw, whereby water may be poured into CD.

Now, the candles at H, &c. being lighted, the air in the contiguous pipes will be thereby rarified, and the jet from the small tube EF will begin to play: as the air becomes more rarified, the force of the jet will increase, and it will continue to play till the water in the lower vessel is exhausted. It is evident, that as the motion of the jet is caused by the heat of the candles, if they be extinguished, the fountain must presently stop.

62
The solar
fountain.
Plate
CCXLV.
fig. 8.

18. This fountain is contrived to play by the spring of the air, increased by the heat of the sun, and serves also for a dial at the same time. GNS is a hollow globe of thin copper, eighteen inches in diameter, supported by a small inverted basin, resting on a frame ABC, with four legs, between which there is a large basin of two feet diameter. In the leg C there is a concealed pipe, proceeding from G, the bottom of the inside of the globe, along HV, and joining an upright pipe uI, for making a jet at I. The short pipe Iu, going to the bottom of the basin, has a valve at u under the horizontal part HV, and another valve at V

above it, and under the cock, &c. At the north pole N, there is a screw for opening a hole, through which the globe is supplied with water. When the globe is half filled, let the machine be set in a garden, and as the sun heats the copper and rarifies the included air, the air will press upon the water, which, descending through the pipe GCHV, will lift up the valve V, and shut the valve u, and the cock being open, spout out at I, and continue to do so for a long time if the sun shines, and the adjutage be small. At night, as the air condenses again by the cold, the outward air pressing into the adjutage I, will shut the valve V, but by its pressure on the basin DuH, push up the water which has been played in the day-time through the valve u, and the pipe uHG into the globe, so as to fill it up again to the same height which it had at first, and the next sun-shine will cause the fountain to play again, &c. The use of the cock is to keep the fountain from playing till you think proper: a small jet will play six or eight hours.

If the globe be set to the latitude of the place, and rectified before it be fixed, with the hour-lines or meridians drawn upon it, the hours marked, and the countries painted, as on the common globe, it will form a good dial: the sun then shining upon the same places in this globe as it does on the earth itself. This fountain was invented by Dr Defagulier.

63
The hy-
draulic di-
vers.

19. There is a pretty contrivance, by which the specific gravity of the body is so altered, that it rises and sinks in water at our pleasure. Let little images of men, about an inch high, of coloured glass, be bespoken at a glass-house; and let them be made so as to be hollow within, but so as to have a small opening into this hollow, either at the sole of the foot or elsewhere. Let them be set afloat in a clear glass phial of water, filled within about an inch of the mouth of the bottle; then let the bottle have its mouth closed with a bladder, closely tied round its neck, so as to let no air escape one way or the other. The images themselves are nearly of the same specific gravity with water, or rather a little more light, and consequently float near the surface. Now when we press down the bladder, tied on at the top, into the mouth of the bottle, and thus press the air upon the surface of the water in the bottle; the water being pressed will force into the hollow of the image through the little opening: thus the air within the images will be pressed more closely together, and being also more filled with water now than before, the images will become more heavy, and will consequently descend to the bottom; but, upon taking off the pressure from above, the air within them will again drive out the water, and they will rise to the same heights as before. If the cavities in some of the images be greater than those in others, they will rise and fall differently, which makes the experiment more amusing.

HYDROTHORAX, a collection of water in the breast. See (the Index subjoined to) MEDICINE.

HYDRUNTUM, (anc. geog.), a noble and commodious port of Calabria, from which there was a shorter passage to Apollonia (Pliny.) Famous for its an-

tiquity, and for the fidelity and bravery of its inhabitants. Now Otranto, a city of Naples, at the entrance of the Gulf of Venice. E. Long. 19° 15'. N. Lat. 40° 12'.

HYEMANTES, (in the primitive church), offenders.