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than when it is full of water, as the quantity of counterpoife. The friction of the piston, being matter contained in the compound vessel NMLP the same in every case, makes no alteration in the is less than the quantity of matter contained in a experiment. cylindrical vessel, whose base is LP, and height To show that the lateral pressure is equal to LF.
the perpendicular pressure upon a larger scale, and 2. The ad case of the proposition is when the
vef- in a manner which relates more to the preceding fel A BOR, fig. 10, is wider at top than bottom. experiment, we have delineated an apparatus, fig. For here also the pressure of any Ruid upon the 1.pl. CLXXXVI. with 3 tubes that communicate bottom, OR, of it, is the same as in a cylindrical with each other. Themiddleone is a large glass tube veffel, STOR, of an equal base, and filled with or cylinder, A B; the lower end is firmly cement. the same fort of fluid to the fame height. For the ed into a strong brass hoop; to the sides of this bottom O R, in either case, sustains just the same hoop are soldered the brass tubes G, H, into each quantity of fluid, and consequently the same quan- of which a glass tube is cemented. One of these, tity of matter. If it is the bottom of a cylinder, EF, is parallel to the large glass vessel AB; but then it fuftains no more than the column STOR, the other C D is inclined thereto. The inclined because the vessel holds no more. If it be the tube is sometimes furnished with a joint, that the bottom of an inverted cone, as A BOR, then it inclination may be varied as may be necessary. sustains only the same column; for, though the If we pour water into the tube E F, this will vefsel holds more than this, yet all the rest of the run through G, into the larger vessel A B, and fluid is supported by the fides A O, BR, and rise therein; and if we continue pouring water therefore does not press on the bottom.
until it comes to any given height, as I K, and Thus, whether a vessel be narrower or wider at then leave off, the surface of the water in the the top than at the bottom, the pressure upon the small tubes E F, CD, will be found at the same bottom is the same as in a cylindrical veffel of the height; the perpendicular altitude is the fame in same base and height; for when it is narrower at all the three tubes, however small the one may the top than at the bottom, though it holds less be in proportion to the other. This experiment water than the cylindrical one would, yet the clearly proves, that the small column of water bapressure is not less, because the re-action of the lances and supports the large column; which it fides supplies the defect; and when it is wider at could not do if the lateral pressures at bottom were the top than at the bottom, though it holds more not equal to each other. Whatever be the incliwater than the cylindrical one would hold, yet nation of the tube CD, still the perpendicular althe pressure is not greater, because the sides sup- titude will be the same as that of the other tubes, port the excess.
though to that end the column of water must be Let us now confirm by experiment, what we much longer than those in the upright tubes. bave thus endeavoured to render plain without it. Hence it is evident, that a small quantity of a fiuid The apparatus, fig. 11, is designed for this pur- may, under certain circumstances, counterbalance pose. It is sometimes called the apparatus of any quantity of the same fluid. Hence also it is PASCHAL, sometimes the apparatus for illustrating evident, that in tubes that have a communication, the HYDROSTATIC PARADOX. It confifts of three whether they be equal or unequal, short or oblique, vefsels, fig. 12, fig. 13, and ABC D, fig. II, each the fluid always rises to the same height. Conseof which are of the same fize at bottom and of quently water cannot be conveyed by means of a the same height, and may be screwed alternately pipe that is laid from a reservoir to any place that on the brass barrel E F, fg. 11, in which a pifton is higher than the reservoir itself. Nides up and down with ease. One of the vefsels, The ancients, it has been said, were ignorant of fig. 13, is cylindrical; the other A B C D, fig. II, this principle, and knew not the ute of pipes for is an inverted cone, wider at top than bottom; conveying water up hills: but this assertion is not the third, fig. 12, is a tube screwed to a plate, true; they did know the use of pipes, but chose which makes: the bottom the same lize as that of to employ aqueducts in their stead, for reasons the other two; it has a funnel at top to prevent we cannot now with certainty account for. the water, in making the experiment, from being Our next experiment proves, with great clear, ipilt. First screw the cylindrical veffel to the ness, the HYDROSTATICA PARADOX, that very barrel, pushing down the piston as low as it will go, great weights may be balanced by a very small then book the wire of the pifton to the rings from weight of water, without its acting to any mecha. the short ends of the steelyards G H, IK. Now nical advantage: but, more particularly, it alsa, pour water in the cylinder up to the inark in the proves, that its pressure upwards is equal to its inside, and find what weights, suspended from the pressure downwards, and all this even to those longer arms of the steelyard, will raise the piston; who have no previous kpowledge of hydrostatical then take the cylindrical vessel from the barrel. principles. The apparatus, fig. 2, pl. CLXXXVI. Subftitute the vessel A B C D, fig. 11, which is confifts of two large thick boards, C D E F, con like an inverted cone, in place of the former; fill nected together by leather, like a pair of bellows; it with water to the mark, as before, and hook hence it is usually called the hydrostatic bellowsa on the wire of the piston to the steelyards; and A long brass pipe is fixed to the bottom board; though the quantity of water is now many times so that water being poured in at the top, will greater than what was in the cylinder, yet the pass between the two boards. We will suppose same counterpoise will raise the pifton. Take off the boards of the apparatus oral; and that the the conical vessel, and screw on the tubular one; longest diameter is 18 inches, the shorter one fixe and though this holds a much smaller quantity teen. Having poured water enough into the bel, than either of the former, fill it requires the same lows to keep the boards arunder, and put fix half
hundred weights on the top of the boards, we er than the upper, to be able to withftand the next pour water into the tube, to the height of greater degree of pressure to which they are exthree feet, and find it will push up all the weights. pofed. Thus the water in the pipe, which weighs but a quarter of a pound, fuftains zoolb. weight. If Sect. IV. Of the ACTION of FLUIDS on BODIES we take off the weights, and try, by pressing upon
IMMERSED in them. the upper board, to force the water out at the ARCHIMEDES is the firft mathematician we upper tube; our strength will be scarce fufficient read of (see his tract De Inhdentibus) who made for the purpose. Thus we clearly fee how great a inquiries concerning the finking and floating of pressure upwards is exerted by the water. bodies in fluids, their relative gravities, their le
Another instrument has been invented, forvities, their situations and positions. He was perproving that the preflure of fluids is in proportion haps also the first who ever attempted to deterio their perpendicular heights, without any regard mine in what proportion bodies differ from one to their quantity.
another as to their specific gravities, and this he ABCD, fig. 3; pl.CLXXXVI. is a box, at one end effected in order to discover the cheat of the work. of which, as at a, is a groove from top to bottom, man who had debased king Hiero's CROWN; for receiving the upright glass tube I, which is and though the means he employed were certainly bent to a right angle at the lower end, as at fig. much inferior to what would now be used, yet 4; and to that end is tied the end of a large blad he was so pleased with his discovery, that not be der K, fig. 4, which lies in the bottom of the box. ing able to contain his joy, like a madman, leap. Over this bladder is laid the moveable board M, ing from the bath naked as he was, he is said to fig. 5, in which is fixed an upright wire. Leaden have run about the streets of Syracuse, crying out weights N N, fig. 3, to the amount of 16 lb. with Eupnna! I have found it! Before we proceed to holes in the middle, are put upon the wire, over explain this interesting subject, some terms wbich the board, and press upon it with all their force. have only been as yet loosely explained, must be The bar p is then put on, to secure the tube from defined. falling, and keep it upright; and then the piece 1. The DENSITY of a body is the QUANTITY EFG is to be put on, to keep the weights in a ho- OF MATTER which it contains under a GIVEN rizontal position, there being a round hole at e. BULK. The density of a body is therefore mea. Within the box are four upright pins, to prevent the fured by the proportion which its quantity of board at first from preshing on the bladder. Pour matter bears to its bulk; for, the more numewater into the tube at top; this will run into the rous the particles of matter are in the fame porbladder : and after the bladder has been filled up tion of space, the greater is the denfity of the to the board, continue pouring water into the body, and the fewer the particles the less the tube, and the upward pressure of the fluid will density. raise the board with all the weight upon it, even 2. The SPECIFIC GRAVITY of a body is the though the bore of the tube thould be so small WEIGHT OF IT when the BULK is given ; or, the that less than an ounce of water would fill it. specific gravity of a body is its weight compared
Upon this principle mathematicians affert, that with another body of the fame magnitude. It is the same quantity of water, however small, may called the specific gravity, because it is the compaproduce a force equal to any affignable one, by in- rative weight of different species or forts of bocreasing the height and bare upon which it preffes. dies. Thus, if the fpecific gravity of gold is faid Dr Goldsmith mentions having seen a frong hogf- to be to that of water as 19 to I, the meaning is, head split by this method. A trong, though small that, bulk for bulk, or under equal dimenfions, tube of tin, twenty feet high, was inserted in the the weight of gold is to that of water as 19 to 1; bung-hole; water was poured in this to fill the or that a cubic inch of gold wilt weigh 19 times bogshead, and continued till it rose within about as much as a cubic inch of water. a foot of the top of the tube; the hogshead then 3. The SPECIFIC GRAVITY of BODIES is as burst, and the water was scattered about with in their denSITY, for the specific gravity is the credible violence.
weight of a given bulk, and the weight of bodies As the bottom of a vefsel bears a preffure pro- is as their quantity of matter; therefore the fpeportional to the height of the liquor, fo likewise cific gravity of a body is as the quantity of matter do those parts of the sides which are contia contained in a given bulk, that is, as its denfity. guous to the bottom, because the pressure of 4. The SPECIFIC GRAVITY of BODIES is inHuids is equal every way; and as the prefe versely as their BULK when their weights are fure, which the lower parts of a fuid sustain equal. The specific gravity of bodies is, we have from the weight of those above them, exerts it- already seen, as their density, and the density of felf equally avery way, and is likewise propor- bodies is inversely as their bulk when the weights tional to the height of the incumbent fluid, the are equal. Thus, if the specific gravity of gold fides of a veflel must everywhere fustain a pref- be to that of filver as 19 to 11, and a cylinder of fure proportional to their diftance from the upper gold or inches high weigh a pound, a cylinder of furface of the liquor. Whence it follows, that Älver having an equal bale and weighing a pound in a veffel full of liquor, the fides bear the great- must be 19 inches high; for since the specific graest stress in those parts next the bottom; and that vities are 19 to 11, the bulks, that is, the heights, the strefs upon the fides decreases with the in- must be as those gravities inverted, or as it to crease of the diftance from the bottom in the fame 19. If the specific gravity of mercury be to that proportion : fo that in veffels of confiderable of water as 14 to 1, and a cylinder of mercury of Leigbt, the lower parts ougbe to be mouch frong- a certain weight is 30 inches bigh, then a cylinder
of water of equal base must be 420 times as high; be differently affected ; we have therefore to conso that the height of the cylinder of water will be fider which of these impressions will prevail. It is 34 times 30, or 430 inches, or 35 feet.
evident that the lateral pressures all balance each The MAGNITUDE of a body is expressed by a other, being equal, as arising from equal altitudes number denoting its relation to some criterion ge- of the fluid, and opposite in their directions ; fo nerally used, and fimilar to itself, as a cubical inch, that from these the body is no way determined foot, &c. The absolute weight of a body is rela. to any motion. But a body immersed in a fuid tive, being expressed by a number denoting its is pressed more upwards than it is downwards ; relation to some arbitrary or conventional stand- for those parts of the fluid which are contiguous ard, as 1 pound, 1 ounce, of which it is a mul- to the under surface have a greater altitude, and tiple or aliquot part; and in the same fort of mat- therefore a greater force, than those that are contiter, supposed to be homogeneous, it depends up- guous to the upper surface; the body muft thereon and varies as the magnitude.
fore be more violently elevated by the former than The specific weight or gravity of the fame spe- depressed by the latter, and would therefore afcend cies of matter, whether its magnitude be great or by the excess of force, were it devoid of gravity. small, as of A, 2A,or 3 A, isthe same, being accord. For when a solid body is immersed in a Auid, it ing to the definition of the weight of a given bulk. presses down, and endeavours to descend by the The object therefore of specific gravities is to dif. force of its gravity; but it cannot descend withtinguish different species of matter from each out moving as much of the liquid out of its place other, in one of their most obvious qualities, weight as is equal to it in bulk; it is therefore relifted, of matter contained in a given space.
pressed upwards by a force equal to the weight The weight of any portion of matter is easily of as much of the fluid as is equal in magnitude afcertained, but it is not always easy to measure the to the bulk of the body ; being the difference in space occupied by a body, or its MAGNITUDE, and weight of two columns of the Auid, whereof one in some instances it cannot be effected without reaches to the upper, the other to the under surartificial methods. It is found expedient to em- face of the body. ploy as a criterion some pure and homogeneous We shall illustrate this by a diagram. When substance, as distilled water, whose specific gra. . any hard body, as a piece of lead, is immersed in vity is nearly the same at all times; and by com- water, the lower part of it, mn, fig. 6. plate paring this with other substances, the ratio of CLXXXVI. muft be continually pressed upwards their specific gravity may be discovered ; and de- just as much as the water itself in the same place noting the specific gravity of water by any num. as the lead is pressed upwards. Now the force with ber, the numbers exprefsing the specific gravities which the water, m n, is pressed upwards, is exof other bodies are hence obtained.
actly equal to the force with which it would be It follows, from what has been already demon. pressed downwards if the lead was out of the way; Arated, that when a solid is immersed in a fluid, for every part of a fiuid is pressed as much upwards it is preffed by that Auid on all fides ; and that as it is downwards. The force with which mn pressure increases in proportion to the height of the would be prefled downwards if the lead was out of Auid above the solid. We may also prove this di. the way, would be equal to the weight of the inrectly by experiment. Thus, tie a leathern bag to cumbent column, or of as much water as would fill the end of a glass tube, and fill it with mercury; the whole space E Hm n; therefore the force with immerge the bag in water, but so that the upper which m n is pressed upwards, and consequently or open end of the tube may be always above the the force with which the piece of lead is pressed surface of the water; the pressure of the water upwards, is equal to the weight of as much water as against the bag will raise the mercury in the tube, would fill the whole space E H mn, or the whole and the ascent of the mercury will be in propor- space HP no, if this space be taken equal to E Hmn. tion to the height of the water above the bag. Let us next consider the force with which this
When a solid is immersed in a fluid to a great piece of lead is pressed downwards ; this force is depth, the pressure against the upper part differs juft equal to the weight of as much water as is very little from the pressure againīt the under part; above it, that is; it is equal to the weight of the whence bodies very deeply immersed are, as it column E Hrs. The difference therefore of the were, equally pressed on all fides; but a pressure two pressures will be the difference in weight be. which is equal on all sides may be suftained by soft tween the 2 columns EH m'n, and E Hrs; for the bodies without any change of figure, and by very weight of the former is equal to the preffure upbrittie bodies without their breaking. Take a wards, and the weight of the latter is equal to the piece of soft wax of an irregular figure, and an egg, preffure downwards ; consequently the pressure and inclose them in a bladder full of water: place upwards will be as much greater than the pressure it in a square box, and put on a moveable cover, downward, as the weight of the water E H m n is which will bear on the bladder ; there may be grcater than the weight of the water E Hrs. But placed on this cover a weight of 100, or even 150 the difference between these two weights is just as Ib. without breaking the egg, or any way altering much as would fill the fpace rsm n, which the body the figure of the wax.
fills; for juft so much water added to EHrs, It has been shewn, that fluids press upon bodies would make it equal to EH mn; confequently the to which they are contiguous every way, and on body is presled more upwards than it is downall fides, but the pressure upon each part is not wards by a force equal to the weight of as much the fame; the altitude of the fluid is everywhere the water as would fill the space taken up by the measure of its force, and the several parts of the body. In other words, the body is acted upon fame body, being at different depths, mult thus by two forces in contrary directions, but the VOL. XI. PART II.
force with which the Auid ads upon it to make it wards, which is all there is to support it; which ascend, exceeds theforce by which it presies down. being too weak to sustain it, the stone links to the
ds; and this excefs is equal to the weight of as bottom. much of the fluid, whatever it is, as would fill the A BODY that is IMMERSED IN A FLUID will rise face taken up by the body.
to the surface, and swim upon it, if it be specif. The case will be the fame whatever be the figure cally lighter than the fluid. A piece of cork, of them is dy'iminersed; for suppose it to be a cone when it is immersed in water, is prefied by the ISLV. g. 7, plate CLXXXVI. then, as every water both upwards and downwards; but the equall part of a fluid at the same depth is pressed preslure upwards exceeds the pressure downwards, raaby in all directions, if V I be equal to L V, and this excess is equal to the weight of as much it follows, that these two parts of a thin sheet of water as is of the same bulk with the piece of frid FE will be pressed upwards by equal forces; cork; therefore, as far as the action of the water but V I is pressed as much upwards as downwards, is concerned, the cork ought to rise to the top; therefore L V is pressed as much upwards as V i and the cork itself being also specifically lighter downwards. Now the force that preises VI down. than water, the force with which it endeavours to wards is the weight of the fluid HPV I that is fink is less than the force which buoys it up; it above it; consequently L V, where the bottom of must therefore on this account rise till it comes to the body is placed, is supported by a force equal the surface. Hence the reason is plain, why fir, to the weight of the column HPV 1, and this.co. oak, and elm, that are specifically lighter than lumn is equal to MHL V. Therefore the body water, will swim in it; while ebony and guaiacum, is prefled upwards with a force that is equal to a that are specifically heavier, will link. weight of as much of the fluid as would fill the There is generally a part of any body that floats whole space MHL V.
on the water below the surface, and this part is The same body is in the mean timepressed down- equal in bulk to as much of the fluid as would wards by the weight of all that fluid that is above weigh what the body weighs. Let p, t, e, i, Piate any part of it, that is, by the weight LTSV HM, CLXXXVI. fig. 8, be a piece of cork, then s, 71, 4, and not merely by the column o WTS, which i, the part below the surface AB of the water, will reaches from the surface to the top of the body. - be equal in bulk to as much water as would weigh From hence it follows, that the difference between what p, t, e, i, the whole cork, weighs. The force the centre column MHL V, or such a columnas' with which the water at e, i, is prefied upwards, this would be if the body was out of the way, and is exactly the force with which it would be presled the column L TSVHM is the difference between downwards, if the cork p, t, e, i, was out of the the prefire upwards and the pressure downwards. way, because every part of a fluid is presied equal. But this difference is plainly equal to as much of ly in all directions. But the force with which ein the fluic as would fill the space the body takes up; would be pressed downwards if the cork was away, the force, therefore, by which the fluid acts upon is equivalent to the weight of as much water as the body to make it ascend, exceeds the force by would fill the space taken up by the part of the whico it presies downwards, and this excess is cork below the water; and consequently the force equal to the weight of as much of the fluid as with which e, in the bottom of the cork, is prefied would fill the space taken up by the body. upwards, is equivalent to the weight of as much
But as all bodies by the force of gravity tend water as would fill up the space, s, n, e, i, or the downwards, it is clear from what has been said, part of the cork below the surface. If therefore that it depends upon the absolute weight of the the part which is below the surface has the same immersed body whether it shall ascend or descend. bulk as a quantity of water that would weigh what 1. If the weight of the body exceed that of an equal the whole cork weighs, then the pressure upwards bulk of the Auid, the excess of force will tend will be equal to the weight of the cork, and keep downwards. 2. If the weight of the body bé less it from sinking. than an equal bulk of the fluid, the upward pref A BODY that has the same SPECIFIC GRAVITY sure will prevail, and it will ascend. 3. If both with the fuid into which it is immersed, will rest be precisely equal, the body will remain at rest in in any part of the fluid wherever it happens to be any part of the fluid.
placed. For the body endeavours to descend by 3. First, then, a body immersed in a fluid will fink its own weight, and is prevented from descending if it be specifically heavier than that fluid; for it by a force equal to the weight of an equal bulk of endeavours to descend by its own weight, and is fluid ; bụt when the body and the fluid are of the fupported by a forcé equal to the weight of an fame specific gravíty, equal masses of each are of equal bulk of fluid, or of as much fluid as will fill the same weight, and consequently the force with the space taken up by the body. If therefore the which the body endeavours to descend, and the body be specifically heavier than the fuid, i.e. force which opposes the descent, are equal to bulk for bulk heavier than the fluid, it's weight each other; and as they act in contrary directions, will be greater than the pressure upwards of the the body will reft between them, so as neither to fuid which is to support it; and, consequently, link by its own weight, nor to ascend by the presthis pressure will not so support as to keep it from sure of the fluid upwards. finking. If we throw a stone into the water, it From these positions, it is plain, that if by finks, for it is specifically heavier than the water; any contrivance the specific gravity of any solid that is, where the bulks are equal, the weight of can be varied so as to be one while greater, anothe stone is greater than the weight of water; ther lefs, and then equal to the specific gravity of therefore the force with which it endeavours to the fluid wherein it is immersed, the body will descend is greater than the excess of pressure up- Ink, or rise, or remain suspended, according to
the variations of its specific gravity. And this is Thus a cubic foot of lead r, s, m, n, hanging by the case in the experiment of the little glass ima. the string Li, fig. 6.pl. CLXXXVI. will weigh leis ges that some philosophers exhibit, which are in the water than it does out of it, because the water made to ascend or descend, or remain suspended by its preffure upward against the lead will support at pleasure.
a cubic foot of water, or 1000 oz. avoirdupois, The images being set to'float on the water, the for so much a cubic foot of water weighs, and top of the vessel must be covered with a bladder consequently so much of its weight the lead must closely bound about the neck of the vessel, that lose. Again, a body endeavours to descend by the air which lies on the surface of the water may its whole weight; when it is immersed in a fluid, not force its way out when it is condensed by the it is supported by a force equal to the fame bulk hand. The images themselves are nearly of the of that fluid ; and since these two forces act in fame specific gravity with the water, but rather a contrary directions, the weight which the body little lighter, and consequently float near the fur- ' retains in the fluid will be the difference between face: the images being hollow are full of air, them, or it loses the weight of an equal bulk of which, by means of small holes in their heads, the fluid. communicates with the air without. When the The following experiment will render the posi. air which lies beneath the bladder is pressed by the tion self-evident: The apparatus for it confifts hand, it presses on the surface of the water; and of a beam, a small hollow cylindric bucket A B, as the pressure is propagated through all the wa. and another cylinder C D, which precisely fits the ter, those portions which are contiguous to the capacity of the bucket A B, fig. 9.
pl. CLXXXVI. heels of the images are thereby forced into the Only a portion of one arm, EF, of the beam is repre. holes; by which means the air within is conden- sented in this figure. First, suspend the bucket led, and at the same time the weight of the ima- by one end of the beam. At the bottom of the ges is increased by the weight of the influent wa bucket is fixed a strong thread of filk with a ter; and when so much water is forced in as to loop on the lower end; to this loop the close cyrender the specific gravity of the images great linder is suspended. It is necessary to counterpoise er than that of the water, the images descend these by a weight at the other end of the beam. to the bottom, where they remain as long as the Then fet a jar of water under the cylinder, and preffure above continues; but when that is taken gently lower the beam, and it will become lighter off by the removal of the hand, the condensed air and lighter upon the beam as the cylinder descends. in the images dilates and expands itself, and in so When it is quite immersed, the equipoise is de. doing drives out the water, upon which account stroyed by the descent of the weight of the other the images become specifically lighter than water, arm. To new how much weight is loft by the and of course ascend. As the pressure on the cylinder, add the weight of a quantity of as much bladder is greater or less, so must the quantity of water as is equal in bulk to the cylinder; that is, water be which is forced into the images; and fill the bucket, which is exactly the same size; therefore, whenever it happens, that during the and by doing it gradually, the equipoise will be ascent or descent of an image, such a pressure is restored by degrees till the bucket is full, and then made as fuffices to force in just as much water as the beam becomes truly horizontal as at first, the is requisite to reduce the image to the same speci- loss of weight being reftored by the equal cylinder fic gravity with the water, the image stops, and of water in the bucket. remains suspended; upon increaling the pressure It is evident from what has been said, whence it defcends, and ascends if it be lessened. Some the loss of weight proceeds. It is no otherwise of the images begin to descend sooner or rise later loft than as it is luftained by the action of a con, iban others, either because they are specifically trary force; and it becomes therefore obvious, why heavier, or because the cavities in their legs are the weight of a bucket of water is not perceived greater in some images in proportion to their while it is in the water, not because that weight is magnitudes, than they are in others. This is but deftroyed, but because it is supported; not because an experiment of mere amusement; many and fluids do not gravitate when they are in fluids of the more imyortant uses are the result of our being same sort, but because there is a pressure in a contra. able to determine the specific gravities of bodies: ry direction which is exactly equal to their gravitya to this, therefore, we shall now proceed.
As the weight which a body loses, when it is All BODIES, when IMMERSED IN A FLUID, lose immersed in a fluid, is always the weight of as the weight of an equal bulk of that Auid; in other much of that fluid as is equal in bulk to itself, it words, every body immersed in a fluid loses a part follows, that the weight loft by the body cannot of its gravity equal to the weight of the buid, at all depend either on the depth of the fluid itself, which would fill the space taken up by the body. or the depth to which it is immersed therein. An A piece of lead, or of any other substance, when anchor loses no more of its weight when it is at it is immersed in water, is not so heavy as when the bottom than when it is just below the furface, it is out of water; for the water presses it more for in either case ir loses the weight of as much upwards than downwards, and the excess of the water as is equal in bulk to itself. It is not more pressure upwards will support part of the weight, easy to swim in deep than in thallow water, proBut this excess was shewn to be equivalent to the vided the water is not so fhallow as to prevent one weight of as much water as has the same bulk with from striking freely; for whatever is the depth of the lead; and consequently fince the body immer- the water, a man loses the weight of as much wafed must lose as much of its weight as the fluid ter as is equal in bulk to his own body; for which san fupport, the lead will lofe the weight of an reason thallow water will buoy bim up with as equal bulk of water.
great force as deep water.