when it is narrower at the top than at the bottom, though it holds lefs water than the cylindrical one would, yet the preffure is not lefs, because the reaction of the fides fupplies the defect; and when it is wider at the top than at the bottom, though it holds more water than the cylindrical one would hold, yet the preffure is not greater, because the fides fupport the excefs.

Let us now confirm by experiment, what I have endeavoured to render plain without it. The apparatus on the table, fig. 10, pl. 1, is defigned for this purpose. It is fometimes called the apparatus of Pafchal, fometimes the apparatus for illuftrating the hydrostatic paradox. It confifts of three veffels, fig. 11, fig. 12, and ABCD, fig. 10, each of which are of the fame fize at bottom, and of the fame height, and may be fcrewed alternately on the brass barrel E F, fig. 10, in which a piston slides up and down with ease. One of the veffels, fig. 12, is cylindrical; the other, ABCD, fig. 10, is an inverted cone, wider at top than bottom; the third, fig. 11, is a tube fcrewed to a plate, which makes the bottom the fame fize as that of the other two; it has a funnel at top, to prevent the water, in making the experiment, from fplashing over.

I fhall firft fcrew the cylindrical veffel to the barrel, pushing down the pifton as low as it will go, then hook the wire of the pifton to the rings from the fhort ends of the fteelyards GH, I K. Now pour water in the cylinder up to the mark in the infide thereof, and find what weights, fufpended from the longer arms of the fteelyard, will raife the pifton; then take the cylindrical veffel from the barrel.

Subftitute the veffel A B C D, fig. 10, which is like an inverted cone, in place of the former; fill it with water to the mark, as before, and hook on the wire of the pifton to the fteelyards; and though

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though the quantity of water is now many times greater than what was in the cylinder, yet the fame counterpoife will raife the pifton.

Take off the conical veffel, and screw on the tubular one; and though this holds a much finaller quantity than either of the former, ftill it requires the fame counterpoife.

The friction of the pifton being the fame in every cafe, makes no alteration in the experiment.

To fhew that the lateral pressure is equal to the perpendicular preffure upon a larger fcale, and in a manner which relates more to the preceding experiment, here is an apparatus, fig. 5, pl. 1, with different tubes, that communicate with each other. The middle one is a large glafs tube or cylinder, A B; the lower end is firmly cemented into a ftrong brafs hoop; to the fides of this hoop are foldered the brafs tubes G, H, into each of which a glafs tube is cemented. One of thefe, E F, is parallel to the large glafs veffel A B; but the other, CD, is inclined thereto. The inclined tube is sometimes furnished with a joint, that the inclination may be varied at pleasure.

Pour water into the tube E F; this will run through G, into the larger veffel AB, and rife therein; and if you continue pouring water until it comes to any height therein, as I K, and then leave off, you will find that the furface of the water in the fmall tubes EF, CD, is at the fame height; the perpendicular altitude is the fame in all the three tubes, however fmall the one may be in proportion to the other. This experiment clearly proves, that the fall column of water ballances and fupports the large column; which it could not do if the lateral preffures at bottom were not equal to each other. Whatever be the inclination of the tube CD, ftill the perpendicular altitude will be the fame as that of the other tubes, though to that

end

end the column of water must be much longer than thofe in the upright tubes.

Hence it is evident, that a small quantity of a fluid may, under certain circumftances, counterballance any quantity of the fame fluid.

Hence alfo it is evident, that in tubes that have a communication, whether they be equal or unequal, bort or oblique, the fluid always rifes to the fame height. Confequently water cannot be conveyed by means of a pipe that is laid into a refervoir, to any place that is higher than the refervoir.

It has been afferted, that the ancients were ignorant of this principle, and knew not the ufe of pipes for conveying water up hills: but this af sertion is not true; they did know the use of pipes, but chose to employ aqueducts in their ftead, for reasons we cannot now with certainty ascertain.

Our next experiment proves, with great clearnefs, the hydroftatical paradox, that very great weights may be ballanced by a very small weight of water, without it's acting to any mechanical advantage; but, more particularly, it alfo proves, that it's preffure upwards is equal to it's preffure downwards, and all this even to those who have no previous knowledge of hydroftatical principles. The apparatus, fig. 1, pl. 2, confifts of two large thick boards, CD, EF, connected together by leather, like a pair of bellows; hence it is usually called the hydrostatic bellows. A long brass pipe is fixed to the bottom board; fo that water being poured in at the top, will pafs between the two boards. In the apparatus before you the boards are oval; the longeft diameter is eighteen inches, the fhorter one fixteen inches. I have poured water enough into the bellows to keep the boards afunder, and have put fix half hundred weights on the top of the boards. I fhall now pour water Cc 3

into

into the tube, to the height of three feet, and it will push up all the weights. Thus the water in the pipe, which weighs but a quarter of a pound, fuftains three hundred pounds weight. Take off the weights, and try, by preffing upon the upper board, to force the water out at the upper tube; your ftrength, you find, is fcarce fufficient for the purpofe. Thus you fee clearly how great a preffure upwards is exerted by the water.*

Upon this principle mathematicians affert, that the fame quantity of water, however small, may produce a force equal to any affignable one, by increafing the height and base upon which it presses. Dr. Goldsmith mentions having feen a ftrong hogfhead split by this means. A ftrong, though small tube of tin, twenty feet high, was inferted in the bung-hole; water was poured in this to fill the hogshead, and continued till it rofe within about a

foot

Fig. 16. pl. 1, represents another inftrument for proving that the preffure of fluids is in proportion to their perpendicular heights, without any regard to their quantity.

ABCD is a box, at one end of which, as at a, is a groove from top to bottom, for receiving the upright glafs tube I, which is bent to a right angle at the lower end (as at fig. 17); and to that end is tied the end of a large bladder (K. fig. 17), which lies in the bottom of the box. Over this bladder is laid the moveable board M, fig. 18, in which is fixed an upright wire. Leaden weights (NN, fig. 16), to the amount of fixteen pounds, with holes in the middle, are put upon the wire, over the board, and prefs upon it with all their force.

The bar p is then put on, to fecure the tube from falling, and keep it upright; and then the piece E F G is to be put on, to keep the weights in an horizontal pofition, there being a round hole at e. Within the box are four upright pins, to prevent the board at firft from preffing on the bladder.

Pour water into the tube at top; this will run into the bladder and after the bladder has been filled up to the board, continue pouring water into the tube, and the upward preffure of the fluid will raife the board with all the weight upon it, even though the bore of the tube fhould be fo finall that lefs than an ounce of water would fill it.

foot of the top of the tube; the hogfhead then burft, and the water was fcattered about with incredible force.

As the bottom of a veffel bears a preffure proportional to the height of the liquor, fo likewife do thofe parts of the fides which are contiguous to the bottom, because the preffure of fluids is equal every way; and as the preffure which the lower parts of a fluid fuftain from the weight of those above them exerts itfelf equally every way, and is likewife proportional to the height of the incumbent fluid, the fides of a veffel muft every where fuftain a preffure proportional to their distance from the upper furface of the liquor. Whence it follows, that in a veffel full of liquor, the fides bear the greatest stress in those parts next the bottom; and that the ftrefs upon the fides decreases with the increase of the distance from the bottom, and in the fame proportion; fo that in veffels of confiderable height, the lower parts ought to be much stronger than the upper, to be able to withstand the greater preffure.

OF THE ACTION OF FLUIDS ON BODIES IMMERSED

IN THEM.

Archimedes, in his two books De infidentibus bumido, is the first we know of who made inquiries concerning the finking and floating of bodies in fluids; their relative gravities, their levities, their fituations, and pofitions. He was alfo probably the first that ever attempted to determine in what proportion bodies differ from one another as to their specific gravities, and this he effected in order to difcover the cheat of the workmen, who had debased king Hiero's crown; and though the means he employed was certainly much interior to what would now be used, yet was he fo pleafed with his difcovery,

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