rected upwards, in B downwards, in C fideways, and in D obliquely, but the preffure is equal in each. If you pour a greater quantity of water into the veffel, it will rife equally in the tubes; fo that fluids prefs in all manner of directions, and that with a force proportionable to their heights.

The fame experiment is perhaps rendered fill clearer by pouring fome mercury into tubes. The tubes for this purpofe are fmaller than those I ufed in the former experiment: fonie of them are frait, and others bent at various angles. Though the tubes are open at both ends, one of the extremities fhould be clofed till after the immerfion, to prevent the mercury from falling out.

On immerging the lower end of these tubes in water, you will find the mercury afcend toward the upper end of the tubes. It is to be remarked, concerning this experiment, that whatever be the angles at which the tubes are bent, and however they are inclined to the horizon, if before immerfion the mercury in all the tubes be on a level, it will continue fo after immerfion, provided all the tubes are immerfed to the fame depth.

Confequently, when it has been proved that the preffures of a fluid are as the furface preffed, and their depths from the furface of the incumbent fluid, it will follow, that the preffure of a fluid is not only propagated in all directions, but that the quantities of the preffure at the fame depths, and on a given furface, are equal in all directions.

On a curiory view of the fubject, you may confider it as a kind of mechanical paradox, that the preflure of a fluid upward, or in a direction contrary to that of gravity, fhould be nothing more than a confequence of gravity itself; but it is very eafy to thew, from mechanical principles, that a force ading in a given direction may communicate prefere through a number of intermediate

bodies,

bodies, fo that the laft body fhall be impelled in any direction whatever, even in that which is directly contrary to the original impulfe; and this is the cafe in respect of the particles which compofe fluids.

From the foregoing experiments it will appear, I hope, very clear to you, that the perpendicular preffure of any fluid column is, from fome UNKNOWN connection of the parts, diffufed laterally in every direction and at the fame depth, the preffures eflimated in any direction are equal to each other. What has been proved of water, obtains in all other fubftances that are fluid, and under the influence of gravity.

OF THE ACTION OF FLUIDS AGAINST THE BOTTOMS, SIDES, AND TOPS, OF THE VESSELS IN WHICH

THEY ARE CONTAINED.

The bottom and fides of a veffel containing a fluid (and the top alfo, when the fluid is raised above it in a tube) are preffed by the parts of the fluids which immediately touch them; and as action and re-action are equal, thefe parts ali fuftain an equal preffure.

But as the preffure of fluids is equal every way, the bottoms and fides of the veffels are preffed as much as the neighbouring parts of the fluid; but this action, you have feen, increafes in proportion to the height of the fluid, and is every way equal at the fame depth.

This preffure depends on the height, not the quantity, of the fluid; confequently, when the height of the fluid, and the area or furface preffed, remain the fame, the action upon this furface will always be equal, however the figure of the veffel be changed. In other words, the preffure which the bottom of the veffel fuftains from the fluid con

Now the fame preffure which would fupport the water in fuch a tube acts upon FE; but the re-action of F E downwards is equal to the action upwards against it: that is, EF keeps the water down with a force equal to that with which it endeavours to rife, equal to the difference of weight between FEI and MNOR: and as FI fuftains both the weight of the water FEI, and the action or force with which the water is kept from rifing, but OR fuftains only the weight of water M NOR, the preffure upon F I will be equal to the preffure upon O R, and the fame may be proved of any other column. Therefore the bottom of the cone is as much preffed by the weight of water which fills the cone, and this re-action together, as the fan. bottom would be preffed by the weight of as much water as would fill up the whole cylindrical space CBFT; that is, the preffure upon the bottom of a conical veffel, is equal to the pressure upon the bottom of a cylindrical one of the fame BASE AND HEIGHT.

The fame mode of reafoning may be applied to the veffel DB LP, fig. 8, pl. 1, which confifts of two cylindrical parts N MI.P, a great cylinder at the bottom, and DBI V a leffer one at the bottom. For the preffure upon LP, when the veffel is full of water, will be as great as if the veffel was as wide at top as it is at bottom; that is, as great as it would be upon the fame bottom LP, fuppofing the veffel was an uniform cylinder, whofe bafe was LP, and height L F.

LA, and OR, two equal drops at the fame depth, are preffed equally; and OR having as much water to fuftain, is as much preffed as if the veffel was an uniform cylinder. Therefore LA, or CP, or any other equal part at the bottom, and confequently the whole bottom, is as much preffed in one cafe as it would be in the other. Indeed L A or CP have lefs water to fuftain than

OR;

OR; but the column NTLA preffes upwards against NT with a force equal to the difference between this column and DBOR, or to the weight of as much water as would fill the space FENT; for if a hole was made at NT, and a tube, FENT, foldered into it, the preffure against the bottom of the tube would fupport water in it to the height NT, the fame height it ftands at in the tube DBIV. Now as the re-action of N T downwards is equal to the action upwards against it, that is, the force with which N T keeps the water below it, down againft LA, is equal to the force with which this water preffes against N T.

LA is therefore preffed down not only with the weight of the water N T L A, but likewise by the re-action of N T, which is equal to the weight of as much water as would fill FENT, and make NT LA equal DB RO; from which it follows, that the weight and re-action together on LA, are equal to the weight on DBR O, by which OR is preffed; and the fame may be proved of every other equal portion of the whole bottom and cover, and therefore, by the weight and re-action, LP is as much preffed as if it was the bottom of a cylindrical veffel FHLP, having the fame dimenfions at the top as at the bottom, and filled with water to the height L F.

Though the preffure upon FT, fig. 6, pl. 1, is equal to the preffure upon CD, when both veffels are filled with water to the fame perpendicular height; yet if they were filled with ice, or any other Jolid fubftance, inftead of water, CD would be more preffed than F T.

For CD, whether the veffel be filled with ice or water, fuftains the whole weight of the body which refts upon it, and no more; but F T, which, VOL. III. befides

Cc.

befides the weight MNF T, fuftains the re-action of the fides MN FT, when the veffel is filled with water, has only the weight to sustain when it is filled with ice; for ice, or any other folid body, does not prefs upwards. This is a property, which, as it only arifes from the nature of a fluid, belongs to fluids only; FT will therefore be only preffed by the weight of the ice, and confequently will be lefs preffed than CD, in proportion as the cone is lefs than the cylinder, when their bases and heights are equal.

For the fame reafon LP, fig. 8, pl. 1, if it were full of ice, would be as much lefs preffed than when it is full of water, as the quantity of matter contained in the compound veffel NM LP is lefs than the quantity of matter contained in a cylindrical veffel, whofe bafe is L P, and height L F.

The fecond cafe of the propofition is when the veffel ABOR, fig. 9, pl. 1, is wider at top than bottom. For here alfo the preffure of any fluid upon the bottom, OR, of it, is the fame as in a cylindrical veffel, STOR, of an equal bafe, and filled with the fame fort of fluid to the fame height.

For the bottom OR, in either cafe, fuftains juft the fame quantity of fluid, and confequently the fame quantity of matter. If it is the bottom of a cylinder, then it fuftains no more than the column STOR, because the veffel holds no more. If it be the bottom of an inverted cone, as A BOR, then it fuftains only the fame column; for though the veffel holds more than this, yet all the rest of the fluid is fupported by the fides A O, BR, and therefore does not prefs on the bottom.

Thus you fee, that whether a veffel be narrower or wider at the top than at the bottom, the preffure upon the bottom is the fame as in a cylindrical veffel of the fame bafe and height; for

when