Confequently the Horizontal prefs'd Part CD, undergoes an equal Preffure from the ftreight Colum CGDH, as from the Curve or oblique one CDFND.

And this would be juft the fame, and remain fo, though the Curve Tube (Tab. XXVI. Fig. 4.) were widen'd as at CE F K D, or even narrow'd in any other manner, fo as to contain a greater or leffer quantity of Liquor; as likewife in which Obliquity, one of the said Tubes ftood upon the Plane B CD, and press'd the Part CD; if only the prefs'd Horizontal Part C D preferv'd the fame Magnitude, and the Perpendicular Height G C, HD, or F M of the Fluids upon the Plane CD continued the fame.

SECT. XXXV. The Hydroftatical Laws of Oblique Preffures

XXXVI. So that the foremention'd Law of Altitude, is here alfo of full Force in the Cafe of Oblique Preffures; and the following Propofition is true :

If a Part C D of a Horizontal Plane B CD, is prefs'd by a Curve or Oblique Column of Water CEFND; the Preffure it undergoes is neither greater nor leffer, than that of the Column of Altitude; that is, of the Perpendicular Column CG HD, which has for its Bafis the press'd part C D, and for its Height the ftreight Perpendicular Lines F M, or G C, which are extended from the prefs'd Part C D, to the uppermoft Superficies A F of the highest Fluid, fuppofing there

to be more than one.

SECT.

SECT. XXXVI. Lateral Preffures do likewife adapt themselves to the Heights or Depths of Fluids.

XXXVII. IT now remains to inquire into the Force of the Lateral Preffure of Fluids, whereby they are thrust or prefs'd along the Horizontal Line.

That this kind of Preffure does alfo obtain in Fluids, appears from the fitting or placing Cocks in the Sides of Barrels, &c.

Or otherwise, fix a Tube EF (Tab. XXVI. Fig. 5.) horizontally, or into the Side of a Veffel ABCD, fill'd with Water to the height MN, and you will fee the Water gufhing out in a Stream F GH; fo that at E F it runs horizontally, and at F G H inclines or bends itself to the Earth.

And in order to know that this Lateral Preffure does alfo adapt itself to the Height, you need only fill the Veffel up to A B, so that there will then be a greater Depth of Water E B above the Tube E F; and you will find that the Stream FIK gushes out fo much farther, and horizontally to K; but that in Proportion to the Decrease of the aforefaid Height, by letting out the Water, the horizontal Force does also decrease, and continually incline nearer to the Veffel, as firft at H and then at P.

Now that this Lateral Preffure does by no means adapt itself to the Breadth or Quantity of the Water, may be feen, if by continually pouring Water into the narrower and wider Veffel, fuch as A B C D (provided it be not too narrow) the Water be kept at the fame height A B ; for then in both Cafes the Stream FIK will preserve the fame Horizontal Line.

VOL. III.

M m m

SECT.

SECT. XXXVII. The Method of difcovering the Greatness of the aforefaid Preffure.

XXXVIII. BU T now in order to compare the true Force of the Lateral Preflures, with that of the Heighth or Depth of Fluids upon equal Horizontal Planes, as we have done in other Preffures, we must bestow somewhat more Pains.

For if we take a quadrangular Veffel (Tab. XXVI. Fig. 6.) AQPK with plane perpendicalar Sides AQ, and PK; and in it conceive the part AE of the Side A Q. against which the Water, wherewith it is fill'd up to AK, preffes laterally, and if you moreover conceive another part E I in the Horizontal Plane O E, and equal to A E; it is clear that upon each Point F, G, H, I, there is an equal Depth of Water a F, c G, e H, g I, and confequently that each of the faid Points is prefs'd downwards with an equal Force; but neverthelefs, that each of thofe Points B, C, D, E, in the perpendicular Part A E, fuffers an unequal lateral Preffure; because, as we have shown before, the lateral Preffure accommodates itself to the perpendicular Height of the Water, and fo is greater or lefs accordingly; and each Point, as A, B, C, D, E, has a different Height of Water above it, or rather above the Horizontal Plane in which each Point lies.

Accordingly the Point A, or the Horizontal Plane A K, has no Height of Water above it. The Point B, or the Plane B L, has the Height A B or ab over it.

The Point C, or the Plane C M, the Height AC, or c d.

The Point D, or the Plane DN, the Height A D, or e f.

The

The Point E, or the Plane E O, the Height A E, or g i.

So that from hence it is manifeft, that in order to know how much greater or fmaller Preffure the Horizontal Plane EI undergoes from the Water that lies in equal Height upon all its Points, than the Perpendicular A E, which has different Heights of Water over all its Points; that by reafon of the great Difference of the Height of Water lying over the highest and lowest Points of the perpendicularly prefs'd Part A E; to avoid Miftakes, we mult First inquire how much greater or fmaller the lateral Preffure (for Inftance) upon one of the Points B or C, &c. is, than the Preffure downwards on one of the Points bord, &c. which have the fame Height of Water over them.

And, Secondly, when this is known in each Height a, b, c, d, ef, g, i, that we compare the Sum of all these different lateral Preffures upon all the Points or little Planes that make up E A, with the Preffure downwards, which all the Points or equal Breadths compriz'd in EI, do bear together.

Thirdly, It is plain, that the fmaller the Parts or Points are into which AE and EI are divided, the leffer is the difference of the Heights or Depths of Water over the uppermoft and undermoft Points of the Part of A E, and confequently thefe Diverfities of the Heights will produce the fmaller Change in the Calculations, which, if these Parts were taken very large, might occafion great Difference; whereas they may be now fafely enough taken, if we confider the Parts of A E, fuch as A, B, C, &c. as very fmall, and mere Points.

SECT. XXXVIII. The Comparison of the Lateral and Perpendicular Preffure of the Air upon an equal Part fhown by an Experiment.

XXXIX. To fhew the First experimentally, to wit, that the lateral Preffure which fuch a little Part as B, having a Height of Water, as A B, above it, undergoes in the Perpendicular A E, is equal, or at least does not fenfibly differ from the Preffure downward, which a Horizontal equal Part that has an equal Height of Water a b over it, fuffers from the incumbent Fluid, may appear from what follows, propos'd, if I miftake not, firft by Mr. Mariotte, but with another View.

Having try'd the fame in the Year 1696, and feveral times fince, I find among others, the following Remarks, which every Body elfe may also make by the help of the little Glafs Inftrument invented by Dr. Muffchenbroek for the fame Purpofe, with little Charge and Trouble.

We caus'd a little Hole a b to be drill'd or bored in the Plane Side V Q of a Bottle A B PQ (Tab. XXVII. Fig. 1.) and another fomewhat bigger at the Bottom of the faid Bottle at P, which laft might be ftopt by putting fomething into the Hole, and the Mouth A B was stopt with a Cork CDF G, thro' which the Glafs Tube E W was thrust, and the Joints were fo well fodder'd with Emplaftrum de Minio, that no Air could pass neither between the Tube and Cork, nor the Cork and the Mouth or Hole.

Then stopping the little Hole ab, and the Glass Tube E with the Finger, we pour'd Water into the Veffel thro' the biggeft Hole P with a Funnel that had a very flender Nofe, till it ascen

ded