above A B, did equally gravitate upon A B in the Veffel; and neither more nor less, than if the said Fluids had been in a narrow afcending Tube, each in its ftreight perpendicular Height.

For fince the Tubes both within and without the Veffel (Tab. XXV. Fig. 3 and 4.) were about the fame Width; if the Side-Fluids in the broad Veffel gravitated more upon A B, than the perpendicular Column A BY X in the Equicrural Tube upon A B Fig. 4; it would follow that the upper Superficies of the Quickfilver rs, in the Veffel, would rife higher above the former Superficies uw of the faid Quickfilver than in the Equicrural Tube.

XXVII. THE contrary of which being found to be true in all the Parts of a Horizontal Plane, (as H I) where-ever the Orifice of the Tube A B is placed, it fhew'd, That when Fluids are incumbent upon each other in a Veffel, fuppofing in one of 'em a Horizontal Plane, as HI, no Part thereof will fuffer either more or lefs Preffure from all the incumbent Fluids, how broad foever the Veffel is, than of a Column A B X Y; the Basis of which is A B, and the Top of it reaching up to the upper Superficies of the highest Fluid NO; and this is what we have call'd the Column of Altitude.

XXVIII. Now as we have defcrib'd above the Column of Altitude in a Fluid, it may be concluded how the fame is fo plainly defcrib'd in this Cafe; to wit, that in feveral Fluids incumbent upon each other, the Column of Altitude confifts of a Pillar, whofe Bafis or Bottom is A B, or E F, for Inftance, or fome part of a fuppofed Horizontal Plane H I, and whofe Top is the upper Surface of the uppermost of all the Fluids that are incumbent

upon

upon each other; as for Inftance, BZ compos'd of the feveral Depths of the Pickle B W, of the Oyl W X, and of the Air X Z (imagining that X Z extends itself to the upper part of the Air) in fuch manner, that each Height as B W, W X, and X Z preffes downwards with the particular Weight of every Fluid of which it is the Height.

XXIX. IT fhould be obferved here, that it is not neceffary that each Part fhould be always preft with fuch a perpendicular Column, fince a b fuffers the fame Preffure, notwithstanding (if we fuppofe K to be a folid Body) that the Column directly incumbing upon a b, or ab mi, can't extend itself in a ftreight Line higher than to mi, provided the Surface of the upper Fluid be at the fame Height as before; but the meaning of all that has been faid is, that both a b and A B are press'd with a Weight which is equal to the Column of Altitude, Num. XXVII.

XXX. So that in order to inquire into the Nature of any Water-Works, with respect to the Preffure of the Water upwards and downwards, you may fingle out a part A B, Fig. 4. of a Horizontal Plane H I, upon or over which the whole Column of Altitude A B Z may be placed; or otherwife you may lengthen out the Horizontal Plane HI towards N or I, even beyond the Veffel that contains the Part A B, (Tab. XXV. Fig. 3.) upon which we feek for the Preffure, and moreover take an equal Part A B, (Tab. XXV. Fig. 4.) of the said Plane extended from I to B, on which the Column of Altitude may be fet and reprefented, if we continue the Superficies ML and NO, &c. of the Fluids incumbent on each other as far as W and X.

So that to know with what Weight ab, in the Veffel, is preft; it may be anfwer'd, with the Column

lumn of Altitude A B Z, which is reprefented in Fig. 4. out of the Veffel; of which Column B W is the Pickle, W X the Oyl, and X Z 8 quite to the Top is Air.

We might also conceive the Column a b mi incumbent upon a b, as paffing thro' a folid Body K, only by afcribing to the Height of each Fluid Matter in it, its particular Part and Weight.

SECT. XXXI. Of the Pressure upon equal Parts of Higher or Lower Horizontal Planes.

XXXI. IT is unneceffary to add farther, that (Tab. XXVI. Fig. 2.) the Part d lying in the Horizontal Plane GT, is preft with fo much more Force upwards and downwards, than the Part c in a higher Plane E F, as the Column of Altitude fm upon G T, is heavier than the Column f h incumbent on the other Plane E F. This every one may apply to a Parte in a lower Plane N H, as alfo to feveral Fluids lying upon each other.

SECT. XXXII.

Hydroftatical Laws of Several FLUIDS incumbent on one another.

XXXII. FROM all which then, there follows this great Hydroftatical Propofition (which does likewife very much contribute to difcover the Powers and Motions in Hydraulicks, or WaterWorks) after a fhort and plain Manner.

It is thus:

If feveral Fluids be incumbent upon each other, and we fuppofe one Horizontal Plane, as HI (Tab. XXV. Fig. 3.) paffing thro' one of 'em :

Two or more equal Parts thereof (as A B, a b, E F, &c) will each of 'em be prefs'd upwards and downwards, with the Weight of their Columns of Altitude, and confequently with equal Force.

From whence it follows,

That

That one of these Parts, fuch as A B, is prefs'd downwards with the fame Force as another ab, or E F, upwards.

And on the contrary:

That the firft AB is prefs'd with as great Force upwards, as another a b, or EF downwards; which we fhall therefore, for Brevity fake, call here the Law of Altitude or Depth, because it adapts itself only to the Height (or Depth) of Fluids, but by no Means to their Breadth or Surface.

XXXIII. IT must be here obferv'd, that in the upward and downward Preffure on equal Parts of the fame Horizontal Plane (we do not now fpeak of higher or lower Planes) it is meant of fuch Parts A B, ab, EF, &c. which have a Communication with each other in the fame Fluid; that is, fuch as from one of which there may be fuppofed a Thread or Line drawn to the other, without being obliged to pass thro' another Fluid, or Solid Body.

It is neceffary to lay down this Caution here, because this fo general Propofition may otherwife not fucceed in fome Cafes.

SECT. XXXIII. The Preffure upwards proceeds only from Lateral Fluids.

WE have no occafion to prove exprefly, that all Parts, as rt, (Tab. XXV. Fig. 2.) of a Horizontal Plane L M, are prefs'd downwards by their own Weight, and that of other incumbent Fluids; but that they are never prefs'd upwards, but by Fluids that are not only higher but also lateral; and other parts of the fame Horizontal Plane L M prefs downwards: So that all up

ward

ward Preffure proceeds from these Lateral Fluids, as from their nearest Causes.

For take away the Lateral Fluids that are in the Veffel a LMb, on the Outfide of the Tube rt TV, the Liquor in the faid Tube, lofing its preffure upwards, will immediately fubfide.

SECT. XXXIV. Oblique Preffures do likewife adapt themfelves to the Height of Fluids.

XXXV. Now to fay fomething concerning the Oblique Preffures of Fluids.

That Fluids may be prefs'd and protruded in various Obliquities, is fo plainly proved by the Cocks and Ajutages of many Fountains, as not to require any farther Demonftration here.

But that thefe Oblique-preffing Fluids do alfo adapt themselves to the direct perpendicular Height of the faid Fluids over the prefs'd Part, as the foregoing, and by no Means according to their Quantity or Obliquity, fhall be likewife briefly shown.

Take a Recurve Tube (Tab. XXVI. Fig. 3. and 4.) A BCD, which being continued from CD, affumes the Form of CEFND; pour Water into it up to A, whereupon you will find that the Water will spread itfelf till it attains to an equal Height in the other Leg E F, of whatsoever Oblique Shape the faid Leg C DEF be, with refpect to the prefs'd Part CD.

Now we know, that if the Tube were extended from CD, ftreight up to CGHD, and and were full of Water as high as GH, or at a Height equal to A L and E F, the perpendicular Column CG HD, would keep the Water in the Tube A B, to the fame Height A B, juft after the fame Manner as here in the Oblique Preffure E F N D.

Confe