[Page 16]

THE Use of this third Table is so Obvious to every Mans Capacity, that it needs no Expla­nation; for if there be occasion to make any Vessel in a Cubical Form, of which the Content ought to be a Pint, a Quart, a Gallon, &c. This Table gives the Cubick Roots of their Re­spective Dimensions.

As for the weight of Water, it is not to be determined abso­lutely, because almost all Wells, Springs and Rivers, are of a dif­ferent weight, and therefore my advice is to all Engineers and Practitioners, to find out the ex­act [Page 52]weight of a Cubick Foot of that particular Water, which they have occasion to make use of; by which means they will easily discover the weight of a­ny Cylinder of Water with these following Cautions.

First Caution. When an Engi­neer desires to force up Water 50, or 100 Feet in Perpendicu­lar Height, and designs to do this by a Forcer of 4, 5, or 6 Inches Diameter; but intends the Water shall be carried up the said 50, or 100 Feet in Perpendicu­lar Height, through a Pipe of of 1 Inch and ½, 1 Inch and ¾, or 2 Inches and ¼ Diameter, the Wa­ter standing in any such perpen­dicular Pipe, is equivalent in weight to a Pipe of the same Perpendicular Height, whose Di­ameter is 4, 5, or 6 Inches, [Page 53] viz. the Diameter of the said For­cer; and indeed the less one of those Pipes is, the greater is the weight against the Forcer to raise up the Water in the same Mo­ment or Interval of Time; that is to say, there is required more Weight to be laid upon that Forcer, to raise the Water through a Pipe of one Inch Di­ameter, than through a Pipe of four Inches Diameter. And what­soever is here said of the weight of Water against a Foreer, in a Forcing Engine, is also true in Suction, by a Drawing Pump.

For Example. A Pump whose Barrel or Pipe of Suction is four Inches Diameter; and the Pipe which reaches from the Barrel to the Water, through which it is drawn up but two Inches Dia­meter, requires more force or [Page 54]strength, than if it were drawn up through a Pipe of four In­ches Diameter. For want of the Knowledge of this, many igno­norant Plummers and Pump-ma­kers, covet to draw their Water through less Pipes, which makes the Work more difficult: And though this seems to be a Para­dox, yet 'tis a real truth; and the want of the right under­standing thereof has occasioned very many great Mistakes by ig­norant Practitioners.

Second Caution. The true weight of Water in all Pipes, is to be determined by the Perpendi­cular Height of those Pipes.

For Example. The weight of Water in Perpendicular Pipes of three Feet (in Height) and three Inches Diameter, is equal to the [Page 55]weight of Water contained in a Pipe of any Length whate­ver (be it a Rod, a Furlong, or more) which rises not more than three Feet above the Horri­zontal Line; which seems like­wise to be a Mystery, but is a real truth, as it lyes in the Pipes; although if it be ta­ken out and laid in a Ballance, it will weigh one Hundred times as much or more, than the Wa­ter in the said Perpendicular Pipe.

I must confess, that the Au­thor had very small Encourage­ment to help our Engineers in things of this Nature, many of them having dealt very disinge­nuously with him; when he had, by near Forty Years Stu­dy and Practise, and the Ex­pence of many a thousand Pounds, [Page 56]produced new and better ways of raising Water, than for ought I know, were ever known to former Ages, viz. by the means of

1. A Forcer moving up and down in a Chamber of Water, through a small Collar or Neck of Leather fastned in a Groove.

2. The Circular Motion of a Crank, reduced to a Perpen­dicular.

3. The Ʋnequal Motion of a Crank exchanged for an Elliptical Equal Motion.

Divers Persons have borrow­ed, some one part, some ano­ther, and making some small Alterations, call it their own Invention. This I am willing [Page 57]to let pass; and after all, to give them the following Items, to prevent their attempting Per­petual Motions, which most of them are apt to do by their Ig­norance in Hydrostaticks; and not a few Gentlemen, in all A­ges, have, by such vain ima­ginations of deceiving Nature, deceived themselves, and Rui­ned their Families.

1. As in Staticks a Pound weight suspended Perpendicular­ly, has a greater force than a Pound weight suspended on a ri­sing Line in Proportion, as the Hypotenuse of a Rectangled Tri­angle, is longer than its Per­pendicular; so in Hydrostaticks, if the two ends of a Syphon turned angular-wise, and a part of it filled with Water, or a­ny other Liquor, be immer­ged [Page 58]in a Vessel of the same Li­quor; that part which hangs Perpendicularly, shall be heavi­er than that which declines in proportion, as one side of that Syphon is longer than the other opposite side.

For Example. Let the two Triangles in Fig. 1. be Isosceles, and the two sides of the Tri­angle ABC (viz. AC and AB) equal. And so likewise the two sides of the Triangle DEF [Page 59](viz. DE and EF) equal. In this case a Pound weight (P) and another (Q) are equally Ponderous; and so is the Wa­ter contained in the Syphon (FN) from the Superfices (GR) to (N) of an equal weight with the Water in the Syphon (DM) between the Super­fices of the Water (GR) and (M)

But now in Fig. 2. because the side (AB) of the Trian­gle (ABC) has double the length of (BC) therefore a [Page 60]Pound weight (D) suspended Perpendicularly from (B) is E­quiponderant to two Pounds (E and F) on the side (AB) according to the Doctrine of Sta­tinks. And therefore an Horse drawing a weight of four Hun­dred Pound, upon an Ascent of thirty Deg. heaves at two Hundred Pound, which is one half, and the Ground bears the rest.

And so in Fig. 3. because the side (DE) of the Triangle (DEF) has twice the Length of (EF) therefore the Water (HF) which hangs Perpendi­cularly, is equal in weight to [...]he Water (DG) which has twice its Quantity and Length, [Page 62]according to the Doctrine of Hy­drostaticks.

2. As in Staticks, a Pound weight on the one side of the Perpendicular Line makes an E­quilibrium, with another Pound Equidistant from the Perpendi­cular Line on the other side: so in Hydrostaticks, one Tube of Water standing at any Height above the Horizontal Line, E­quiponderates any other Tube o [...] Water that stands at the same Height, and is of the same Di­ameter.

3. As in Staticks if a les [...] weight raise a greater, it mus [...] be proportionably at a greate [...] distance from the Perpendicu­lar Line, and have a greater Mo­tion. So in Hydrostaticks, i [...] a less Tube of Water raise a [Page 63]greater Tube, it must be pro­portionably of a greater Length above the Horizontal Line than the other; and consequently the Descent of the Water in a lesser Tube, must have a greater Length than the Ascent of the Water in a greater Tube in proportion, as the Square of the Diameter of the greater Tube, exceeds the Square of the Diameter of the lesser Tube.

And this length of Ascent and Descent of the lesser Tube of Water above the Horizontal Line, compared with the Ascent and Descent of the greater Tube, together with the proportion that the Square of the Diameter of the lesser Tube, bears to the Square of the Diameter of the [Page 64]greater Tube; answers exactly to the force and Motion of a Lea­ver, or rather of a lesser weight placed on a Ballance at a grea­ter distance from the Perpendi­cular to Counterpoise or raise a greater weight placed on the o­ther side at a lesser distance according to the Doctrine of Sta­ticks.

As in Fig. 1. A pound weight (A) is equiponderant to ano­ther (B) because equidistant from the Perpendicular (CD) So that part of the Tube (EL) [Page 65]whose Height above the Horizon­al Line (FE) is of an equal weight with that part of the Tube (GM) which is of an equal leight above (FH) viz. (GH.)

In Fig. 2. as a pound weight A equiponderating three Pound (B, C, D,) must have thrice the Distance from the Perpendicu­cular (EF) and for every Foot or Inch (B, C, D,) ascends or descends A must ascend or descend three Feet, or 3 Inches, viz. from (G) to (H.)

So the Tube (RM) being less than the Tube (NQ) in Proportion as (1) is less than three. The Water must descend from (G) to (H) to raise the Wa­ter in the Tube (NQ) from (O) to (P) which is ½ of the Height.

And which is admirable, if the Liquor from (O) to (N) be Wine by turning the Cock (S) gently the Water shall carry up the Wine in an entire Body.

And this is a pretty Experi­ment in Hydrostaticks; and these Cautionary Reflections will, I presume, if throughly under­stood, discourage young Practi­tioners from ever attempting to deceive the Order of Nature, and confound the Equilibrium of Weights (whether liquid or dry) by imaginary Perpetual Motions.