An extract of some physico-mathematical discourses contained in Mr. Cotes's Hydrostatical and pneumatical lectures : printed for the use of those that go the course of experiments.

Roger Cotes

Date:: [1740?]

Credit: An extract of some physico-mathematical discourses contained in Mr. Cotes's Hydrostatical and pneumatical lectures : printed for the use of those that go the course of experiments. Source: Wellcome Collection.

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$An Extra&of fome Phyfico-Mathermtical Diitourfcs con¬ tained in Mr. C o t e s’s Hydroilatical and Pneumaticai Lectures: printed for the u.!e of tho(e that go the Courts of Experiments. The exact eftimate of all manner of Prejfares, The invention of the Center f Preffure upon any propofed Plane reduced to the Problem of finding the Center of percuffioft. 'TE are now to determine the quantity of that Preffure whicK \y \ / any furface fufiains that is expos’d to the Gravitation of a ▼ Fluid, this muft be done gradually beginning with thofe Cafes which are moft fimple and eafy, and afterwards proceeding to thofe which are more complex and difficult. Let a Veffel ABGD ( Fig. i. ) be pro¬ pos’d containing any Fluid, fuppofe Water, let AB be the upper furface of the Water, and CD the Bottom of the Veffel ; the preffure upon any part of that Bottom fuppofe GH will be equivalent to the weight of a Column of Water GHIK, having the part GH for its bale and 67 or HK the depth under Water for its altitude. This feems to be felf evident and may befit be prov’d by the.absurdity of any contrary fuppofition; for if it be faid that GPP fufiains a greater weight than that of the Column GHIK> the excefs muft come from the adjoyning Columns ACGI and KHDB, now for the like reafon it ought to be faid that CG fufiains a greater weight than that of the Column ACGI, and HD a greater than that of the Column KHDB.; but if this were true, then would all the parts 66,67/and/7D together, of that whole plane CD fuflain a greater we'ight than that of the Columns together, or the whole Water which is above it namely ACDB, which is abfurd. The like abfur- dity will follow if it be faid that GH fufiains a Idler preffure than the weight of the Column GPIIK; the weight of that Column then, which is perpendicularly incumbent upon it is exa&ly equivalent to the preffure which it fufiains. This is the Quantity of preffure upon the Plane Gl in the cafe that has already been deferib’d. If the Figure of the Veffel be any way alter’d, the preffure will ftill be the fame if the perpendicular difiance of the Plane GH from the upper furface of the Water contain’d in the Veffel of what ever Figure it be, remain unalter’d. Thus (in Fig. 2. 3.) if LNGHOM be a Veffel of any irregular Figure, LAP be the upper furface of the Water, and the Perpendicular difiance of GH below LAP namely 6/ or HK be the fame as before; the preffure of the Veffelled Water LNGHOAP upon the Bottom GH will be equal to the fame weight of the Column GHIK as before, though the VeffelPd Water LGHAP be much A : • ; . .Xy t: left$