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.

  • Cotes, Roger, 1682-1716.
Date:
[1740?]
Catalogue details

Licence: Public Domain Mark

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.

    6/28 (page 6)
    C<5) tempted it only in a few Xnftances, and thofe of plane Surfaces, and a- mongft plane Surfaces he meddles only with fucn which he calls re¬ gular, neverthelefs he has gone the furtheft in this matter of any Writer I have met with. To fnpply then this defect I will here lay down another Rule, which is not only univerfal, but alfo as eafy and expe¬ ditious as can be defir’d. It is this, that the Preffure upon any Surface whatever, however it be htuated is equal to the weight of a Body of Water whole magnitude is found by multiplying the Surface propos’d into the depth of its Centre of Gravity under Water. So the preffure upon any number of Surfaces of different Bodies, however differently ii- tuated, is equal to the weight of a Body of Water whofe magnitude is found by multiplying- the Sum of all thofe Surfaces into the depth of their common Centre of Gravity under Water. The Dcmonftration of this Rule may not perhaps he fully underftood by thofe who are unac¬ quainted with Staticks and the Nature of the Centre of Gravity, how¬ ever I will here produce it, that thofe who can may underftand it, and that others taking now for true what I lhall affume as demonftrated by the Writers of Mechanicks imy afterwards be fully fatisfied of it, when they come to underftand that Theorem it is grounded upon; which is, that if every indefinitely fmall Part of any Surface or number of Surfaces be multiplyed refpedively into its Perpendicular diftance from any propos’d Plane, the Sum of thofe Produds will be equal to the Produd of the whole Surface or number of Surfaces multiply’d into the Perpendicular diftance of the Centre of Gravity of the fingle Surface, or of the com¬ mon Centre of Gravity of the whole number of Surfaces from the fame Plane. Now taking the upper Surface of Water for that Plane to which we refer the indefinitely fmall Parts of the Surface which is expos’d to the preffure we are concern’d with, ft nee it has been already fhewn that the preffure upon the whole is equivalent to the weight of a Body of Water which is equal in magnitude to the Sum of all the Produces, made by multiplying every little Part by its diftance from the upper Plane of the Water, and this Sum of Produds is by the Statical Theorem I have been mentioning exadly equal to the Produd of the whole Surface or number of Surfaces multiplyed into the diftance of the Centre of Gravity from the upper Plane of the Water, it will follow that the fame Produd is the meafure of a magnitude of Water whofe weight is equivalent to the pref¬ fure requir’d. The fame Rule may be demonftrated by feveral other me¬ thods, but I have pitch’d upon this as the fitteft for my purpofe. Another thing which Stevinm propofes to himfelf is to determin the Centre of preffure upon any Plane. Before we can diicourfe any further about this we muft declare what is meant by that Centre. It is then the point to which if the total preffure were apply’d, its effed upon the Plane would be the fame as when it was diftributed unequally over the whole