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?]
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.

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    («) the velocity is as the diftance BD of the point from the Axis of Mo¬ tion ; fo the percuffive force of A is as AD, of C as CD, fince then the percuffive forces of A, B, C are as the Lines DA, DB, DC and thole Lines are as the Lines EA,FB, GC perpendicular to the Surface of the Water, and thefe laft Lines are as the preffures upon A, B, and C, it follows that the percuffive forces taking the interfe&ion D for the Axis of fufpenfion or motion are refpe&ively as the preffures upon the fame points: there¬ fore the Centre of Percuifion or Ofcillation is the fame with the Centre of preffure. The Geometers of the laft Age have profecuted the Problem of finding the Centre of Ofcillation very diligently, being excited there¬ to chiefly by the noble Invention of Pendulum Clocks: the Rules they have laid down for that purpofe are eafy enough, and the Applications they have adually made of thofe Rules are not a few. Having there¬ fore fhewn how the Centre of Ofcillation may be made ufe of for de¬ termining the Centre of preffure, I prefume I have by this time fufficient- ly clear’d up what I propos’d. For further illuftration I will add a ^couple of Examples. Let it be requir’d to find the preffure which a Diver fuftains when the Centre of Gravity of the Surface of his Body is 32 feet under Water. The Surface of a middle fiz’d humane Body is about 10 fquare feet. Multiply then 32 the depth of the Centre under Water by 10 the Surface of the Body, and the product or 32 times 10 folid feet will be a magnitude of Water whofe weight is equivalent to the preffure which the Diver fuftains by the Rule before laid down. A Cubick foot of Water has been found by Experiment to weigh 1000 Averdu- pois Ounces, therefore 32 times 10 feet or 16 times 20 feet of Water will weigh 16 times 20000 Averdupois Ounces or 20000 Averdupois Pounds. This therefore is the preffure of the Water to which a Diver at 32 feet depth is expos’d. Again in (Fig. 11.) let the right angled Paral¬ lelogram ABCD be a Wall, Dam, or Pen of Timber perpendicular to the Horizon made to keep in a Pond of Water, whofe upper Surface reaches to AB: let AB be 20 feet, and AC 12. Let K be the Centre of Gravity of the Plane, the depth of that Centre K will be equal to half GH or half AC, that is 6 feet. The Area of the Plane is found by multiplying AC by AB or 12 by 20, it is therefore 240 fquare feet: multiply according to the Rule the Area 240 by GK which is 6 and the produft will be 1440 Cubick feet of Water, which weighs fo many thoufand Ounces that is 90000 pounds, and that is the preffure which the Dam ABCD fufhiins. To find the Centre of that preffure we muft make the Line AB which is the common Se&ion of the Dam and the upper Surface of the Water, the Axis of fufpenfion of the Plane ABCD ; now it appears by the difcovery of Hagens, Wallis and other Geometers that Z the Centre of Ofcillation of this Plane fo fufoended will be in the Line v - - * - — clI
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