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.

    16/28 (page 16)
    the lower Valves: fuch you may remember are the cavity of the Pipe which conveys the Air to the Barrels, and the cavity in the up, er part of the Gage above the Quickftlver. Thefe additional Spaces are very fmall and inconliderable; yet if we would be exaft, they alio muft be taken into the account and look’d upon as parts of the Receiver. Now to underhand the truth of this Rule, we muft obferve that as the Em¬ bolus is moved upwards from the bottom of the Barrel, it would leave a void Space behind it, but this effect is prevented by the ruftiing in of Air from the Receiver. The Air you know, by it’s Elafticity, is always endeavouring to expand it felf into larger Dimenfions, and it is by this endeavour that it opens the lower Valve and paffes into the hollow part of the Barrel as the Embolus gives way to it, and this it will continue to do, till it comes to have the fame Denftty in the Barrel as in the Re¬ ceiver : for fhould its Denftty in the Barrel be lefs than in the Receiver, its Elaftick force which is proportionable to its Denftty would be lefs alfo, and therefore it muft ftill give way to the Air in the Receiver till at length the Denftties become the fame. The Air then which immediately before this ftroke of the Pump, (by which the Sucker is rafted,) was contained in the Receiver only, is now uniformly diffufedinto the Receiver and the Barrel; whence it appears that the quantity of Air in the Barrel is to the quantity of Air in the Barrel and Receiver together as the capacity of the Barrel is to the capacity of the Barrel and Receiver together. But the Air in the Barrel is that which is excluded from the Receiver by this ftroke of the Pump, and the Air in the Barrel and Receiver together is what was in the Receiver immediately before the ftroke. Therefore the truth of the Rule is very evident: that the quantity of Air which is drawn from the Receiver at each ftroke of the Pump bears the fame propor¬ tion to the quantity of Air in the Receiver immediately before that ftroke, as the capacity of the Barrel into which the Air paffes from the Receiver, does to the capacity of the fame Barrel and the capacity of the Receiver taken together. To illuftrate this further by an Example: let us fuppofe the capacity of the Receiver to be twice as great as the capacity of the Barrel; then will the capacity of the Barrel be to the capacity of the Barrel and Receiver together as i to 3, and the quantity of Air ex- haufted at each turn of the Pump is to the quantity of Air which was in the Receiver immediately before that turn, in the fame proportion. So that by the firft ftroke of the Pump, a third part of the Air in the Receiver is taken away ; by the fecond ftroke a third part of the re¬ maining Air is taken away, by the third ftroke a third part of the next remainder is exhaufted, by the fourth a third part of the next, and fo on continually ; the quantity of Air evacuated at each ftroke diminifhing in the fame proportion with the quantity of Air remaining in the Re¬ ceiver immediately before that ftroke: for ’tis very evident that the third part.