Volume 1

Lexicon technicum: or, an universal English dictionary of arts and sciences / [John Harris].

  • Harris, John, 1667?-1719
Date:
1736
Catalogue details

Licence: Public Domain Mark

Credit: Lexicon technicum: or, an universal English dictionary of arts and sciences / [John Harris]. Source: Wellcome Collection.

    758/782
    CASE n. In the Veifel L CF\ (as in the foregoing Figure) ’twill be .an eafy thing to find the Momenta of the Fluid preffing upon the leveral imaginary prrallel Funds, as C F, I Ky&c. for the Momen¬ tum of LCF: Is to the Momentum of L IK :: As the Momentum of the Cylinder B CF E : to the Momentum of the Cylinder GIKH. But univerlally, the Momenta of Cylinders are as their Altitudes, by the laR ; Therefore let LCF be what Figure it will, the Preffure upon a Fund, as IK: Is to thePrelfure upon a Fund, as CF in the Veifel continued fo far :; as the Abfciffa La'.' Is to the Ablcilfa L 0 ; that is, as la to CO: And if you fuppole it a parabolick Veifel, as I a ({■, to CO </, &c. N. B. We here con/lder the Fund I K, as making a diJiinSl VeJJel, and not meerly an imaginary one; fo that L I K and LCF may be confidered as two diJiinSl Vejftls. From what is faid may be found the Proportion of the prelfive Velocities in the Velfels ACF, LI K; for we know the Ratio of their Momenta, and the Ratio of their Magnitudes; therefore that alfo of their preffive Velocities, the other Faftor of their Momenta, will be known too. But the Momenta of Velfels of different Heights, having the lame common Fund, will be as thole Altitudes. 7) F Suppofe A D and A C two parabolick Velfels, having the fame common Ablcilfa A B ; then will their Momenta upon the common Fund A By be as their Ordinates B Cand B Dy /. e. as the Area’s of the two Semi-parabola’s A D B and A CBy or in a Sub-duplicate Ratio of their Parameters, as is evident from Conicks. Likewile in Hyperbolical and Elliptical Velfels, having the fame tranfverfe Diameter and Ablcilfa common to both, the Prelfure upon the common Ablcilfa, as a Fund, will be as the Area’s A C B and A C D of the Semi-Ellipfis and Semi-Hyper¬ bola. CASE III. But now we come to confider the Velfels L IK and LCF, (Fig. 6.) as communicating with each other : And here the preffive Velocities will be very different from what they were in the former Suppofition : In order to exprefs the Proportions of which, we mull confider the Momenta of the leveraj. Portions of the Fluid taken from the Ver¬ tex, and imagin’d to be cut off by Plains parallel to the Bafe : And firfi, the Momentum of the Portion L IK, upon the Fund CF, is equal Mo¬ mentum of A M B Ny on the Fund D C y there¬ fore the Momentum LC F: Is to the Momentum of LIK:: As the Momentum of the Cylinder AB DC : To the Momentum of the Cylinder A M B N, i. e. as L <9, L a. But having the Momenta’s and Quantities of Matter, we can eafily find the other Faftors ; that is, the preffive Velocities of LCF and A / AT, upon the Fund C F $ which may be exprelfed thus : The Ratio of the Momenta’s is equal to LCF and the Ratio of the Magnitudes is equal to FTki therefore the Ratio of the preffive Velocities will , LO x L1 K be — ■ ■ • L a x L C P CASE IV. To compare together the preffive Velocities in both thefedifiintt Cafes, (viz. 2, 3.) ’twill be only necelfaryto confider, That in the Firfi Cale, where we imagined a different Fund, as 1 Ky the Mo¬ mentum of the Portion L I Ky is equal to that of the Cylinder G HIK; and in the latter Cafe, where we fuppofe all one and the lame Veifel, and fo the Fluid L IK preffing on the Fund CF, that then the Momentum of that Portion L IKy will be equally the Momentum of the Cylinder AMBN, therefore the two Momenta’s being as the Cylinders A M B N; and GIK /Z, (which have equal Altitudes) will be as M N to I Ky i.e. as NP : IK. But having the Ratio of the Momenta’s, wp have alfo that of the preffive Velocities of one and the fame Quantity of the Fluid L I Ky when concei¬ ved as preffing upon the Fund IK in one Cafe, and on the Fund CF in the other. Let B E ( Fig. 8.) be a Vefiel fill’d with Mer¬ cury to the Altitude A E ; then, as in the way of making the Torricellian Experiments, take a pretty long Glafs Tube, Ihut at the End D, but open at Cy which fill with Mercury ; and flopping the open End Cy invert the Tube, and put the faid End C into the Mercury BE: ’Tis evident from the firfi and general Propofition, That if the Mer¬ cury contained in the Tube, prefs more upon C, than the Air upon the other Parts of the Mercury < which