Hydrostatics.
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IX. Hence if the Vessel AC be of a pi. xv.Cubical Form, the Pressure against a Side Fig. 1.
BC
no Gravity, and consequently no Pressure ; thereforethe Beginning of the Series, or first Term is 0, or no-thing. The Body of the first Particle presses the secondParticle 2 with its own Weight which is as 1, and itpresses the Side of the Vessel with the fame Force, andtherefore the second Term of the Series will be 1. Thesecond Particle presses the third Particle 3 with theForce of its own Weight, and the Weight of thatabove it, that is, with a Force as 2 ; and since it pressesthe Side of the Vessel with the fame Force, the thirdTerm of the Series will be 2. After the fame Mannerit is shewn, that the fourth Term will be 3, the fifthTerm 4, and so on. Whence it is evident the severalPressures will be as the Series, o, I, 2, 3, 4, 5, 6,
7, 8, g, 10, £*.
4. Now that the Sum of such a Series is equal tothe greatest Term multiplied by half the Number ofTerms, is known to every Person versed in commonArithmetick, and may be easily shewn by an Example.
For suppose the Series were 0, 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, then the Number of Terms is 12, andthe half thereof 6 ; also the greatest Term is 11 ; but6 X 11 — 1 4-2 + 3 + 4 + 54*6 + 74 - 84 - 94 -10 + 11 = 66 =: the total Pressure against the Side ofthe Vessel. Now this is manifestly but half the Pressureupon a Line of the fame Length in the Bottom of theVessel, iiz. a Line of 12 Particles, for since each Pointsustains the Pressure of 11 Particles, the whole must be12X11= 132.
5. It may here be objected that I have taken 12 Par-ticles in a Line at the Bottom, whereas there is but 11at the Side, and therefore the Length of the Side andBottom is not the fame, as in the Supposition we makeit. But it is to be considered, that when the Particlesare supposed indefinitely small and numerous, as is thereal Cafe of Fluids, the Difrercnce^of Length occa-sioned by one single Particle will he infinitely small,find therefore will make no Error in the Computation,
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