z6o

Hydrostatics.

will be as a Series of Numbers in Arith-metical Progrelsion, whose first Term is o ;therefore the Sum of all the Pressures is equalto the Number of Pressures multiplied by halfthe greatest Pre sure: But the Number ofPressures is as the Number of Particles, orAltitude of the Fluid BC ; also the greatestPressure is as the same Altitude: Whereforethe total Pre sure againfl the Side of a Vefelis as the Square of the Altitude of the Fluid(IN).

IX. Hence

(LV) i. That the perpendicular Pressure of Fluidson the Bottoms of Vessels is estimated by the Area of thtBottom multiplied by the Altitude of the Fluid , is evident,

1 suppose, to every Reader. For suppose a Vessel were

2 Feet wide, 3 Feet long, and 4 Feet deep, and fill’dwith Water to the Brim ; then the Area of the Bottomis 2 X 3—6 square Feet, and every square Foot be-ing prels’d by the Column of Water, containing 4cubic Feet, 'tis plain the whole Bottom will be press’dby 6 X 4 — 24 cubic Feet, that is, by the whole Num-ber of cubic Feet which the Vessel contains.

2. But the Quantity of the lateral Pressure, or thatagainst the Side of the Vessel, is not so obvious; yetamong the several Ways of computing it, I think noneso easy, natural, and universal, as that I have men-tion’d, viz. by considering it in a single Column ofParticles, as a Series of Quantities in Arithmetical Pro-grefjion , because this depends entirely on the single Prin-ciple already established, viz. that the Action or Pressureof Fluid Particles is every IVay equal. By which I shallendeavour farther to illustrate this Matter, and facilsotate the Method of Computation.

3. Upon the uppermost Surface of the first Particle 1,which coincides-with the Surface of the Fluid, there is

no