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Hydrostatics. 257

VI. From the mutual Pressure and equalAction of the Particles it follows, that theSurface of a Fluid mufl be perfedlly smooth

and

2. This likewise may be /hewn from mechanical pj ^Principles, for let the Sphere A be supported by two p-' A1V *others in an horizontal Position B and C ; join the ’S* 3 -Centres a, b, F; and draw the Perpendicular as ; let

er be a Tangent to the Sphere B in the Point c, wherethe Sphere A touches and presses it, intersecting thePerpendicular as in r; and let ae express the Forceof A downwards; then since ae is resolvable into twoForces ac and ce, of which the latter being in theTangent to B, does not at all affect it, and the othera c being perpendicular to the Surface; this other Forceac is that alone by which the Body A presses B.

3. But since ac is an oblique Force, that is, neitherperpendicular nor lateral, let it be resolved into thetwo Forces ad and dc\ of which the former is perpen-dicular, and so does not affect the Body B in press-ing it sideways; but the other dc being in an horizon-tal Direction is all the Force with which A presses Bin a lateral Direction; but since dc is parallel tabs,we have a c : dc :: ab : fb-, and since the Particles ofa Fluid are equal, we have fb — b c ~ ac-, thereforefb — I ab , and consequently dc z=.\ ac-, that is, theForce with which A prejses B laterally is jujl half theForce with which it presses it directs. *

4. And since by the third Law of Motion the Pres-sure of the Sphere D upwards is equal to that of A down-wards, and so the Force upon the Bodies B and C in alateral Direction is the fame, that is, half the directForce ; therefore the whole Force with which the BodyB orC is urged laterally by the joint Action of A and Dis equal to the whole Force with which either of them act uponthem fngly. From what has been said, it appears, thatthe Force with which the Body A or D presses theBody B or C, is less than the Force of Gravity, orthat by which they act perpendicularly, that is, ac isless than a e.

Vol. I.

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