As fluids press in all directions, it is evident their whole weight cannot be ap plied against one part or side ; while on the other hand it is equally true, that, in some instances, the bottoms of vessels re ceive a pressure which does not appear to be their due. Thus, in a pan whose base is narrower than its brim, the b ottom sustains only the weight of a column equal to its area, multiplied by its height ; yet if the pan be of a bell-shape, having its base broaderthan its brim, the bottom will sus tain a weight equal to its area,alsomultipli ed by its height. Consequently, in a vessel of a conical form, the base would be op pressed as much as if the sides were cy lindrical. This is called the hydrostatic paradox; but will be easily reconciled by the consideration, that if a tube of glass be made with a curved bottom, so as to in the form of the letter U, but with one leg or part much wider than the other, the water will rise equally in both. If to each a piston be fitted, their weights being equal, and that one piston be first put into the wider leg of the tube, it will cause the fluid to rise in the other in pro portion to its weight; but on applying the lesser piston to the corresponding smaller tube, the two will be held in equi librio. We have indeed further proof of the pressure of water upwards, by means of two boards, whose sides are joined by leather, as in a pair of bellows; these may be of any form, or of any size. At the top of one of the boards cut a hole, and insert a tube of about four or five feet in length, so as to be perfectly tight : place on the board several weights, according to the size of the machine, and pour water into the tube. The upper board will bear up against the weights, provided they be not disproportionately heavy; and will admit the water between the top and bottom to the extent admitted by the pliable sides. Some water ought to be poured in before the weights are set on. A circle of about twenty inches in diameter will thus lift and support three weights, of 1001b. each. Where either air or any other fluid is de barred from access between two planks annexed in the Iwater, the lower one be ing kept to the bottom forcibly, they will not separate, unless a force equal to the weight of the superincumbent fluid be applied; because the lateral and superior parts of the fluid are prevented from ex erting their pressure, except in that di rection which keeps the two !planks to gether ; but if the smallest opening be given, the pressure of the atmosphere will urge the fluid between them, and by confining it to act as a wedge; force the upper one to the surface. The com parative weights of fluids are ascertained by the IIYDROMETER, which see.
The comparative weight of fluids is given with the table of specific gravities, (see GRAVITY, specific); but it may be as well to point out in this place, that a gal Ion of proof spirit weighs 71b. 12oz. avoir dupois.
If a vessel contain two immiscible fluids (such as water and mercury), and a solid of some intermediate gravity be immers ed under the surface of the lighter fluid, and float on the heavier, the part of the solid immersed in the latter will be to the whole solid, as the difference between the specific gravities of the solid and of the lighter fluid is to the difference between the specific gravities of the two fluids.— For a body immersed in a fluid will, when left to itself, sink, if its specific gravity be . greater than that of the fluid ; if less, it will rise to the surface : if the gravities be equal, the body will remain in what ever part of the fluid it may be placed.— But in the case adverted to, the one fluid being heavier and the other lighter than the body immersed, it is necessary to combine their gravitie s by the mode above shown.
Balloons are properly hydrostatic ma chines, and derive their property of as cending from the earth into the upper part of our atmosphere entirely from the difference between the specificgravity of the air, or gas, with which they are filled, and the exterior, or atmospheric, air in which they float. The weight of the ma
terials must be taken into consideration ; for unless the specific gravity of the inte rior be so much less than that of the ex terior air, as to allow for the weight of the materials as a counterpoise, the bal loon cannot be made to float even in a stationary manner ; but when liberated will fall to the ground. The contents of the balloon being ascertained in cubic feet, it will be easy'•to ascertain what weight the balloon can lift, when filled with vilified air, according as that may have been rendered more light than the atmospheric air :. if filled with gas, the interior will be at least seven times light er than an equal quantity of atmospheric air. From this it will be seen, that to bear up a weight of 3001b. the balloon must be large, and the specific gravity of its contents be adequate to overcome the resistance of that impediment. As the air of the upper part of our atmosphere becomes gradually more rare, and conse quently lighter; according to its distance from the earth's surface, we may con clude that there is a point in its altitude, beyond which a balloon could not soar ; because its own weight, even if nothing were appended, would at such point perfectly equipoise the difference be tween the confined gas and the surround ing atmosphere. And this is the more perfectly to be admitted, from the know ledge we have acquired of the difficulty with which balloons are made to reach certain heights, and of their ascent being shown (by the slower fall of the mercury within the barometer) to be slower in the upper regions when they approach that state of equipoise. Were it not for the opposition offered by the superior air, a balloon would rise instantaneously, 'from the moment of its liberation, in a most rapid manner, to that height where its equipose should be found. We have said thus much in explanation of the na ture of the balloon, as appertaining-lo the laws of hydrostatics, referring the reader to the article AEROSTATION, for whatever appertains to the practical experience we have had of that science, which at first seemed to promise the most import4nt aid to various others, but in.which it has completely failed : the whole of the•prin-, ciples on which aerostation depends have been long understood.
We shall now speak of the diving-bell,. which also depends on hydrostatic prin ciples, though, like the balloon, it has close connection with pneumatics. The upper part of a diving-bell is always made to contain a certain of air, more or less compressed, in proportion to the depth to which the bell sinks. Thus, if we invert a small tumbler into a verse nearly filled with water, and allow it t ' cy descend perpendicularly, so that n air may be allowed to escape, the water will ... rise a very little way within it. If the ,'' tumbler be but partially immersed, the water could at the utmost but rise to its own level; but if immersed so deep as to ' exceed its own interior, and bot tom edge of the tumbler does not touch the bottom of the vessel, the water will, in consequence of its own greater weight at a greater depth, rise rather, though scarce perceptibly,. higher in the tum bler, and • occasion the au- to be ' ed into a smaller space. But the quantity of vital principle in the compressed air will be equal to that quantity of air in the open atmosphere which would fill the in terior of the tumbler. If the inverted tumbler were first placed at the bottom of an empty vessel, and that water were afterwards poured into the latter, the ef fect would he precisely the same. .