were equal in breadth to the cask, and at the same time 12 or 15 feet in height.

Another Method. (Plate 3 fig. 13).

SUSPEND from a hook, well fixed in a wall, or any other firm support, a body weighing 100 pounds. or more; then provide a vessel of such dimensions, that between that body and its sides, there shall be room for only one pound of water; and let the vessel be suspended to one of the arms of a balance, the other arm of which has suspended from it a scale, containing a weight of 100 pounds. Pour a pound of water into the vessel suspended from the one arm of the balance and it will raise the scale containing the 100 pounds.

Those who have properly comprehended the preceding explanation, will find no difficulty in conceiving the cause and necessity of this effect; for they are both the same, with this difference only, that the water, instead of being collected in a cylindric tube, is in the narrow interval between the body L and the vessel, which surrounds it; but this water exercises on the bottom of the vessel the same pressure that it would experience if entirely full of water.

Another Method.

PROVIDE a cubic foot of very dry oak, weighing about 60 pounds, and a cubical vessel about a line or two larger every way. If the cubic foot of wood be put into the vessel, and water be poured into it, when the latter has risen to nearly two thirds of its height, the cube will be detached from the bottom,

and float. Thus we see a weight of about 60 pounds overcome by half-a-pound of water and even less.

REMARK.

It

Hence it appears that the vulgar are in an error, when they imagine that a body floats more readily in a large quantity of water than in a small one. will always float, provided there be a sufficiency to prevent it from touching the bottom. If vessels are lost at the mouths of rivers, it is not because the water is too shallow; but because the vessels are loaded so much, as to be almost ready to sink, even in salt water. But as the water of the sea is nearly a thirtieth part heavier than fresh water, when a ship passes from the one into the other, it must sink more and go to the bottom. Thus, an egg, which sinks in fresh water, will float in water which holds in solution a great deal of salt.

The principle on which the foregoing experiments are performed, is no other than the famous hydrostatical paradox, and on which principle Mr. Bramah, an ingenious engine maker, has invented a new power, in mechanics, of such efficacy as to raise, with great ease, the heaviest loads, or crush the hardiest bodies.

PROBLEM XIV.

To find the weight of a cubic foot of water.

To know the weight of a cubic foot of water is one of the most essential elements of hydrostatics and hydraulics; and for that reason we shall here shew how it may be accurately determined.,

Provide a vessel, capable of containing exactly a cubic foot, and having first weighed it empty, weigh it again when filled with water. But as liquids always rise considerably above the edges of the vessel that contains them, the result in this case will not be very correct. There are means indeed to remedy this defect; but we are furnished with a very accurate method of doing it by hydrostatics.

Provide a cube of some very homogeneous matter, such as metal, each side of which is exactly four inches; weigh it by a good balance, in order to ascertain its weight within a few grains; then suspend it by a hair, or strong silk thread, from one of the scales of the same balance, and again find its weight when immersed in water. We are taught by hydrostatics that it will lose exactly as much in weight as the weight of an equal volume of water. The difference of these two weights therefore will be the weight of a cube of water, each side of which is four inches, or of the twentyseventh part of a cubic foot.

If very great precision is not required, provide a cube or rectangular parallelopipedon, of any homogeneous matter, lighter than water, such, for example, as wood; and, having weighed it as accurately as possible, immerse it gently in water, in such a manner that the water may not wet it above that point at which it ought to float above the liquid. We shall here suppose that I MD (fig. 14 pl. 3) is the line, which exactly marks how much of it is immersed. Find the content of the solid ABCDMI, by multiplying its base by the height;. the product will be the volume of water displaced by the body; and this volume, according to the principles of hydrostatics, must weigh as much as

the body itself. If this volume of water be 726 cubic inches, for example, and if the weight of the body be 26.0416 pounds, we consequently know that 720 cubic inches of water weigh 26.0416 pounds. Hence it will be easy to determine the weight of a cubic foot, which contains 1728 cubic inches. Nothing is necessary but to make this proportion as 720 cubic inches are to 1728, so are 26.0416 pounds to a fourth term, which will be 62.5 pounds, or 62 pounds and a half; which therefore is the weight of the cubic foot of water.

PROBLEM XV.

Two liquors being given; to determine which of them is the lightest.

THIS problem is generally solved by means of a well known instrument called the areometer or hydrometer. This instrument is nothing else than a small hollow ball, joined to a tube 4 or 5 inches in length (fig. 15 pl. 3); a few grains of shot, or a little mercury, being put into the ball, the whole is so combined, that in water of mean gravity, the small ball and part of the tube are immersed.

It may now be readily conceived that when the instrument is put into any fluid, for example river water, care must be taken to observe how far it sinks in it; if it be then placed in another kind of water, such as sea water, for instance, it will sink less; and if immersed in any liquor lighter than the first, such as oil for example, it will sink farther. Thus it can be easily determined, without a balance, which of two liquors is the heavier or lighter. This instrument has commonly on the

tube a graduated scale, in order to shew how far it sinks in the fluid.

But this instrument is far inferior to that presented, in 1766, by M. de Parcieux, to the academy of sciences, and yet nothing is simpler.

This instrument consists of a small glass bottle, two inches or two inches and a half, at most, in diameter, and from six to eight inches in length. The bottom must not be bent inwards, lest air should be lodged in the cavity when it is immersed in any liquid. The mouth is closed with a very tight cork stopper, into which is fixed, without passing through it, a very straight iron wire, 25 or 30 inches in length, and about a line in diameter. The bottle is then loaded in such a manner, by introducing into it grains of small shot, that the instrument, when immersed in the lightest of the liquors to be compared, sinks so as to leave only the end of the iron wire above its surface, and that in the heaviest the wire is immersed some inches. This may be properly regulated by augmenting or diminishing either the weight with which the bottle is loaded, or the diameter of the wire, or both these at the same time. The instrument, when thus constructed, will exhibit, in a very sensible manner, the least difference in the specific gravities of different liquors, or the changes which the same liquor may experience, in this respect, under different circumstances; as by the effect of heat, or by the mixture of various salts, &c.

It may be readily conceived, that to perform experiments of this kind, it will be necessary to have a vessel of a sufficient depth, such as a cylinder of tin-plate, 3 or 4 inches in diameter, and 3 or 4 feet in length.