An example may, perhaps, render this more clear. A lump of glass is found to weigh in air 577 grains; it is delicately suspended by a horsehair from the bottom of the scalepan, and immersed in a vessel of pure water, it is found to weigh 399.4 grains; the loss, therefore, or the weight of an equal bulk of water, is 177.6 grains; then 177.6: 1:577 : 3.2; the working of which sum resolves itself into the division of the third term by the first, or of the weight in air by the weight in water, according to the rule. The quotient 3.2 being the specific gravity of the glass.

Solid bodies lighter than water, such as cork, may be weighed by attaching to them a mass of metal or glass previously balanced in water for that purpose, which may cause them to sink, and then proceeding with the combined mass as before.

37. The same principles may be applied to ascertain the specific gravity of liquids instead of the specific-gravity bottle; for as a bulb of glass immersed in water is buoyed up by a force equivalent to the weight of an equal bulk of water, so, when immersed in any other liquid, it will be supported by a pressure equal to the weight of a similar bulk of that liquid. Thus the mass of glass which lost 177.6 grains by immersion in water, was found to lose only 149 grains by being plunged into the spirits of wine, and their two amounts are consequently the weights of equal bulks of water and spirit; therefore 177.6: 1:: 149: 0.839, the specific gravity of the spirit.

38. It is upon the same principle that the specific gravities of liquids, which do not differ much from one another, may be determined by the hydrometer. This instrument consists of a hollow ball of glass or metal, with a weight below it and a slender stem above, divided into a certain number of degrees by marks; in pure water it is adjusted to float to a particular mark; that part of the stem which is out of the liquid acts as a weight to keep

it in its place. When immersed in a lighter liquid, such as spirit, the lateral pressure which supports it is diminished, and, not being sufficient to support the same weight as before, the instrument sinks, till a portion of the stem becoming immersed, its weight is decreased, and the balance again restored. Sometimes the instrument is adjusted to different liquids by moveable weights, while the gradations of the scale are made to express the specific gravities by the degree to which it sinks. (2)

39. From what has been said, it will, upon reflection, be clear, that when in ordinary circumstances a bulky body is counterpoised by a weight of very dense matter, an allowance ought to be made for the unequal buoyancy of the air; and this may be rendered evident by balancing a piece of cork with a counterpoise of metal, and afterward placing them in a space devoid of air, when the former will preponderate. If the volume of the cork were 2.5 cubic inches, it would require nearly half a grain to restore the balance, this being about the difference of the weights of the air which the two bodies displaced. For ordinary purposes the effect is too

E

10

F

B

small to require to be taken into consideration, but in nice scientific investigations it is often estimated.

(2) The annexed figure represents Sikes's hydrometer. A is a brass ball, into which a conical stem, F, is inserted, terminating in a loaded ball, B; at D a flat stem is inserted, which is graduated into eleven equal parts, each of which is subdivided into two; eight circular weights, E, are adjusted to the instrument, in which a slit is cut, so as to admit A the slender part of the lower stem into the hole in the centre of the weight; their use is to adapt the instrument to liquids heavier than water. A set of tables is furnished with the instrument, by which the specific gravity of a spirit is easily ascertained after an observation of the degree upon the stem to which it sinks.

But the force with which a body is attracted to the earth, and, consequently, the quantity of matter which it contains, may be measured by opposing to it other forces than that of gravity. We can even roughly judge of different weights by the different degrees of muscular exertion necessary to support them; and we have already had occasion to refer to a method of estimating them by the compression of a spring. This observation will naturally lead us to the consideration of our next force; namely,

ELASTICITY.

§ 40. The immediate resistance of a body to compression or extension, is properly called its elasticity. It has been exemplified by the sensible effort of a compressed spring and a bent bow to recover from their forced state of flexure. It is directly proportionate in perfectly elastic bodies to the compressing force; and this is the law of its action. If a bow be drawn to a certain extent by a sevenpounds weight, it will be drawn to double that extent by fourteen pounds; and upon this principle various spring-balances have been contrived.

The kind of elasticity to which we have hitherto referred arises from a force longitudinally applied, and a partial displacement of the particles of a solid in length, and is denominated flexure: a second kind consists in the lateral displacement of the opposite parts of a solid, in opposite directions, the central parts only remaining in their natural state, and is called torsion or twisting. Elasticity, thus elicited, may be very accurately measured by the angular displacement; the angle of torsion being exactly proportionate to the degree of elasticity. Balances of the greatest delicacy have been constructed upon this principle for the estimation of minute degrees of force.

But solid bodies are only more or less elastic within certain limits; the operation of forces beyond these limits first produces a permanent altera

tion or change of figure, which is called setting, and afterward fracture. The most perfect examples of elasticity are afforded by aeriform bodies, and the atmosphere which surrounds us furnishes a beautiful illustration of the equilibrium of this force and gravity, a correct understanding of which is of the greatest importance.

§ 41. With regard to matter in the aeriform state, common experience is by no means sufficient, as with solids and liquids, to teach us how to collect, confine, or weigh it; and it was not, till the time of Galileo (or early in the seventeenth century), proved that the air had a definite weight and pressure; and it was some time after this that Dr. Priestley contrived the simple means which are still in use for experimenting with such fluids. Aristotle, indeed, appears to have happily guessed the truth; and Plutarch informs us that he assigned the gravity of air to be between that of fire and earth; but the surmise appears to have led to no particular consequences, and to have been forgotten.

42. If we take a bell-glass, and press it with its mouth downward into a deep vessel of water, we find a strong resistance to its descent, which arises from the body of air confined beneath it; as we press upon it more and more, we feel a stronger and stronger opposition or repulsive force; the water rises farther into the interior, and the air occupies a less space; as we withdraw the pressure, it returns to its former bulk, and totally displaces the water. Hence we may learn that the air is elastic, like the spring to which we have just referred; and we can roughly estimate by our feeling that its elasticity increases in proportion to the force with which it is compressed. We learn, likewise, from the same simple experiment, that the volume decreases with the increase of pressure. The law of its elasticity was originally developed by Boyle; but Mariotte more accurately determined, by experi

ment, that the volume of air was always inversely as the pressure. (3) Elastic fluids of this nature always occupy the whole of any vessel in which they may be contained, whatever their quantity of matter may be, as determined by their weight; liquids or fluids devoid of this power of elasticity, in vessels which they do not fill, always present a level surface, i. e., a surface parallel to the general surface of the globe. This is determined by gravity, the law of which they are free to obey, unopposed by any counteracting force; the surface of an elastic fluid is always coincident with that of the containing vessel in which it is confined.

§ 43. If we take a strong tube or barrel of metal or glass, close at one end, and closely fitted at the other with a piston or moveable plug of leather, which will not allow of the passage of air at its sides, on pressing it downward we shall find the same kind of increasing resistance from the inclu

H

H

ded air, as in the case of the bell-glass under water. This elastic force may be made to perform mechanical work; and if the piston be perforated, and the per

(3) This figure represents the form of Mariotte's experiment. A B is a glass tube, turned up, and closed at the end, c; it is divided and graduated into equal parts; mercury is poured into it, so as to occupy the lower part of the tube to the first horizontal line, and a portion of air is enclosed at c of the ordinary elasticity, which it will be hereafter seen is equal to the pressure of about thirty inches of mercury. If more mercury be now poured into the longer leg, so that it may stand at thirty inches above the level of the mercury in the shorter leg, it will press with its whole weight upon the included air, which will then be found to occupy only half its former space. If, in like manner, the column of mercury be increased to twice this length, the pressure upon the included air will be tripled, and the space occupied by it will be reduced to one third, &c.