A simple experiment suffices to show the relation between the density and elasticity of a fluid and the compressing force. Let mercury be poured into a bent tube open at one end and closed at the other ; the sum of the weights of the column or mercury and of the atmosphere above it in the open tube, will reduce the air in the closed tube to a volume less than that which it previously occupied. Let, then, more mercury be added, and the volume of air will be still further reduced at every addition of mercury : and it will be found that the volumes of air vary inversely as the sums of the weights of the mercury and atmosphere. Therefore, since the density of an elastic fluid is inversely proportional to the space it occupies, it follows that the densities are directly proportional to the compressing weights ; and since the weights of the mercury and atmosphere together, in the open tube, are balanced by the elastic force of the condensed air in the close tube, that elastic force is also directly proportional to the com pressing force, that is, to the density. [Ain.] This is the law of Boyle and Marlette, and though it cannot be said to be absolutely correct for very great pressures, it is sufficiently so for all practical purposes. (See the elaborate experiments of Magnus, Annales de Chirnie et do Physique,' 3 aerie, iv.; and of Regnault, iv. and v.) The following table, extracted from the results of the experiments made by MM. Prony, Arago, and ethers, exhibits the volumes and elasticities of a given quantity of atmospheric air under different pressures, the temperature being nearly constant, and expressed by of the centigrade thermometer Fahr.), and, as far as it extends, it confirms the law above mentioned. The first of the columns expresses the pressure or elasticity in multiples of the weight of an atmospherical column ; the second expresses the same by the height, in inches, of the column of mercury supported In a barometer tube ; and the third column contains the corresponding volumes.
The law being admitted, it may be proved that the particles of an elastic fluid repel each other with a force which varies inversely as the distance between them. For let the volume of fluid be in the form of a cube, and let the compressing force act perpendicularly on one of its faces; then, if d represent the distance between any two adjacent particles of fluid, the number of particles in the surface pressed will 1 vary as Now assume that the repulsive force (perpendicularly to that surface) between any two adjacent particles in the volume varies as d^ ; then the whole repulsive force on that surface, and, con sequently, the compressing force, will vary as If D represent the 1 density of the fluid, d will vary as or ; therefor*, substituting for d in the last expression, the whole repulsive force varies as But, agreeably to the law above mentioned, the compress ing force varies as D; therefore the exponent —1(a - 2) must be equal to unity, and hence a = —1. It follows therefore that the repulsive force between any two adjacent particles varies as d—i, or inversely as the distances of those particles from each other. Sir 1. Newton however observed (lib. ii., prop. 23, sehoL) that this law holds good only when the repulsive power of any putiele does not extend much beyond those which are nearest to IL If r and r' represent the pressures exercised upon a square unit of the superfices bounding an elastics fluid, and the volumes of the fluid under those pressures v and v'; also if the densities be D and D' respectively, we shall have • Considerable difficulty is found in determining the specific gravities of gases with precision, and different experimenters have obtained results which do not exactly agree. The value generally adopted when the height of the column of mercury in the barometer is 30 inches, and the temperature is 60' Fehr., is grains as the weight of 100 cubic iuches of dry air. Other physicists have found it as low as 31'0117 and grains ; but the former is probably most correct, as it agrees with the density of air as deduced from that of a mixture of oxygen and nitrogen in the proper proportions to form air. Air is
therefore of the density of water. The experiments of Dalton have led to the conclusion that the weight of a cubic foot of steam when at the temperature of 212' Fahr., the height of the barometrical column being 30 inches, is 253 grains troy ; by others it has been found to be 254'7 grains ; and it appears that within considerable limits the expan sion of the volume of any gas is proportional to the increments of temperature, measured by the degrees of the thermometer. The absolute value of the expansion is not precisely known ; that of air is stated to be equal to about and that of steam about of the volume, for one degree of Fahrenheit's thermometer. (Ant] The following table, from the observations of )1111. Dulong and Petit, exhibits the volumes assumed by a given quantity of air at different temperatures between the boiling-point and near the freezing point of mercury :— It has been mentioned that the rate of expansion of all gases is equal and uniform at .a1 degrees of temperature and pressure, and that the amount of the expansion is of the bulk occupied at 32' Fahr., for every degree of temperature, so that a quantity of any gas, which, at Fabr., measured 491 parts, will, at 33' Fahr., measure 492 parts, and so on. lf, then, it were required to find the volume which 9'2 cubic inches of any gas, measured at 70' Fehr., would have, when reduced to 60' : since 70 - 32 = 36, 491 parts of the gas at 32', would become 529 parts at 70'. Again, 60 - 32 = 28, so that the gas at 60' would, similmay, occupy 519 parts. Hence, we have the pro' ortion, 529 : 519 : : 9'2 : x (= cubio inches).
From experiments It has been concluded that, while steam is in contact with the water from which it is formed, its expansive force increases in a geometrical progression, so long as its temperature is at the same time increased In an arithmetical progression, but the relation between the elastic; force of this gas and its temperature, in that state, is as yet far from being certainly known. Under the word ELASTICITY is given a table of the elastic forces of steam at temperatures between the freezing and boiling states of water ; and the following table, extracted from those which have been formed from the results of the experiments of Mr. Dalton, Dr. Uro, and the French physicists, may also be useful as a means of affording a near estimate of the force at high temperatures. The first column contains the temperature of the water and steam in degrees of Fahrenheit's thermometer ; the second is the measure of the expansive force by the number of inches in the height of the column of mercury which on a given superfleles would counterbalance it; and the third, the like measure expressed by mul tiples of the weight of the atmospheric column when the air Is In its ordinary state:— When Steam is not in 'contact with the water from whence it is formed, and when it is subject to a constant pressure under which it may expand in every direction (as when it is formed in the atmosphere), an Increase, of temperature will not produce an increase of density, but merely of its elastic power. Again, if steam be in contact with its water, and the temperature remain constant, its density, whether in air or in rectos, will remain constant, and its volume only will vary. But if, in this case, its volume be kept constant, and the temperature be increased, its density will rapidly increase, as before, until tho whole of the liquid is evaporated, and then the expansion of the steam will follow the usual laws of permanent gases. The only difference in these experiments between using a vessel containing air, and one having a vacuum inside is, that in the former case the results do not at once appear, until time has been allawed for diffusion.