G by the pressure of the column He; and when the quicksilver From the foregoing principles may be deduced many useful remarks, as in the following corollaries, viz. 354. Corol. 1. The space which any quantity of air is confined in, M as reciprocally as the same, or reci- will be directly as the corresponding ordinates AG, BG, CG, 355. Corol. 2. All the air near the earth, is in a state of compression, by the weight of the incumbent atmosphere. 356. Corol. 3. The air is denser near the earth, than in high places; or denser at the foot of a mountain, than at the top of it. And the higher above the earth, the less dense it is. 357. Corol. 4. The spring or elasticity of the air, is equal to the weight of the atmosphere above it; and they will produce the same effects: since they always sustain and balance each other. 358. Corol. 5. 358. Corol. 5. If the density of the air be increased, preserving the same heat or temperature its spring or elasticity is also increased, and in the same proportion. 359. Corol. 6. By the pressure and gravity of the atmosphere, on the surface of the fluids, the fluids are made to rise in any pipes or vessels, when the spring or pressure within is decreased or taken off. PROPOSITION LXXIV. 360. Heat Increases the Elasticity of the Air, and Cold Diminishes it. Or, Heat Expands, and Cold Condenses the Air. This property is also proved by experience. 361. THUS, tie a bladder very close with some air in it; and lay it before the fire: then as it warms, it will more and more distend the bladder, and at last burst it, if the heat be continued and increased high enough. But if the bladder be removed from the fire, as it cools it will contract again, as before. And it was on this principle that the first air-balloons were made by Montgolfier: for, by heating the air within them, by a fire beneath, the hot air distends them to a size which occupies a space in the atmosphere, whose weight of common air exceeds that of the balloon. 362. Also, if a cup or glass, with a little air in it, be inverted into a vessel of water; and the whole be heated over the fire or otherwise; the air in the top will expand till it fill the glass, and expel the water out of it; and part of the air itself will follow, by continuing or increasing the heat. Many other experiments, to the same effect, might be adduced, all proving the properties mentioned in the proposition. SCHOLIUM. 363. So that, when the force of the elasticity of air is considered, regard must be had to its heat or temperature; the same quantity of air being more or less elastic, as its heat is more or less. And it has been found, by experiment, that the elasticity is increased by the 435th part, for each degree of heat, of which there are 180 between the freezing and boiling heat, of water. 3 364. N. B. Water expands about the part, with each degree of heat. (Sir Geo. Shuckburgh, Philos. Trans. 1777, p. 560, &c.) 4 365. The Weight or Pressure of the Atmosphere, on any Base at THIS is proved by the barometer, an instrument which measures the pressure of the air, and which is described below. For, at some seasons, and in some places, the air sustains and balances a column of mercury, of about 28 inches: but at other times it balances a column of 29, or 30, or near 31 inches high; seldom in the extremes 28 or 31, but commonly about the means 29 or 30. A variation which depends partly on the different degrees of heat in the air near the surface of the earth, and partly on the commotions and changes in the atmosphere, from winds and other causes, by which it is accumulated in some places, and depressed in others, being thereby rendered denser and heavier, or rarer and lighter; which changes in its state are almost continually happening in any one place. But the medium state is commonly about 291 or 30 inches. 366. Corol. 1. Hence the pressure of the atmosphere on every square inch at the earth's surface, at a medium, is very near 15 pounds avoirdupois, or rather 143 pounds. For, a cubic foot of mercury weighing 13600 ounces nearly, an inch of it will weigh 7.866 or almost 8 ounces, or nearly half a pound, which is the weight of the atmosphere for every inch of the barometer on a base of a square inch; and therefore 30 inches, or the medium height, weighs very near 14§ pounds. . 367. Corol. 2. Hence also the weight or pressure of the atmosphere, is equal to that of a column of water from 32 to 35 feet high, or on a medium 33 or 34 feet high. For, water and quicksilver are in weight nearly as 1 to 136; ᎦᏅ so that the atmosphere will balance a column of water 13-6 times as high as one of quicksilver; consequently 13:6 times 28 inches 381 inches, or 313 feet, 13.6 times 29 inches 394 inches, or 323 feet, 13.6 times 30 inches 408 inches, or 34 feet, 13.6 times 31 inches = 422 inches, or 35 feet. And, hence a common sucking pump will not raise water higher than about 33 or 34 feet. And a siphon will not run, if the perpendicular height of the top of it be more than about 33 or 34 feet. 368. Corol. 3. If the air were of the same uniform density at every height up to the top of atmosphere, as at the surface of the earth; its height would be about 51 miles at a medium. For, the weights of the same bulk of air and water, are nearly as 1∙222 to 1000; therefore as 1-222: 1000 :: 332 feet: 27600 feet, or 51 miles nearly. And so high the atmosphere would be, if it were all of uniform density, like water. But, instead of that, from its expansive and elastic quality, it becomes continually more and more rare, the farther above the earth, in a certain proportion, which will be treated of below, as also the method of measuring heights by the barometer, which depends on it. 369. Corol. 4. From this proposition and the last it follows, that the height is always the same, of an uniform atmosphere above any place, which shall be all of the uniform density with the air there, and of equal weight or pressure with the real height of the atmosphere above that place, whether it be at the same place, at different times, or at any different places or heights above the earth; and that height is always about 51 miles, or 27600 feet, as above found. For, as the density varies in exact proportion to the weight of the column, therefore it requires a column of the same height in all cases, to make the respective weights or pressures. Thus, if w and w be the weights of atmosphere above any places, D and d their densities, and H and h the heights of the uniform columns, of the same densities and weights; Then H X D W =w, and ḥ × d=w; therefore or is equal to or h. The h X temperature being the same. D H PROPOSITION 370. The Density of the Atmosphere, at Different Heights above the Earth, Decreases in such Sort, that when the Heights Increase in Arithmetical Progression, the Densities Decrease in Geometrical Progression. LET the indefinite perpendicular line ar, erected on the earth, be conceived to be divida ed into a great number of very small equal parts, A, B, C, D, &c. forming so many thin strata of air in the atmosphere, all of different density,' gradually decreasing from the greatest atA: then the density of the several strata, A, B, C, D, &c. will be in geometrical progression decreasing. For, as the strata A, B, C, &c. are all of equal thickness, the quantity of matter in each of them, is as the density there; but the density in any one, being as the compressing force, is as the weight or quantity of all the matter from that place upward to the top of the atmosphere; therefore the quantity of matter in each stratum, is also as the whole quantity from that place upward. Now if from the whole weight at any place as B, the weight or quantity in the stratum в be subtracted, the remainder is the weight at the next stratum c; that is, from each weight subtracting a part which is proportional to itself, leaves the next weight; or, which is the same thing, from each density subtracting a part which is proportional to itself, leaves the next density. But when any quantities are continually diminished by parts which are proportional to themselves, the remainders form a series of continued proportionals: consequently these densities are in geometrical progression. Thus, if the first density be D, and from each be taken its nth part; there will then remain its part, or the n— 1 n part, putting m for n-1; and therefore the series of den m m2 m3 ms D, D, of the series being that of n to m. SCHOLIUM. D, &c. the common ratio 371. Because the terms of an arithmetical series, are proportional to the logarithms of the terms of a geometrical series: therefore different altitudes above the earth's sur face, |