All elastic fluids are compressible or condensible in proportion to the weight with which they are loaded. Perhaps this law, which is ascertained by general experience, may suffer some irregularity when these fluids are under a degree of condensation almost sufficient to reduce them to the liquid state, or when either in a state of extreme rarefaction or condensation; but we seldom approach either of these limits with most of the gasses which we submit to our experiments. I understand this proposition of gasses being compressible, in proportion to their superincumbent weights, as follows:
A barometer, which is an instrument generally known, is, properly speaking, a species of syphon, ABCD, Pl. XII. Fig. 16. whose leg AB is filled with mercury, whilst the leg CD is full of air. If we suppose the branch CD indefinitely continued till it equals the height of our atmosphere, we can readily conceive that the barometer is, in reality, a sort of balance, in which a column of mercury stands in equilibrium with a column of air of the same weight. But it is unnecessary to prolongate the branch CD to such a height, as it is evident that the barometer being immersed in air, the column of mercury AB will be equally in equilibrium with a column of air of the same diameter, though the leg CD be cut off at C, and the part CD be taken away altogether.
The medium height of mercury in equilibrium with the weight of a column of air, from the highest part of the atmosphere to the surface of the earth is about twenty-eight French inches in the lower parts of the city of Paris; or, in other words, the air at the surface of the earth at Paris is usually pressed upon by a weight equal to that of a column of mercury twenty-eight inches in height. I must be understood in this way in the several parts of this publication when talking of the different gasses, as, for instance, when the cubical foot of oxygen gas is said to weigh 1 oz. 4 gros, under 28 inches pressure. The height of this column of mercury, supported by the pressure of the air, diminishes in proportion as we are elevated above the surface of the earth, or rather above the level of the sea, because the mercury can only form an equilibrium with the column of air which is above it, and is not in the smallest degree affected by the air which is below its level.
In what ratio does the mercury in the barometer descend in proportion to its elevation? or, what is the same thing, according to what law or ratio do the several strata of the atmosphere decrease in density? This question, which has exercised the ingenuity of natural philosophers during last century, is considerably elucidated by the following experiment.
If we take the glass syphon ABCDE, Pl. XII. Fig. 17. shut at E, and open at A, and introduce a few drops of mercury, so as to intercept the communication of air between the leg AB and the leg BE, it is evident that the air contained in BCDE is pressed upon, in common with the whole surrounding air, by a weight or column of air equal to 28 inches of mercury. But, if we pour 28 inches of mercury into the leg AB, it is plain the air in the branch BCDE will now be pressed upon by a weight equal to twice 28 inches of mercury, or twice the weight of the atmosphere; and experience shows, that, in this case, the included air, instead of filling the tube from B to E, only occupies from C to E, or exactly one half of the space it filled before. If to this first column of mercury we add two other portions of 28 inches each, in the branch AB, the air in the branch BCDE will be pressed upon by four times the weight of the atmosphere, or four times the weight of 28 inches of mercury, and it will then only fill the space from D to E, or exactly one quarter of the space it occupied at the commencement of the experiment. From these experiments, which may be infinitely varied, has been deduced as a general law of nature, which seems applicable to all permanently elastic fluids, that they diminish in volume in proportion to the weights with which they are pressed upon; or, in other words, "the volume of all elastic fluids is in the inverse ratio of the weight by which they are compressed."
The experiments which have been made for measuring the heights of mountains by means of the barometer, confirm the truth of these deductions; and, even supposing them in some degree inaccurate, these differences are so extremely small, that they may be reckoned as nullities in chemical experiments. When this law of the compression of elastic fluids is once well understood, it becomes easily applicable to the corrections necessary in pneumato chemical experiments upon the volume of gas, in relation to its pressure. These corrections are of two kinds, the one relative to the variations of the barometer, and the other for the column of water or mercury contained in the jars. I shall endeavour to explain these by examples, beginning with the most simple case.
Suppose that 100 cubical inches of oxygen gas are obtained at 10° (54.5°) of the thermometer, and at 28 inches 6 lines of the barometer, it is required to know what volume the 100 cubical inches of gas would occupy, under the pressure of 28 inches[58], and what is the exact weight of the 100 inches of oxygen gas? Let the unknown volume, or the number of inches this gas would occupy at 28 inches of the barometer, be expressed by x; and, since the volumes are in the inverse ratio of their superincumbent weights, we have the following statement: 100 cubical inches is to x inversely as 28.5 inches of pressure is to 28.0 inches; or directly 28 : 28.5 :: 100 : x = 101.786—cubical inches, at 28 inches barometrical pressure; that is to say, the same gas or air which at 28.5 inches of the barometer occupies 100 cubical inches of volume, will occupy 101.786 cubical inches when the barometer is at 28 inches. It is equally easy to calculate the weight of this gas, occupying 100 cubical inches, under 28.5 inches of barometrical pressure; for, as it corresponds to 101.786 cubical inches at the pressure of 28, and as, at this pressure, and at 10° (54.5°) of temperature, each cubical inch of oxygen gas weighs half a grain, it follows, that 100 cubical inches, under 28.5 barometrical pressure, must weigh 50.893 grains. This conclusion might have been formed more directly, as, since the volume of elastic fluids is in the inverse ratio of their compression, their weights must be in the direct ratio of the same compression: Hence, since 100 cubical inches weigh 50 grains, under the pressure of 28 inches, we have the following statement to determine the weight of 100 cubical inches of the same gas as 28.5 barometrical pressure, 28 : 50 :: 28.5 : x, the unknown quantity, = 50.893.
The following case is more complicated: Suppose the jar A, Pl. XII. Fig. 18. to contain a quantity of gas in its upper part ACD, the rest of the jar below CD being full of mercury, and the whole standing in the mercurial bason or reservoir GHIK, filled with mercury up to EF, and that the difference between the surface CD of the mercury in the jar, and EF, that in the cistern, is six inches, while the barometer stands at 27.5 inches. It is evident from these data, that the air contained in ACD is pressed upon by the weight of the atmosphere, diminished by the weight of the column of mercury CE, or by 27.5 - 6 = 21.5 inches of barometrical pressure. This air is therefore less compressed than the atmosphere at the mean height of the barometer, and consequently occupies more space than it would occupy at the mean pressure, the difference being exactly proportional to the difference between the compressing weights. If, then, upon measuring the space ACD, it is found to be 120 cubical inches, it must be reduced to the volume which it would occupy under the mean pressure of 28 inches. This is done by the following statement: 120 : x, the unknown volume, :: 21.5 : 28 inversely; this gives x = 120 × 21.5 / 28 = 92.143 cubical inches.
In these calculations we may either reduce the height of the mercury in the barometer, and the difference of level in the jar and bason, into lines or decimal fractions of the inch; but I prefer the latter, as it is more readily calculated. As, in these operations, which frequently recur, it is of great use to have means of abbreviation, I have given a table in the appendix for reducing lines and fractions of lines into decimal fractions of the inch.
In experiments performed in the water-apparatus, we must make similar corrections to procure rigorously exact results, by taking into account, and making allowances for the difference of height of the water within the jar above the surface of the water in the cistern. But, as the pressure of the atmosphere is expressed in inches and lines of the mercurial barometer, and, as homogeneous quantities only can be calculated together, we must reduce the observed inches and lines of water into correspondent heights of the mercury. I have given a table in the appendix for this conversion, upon the supposition that mercury is 13.5681 times heavier than water.