We come next to a confirmatory piece of evidence which greatly strengthens the view that the atomic weight of mercury must be 200; but before entering into detail let us see what an atomic weight of 200 involves. The density of mercury gas is 100, and its molecular weight must be 200. But if its atomic weight is also 200, it follows of necessity that its molecule and its atom must be identical; that unlike oxygen and hydrogen, its molecule consists, not of two atoms, but of one single atom. There is nothing strange in this conclusion; there is no evident reason why single atoms should not act as molecules, or independent particles, able to exist in a free state, uncombined with each other or with any other molecules.

The specific heat of a gas is measured in much the same manner as that of a solid. A known volume of the gas is caused to pass through a spiral tube, heated to a certain definite high temperature; it then enters a vessel containing a known weight of water, traverses a spiral tube immersed in the water, and parts with its heat to the water. Knowing, therefore, the weight of the gas and its initial temperature, and also the rise of temperature of the water, the specific heat of the gas can be compared with that required to raise an equal weight of water through one degree. But gases are found to possess two specific heats. If the volume of the gas is kept constant, so that the gas does not contract during its loss of heat, one number for its specific heat is obtained; while if it is allowed to alter its volume a higher figure represents its specific heat. It will be necessary to consider the cause of this difference, in order to understand what conclusions can be drawn respecting the molecular nature of argon from a determination of the ratio between its two specific heats—that at constant pressure and that at constant volume.

If a gas is allowed to expand into a vertical cylinder so as to drive up a piston loaded with a weight, it is said to “do work.” The work is measured by the weight on the piston, and also by the height to which it is raised. Thus, if the weight is one pound, and the height one foot, one foot-pound of work is done; if the mass is one gram and the height one centimetre, one gram-centimetre of work is done. During this process the gas must expand; and if it were enclosed in some form of casing through which heat could not pass—we know of no such casing, but we can contrive casings through which heat passes very slowly—the temperature of the gas would fall during its expansion, and it would lose heat. For each loss of one heat-unit or calory—i.e. the amount of heat given off by 1 gram of water in cooling through 1° Centigrade—the gas would perform 42,380 gram-centimetres of work; it would raise a weight of nearly 4¼ kilograms, or about 9⅓ lbs., through 1 centimetre, or nearly half an inch.

When a gas expands into the atmosphere it may be regarded as “raising the atmosphere” through a certain height, for the atmosphere possesses weight, equal on the average to 1033 grams on each square centimetre of the earth’s surface, or between 15 and 16 lbs. on each square inch. Suppose a quantity of air, weighing 1 gram, to be enclosed in a long cylindrical tube of one square centimetre in section. At the usual pressure of the atmosphere on the earth’s surface, and at 0° Centigrade, the volume of the air would be 773·3 cubic centimetres; and, as the sectional area of the tube is 1 square centimetre, the air would occupy 773·3 centimetres’ length of the tube. If heat be given to this air, so that its temperature is raised from 0° to 1°, it will expand, as Gay-Lussac showed, by 1⁄273rd of its volume. Now the product of 773·3 and 1⁄273 is 2·83 centimetres; the level of the surface of the air will rise in the tube through that amount. In doing so it will perform the work of raising 1033 grams through 2·83 centimetres, or 2927 gram-centimetres. Careful measurements have shown that, in order to do this work, heat to the amount of 0·0692 calory must be given to the gas. But it has been found that to heat the air through one degree, without allowing it to expand, requires 0·1683 calory; that is, the same amount of heat which would raise a gram of air through one degree, its volume being kept constant, will raise a gram of water through 0·1683°; or, in other words, the specific heat of air is 0·1683. But if allowed to expand, more heat is required—an additional 0·0692 calory must be given it; consequently its specific heat at constant pressure is greater; it is actually the sum of these two numbers, 0·1683 + 0·0692 = 0·2375.

We have thus—

Specific heat at constant pressure 0·2375
" " " volume 0·1683
Ratio between these numbers:0·2375 = 1·41
0·1683

This ratio is termed the ratio between the specific heats of air, and such a ratio is represented usually by the letter γ.

But it is not necessary to determine both kinds of specific heat in order to arrive at a knowledge of the value of this ratio. One plan, adopted by Gay-Lussac and Désormes at the suggestion of Laplace,[28] is to actually measure the fall of temperature by allowing a known volume of gas, of which the weight can of course be deduced, to expand from a pressure somewhat higher than that of the atmosphere to atmospheric pressure. It is true that heat will rapidly flow in through the walls of the vessel; but by choosing a sufficiently large vessel, and surrounding its walls with badly-conducting material, the entry of heat will be so slow that it may, for practical purposes, be neglected. The number for this ratio, actually found by Gay-Lussac and Welters for air, was 1·376; but subsequent and more accurate experiments have given as a result 1·405, which is almost identical with that calculated above.

This method, however, can be employed only when an unlimited supply of gas is at disposal, for it entails the use of large vessels, and the compressed gas must be allowed to escape into the atmosphere, and is lost. There is, fortunately, another method by which the same results can be obtained, and which requires only a small amount of gas.

Sir Isaac Newton calculated that the velocity of sound in a gas was dependent on its pressure and on its density, in such a manner that