From this view it is evident that the specific heat of elastic fluids can only be considered as approximately determined. If equal spaces possess equal momenta, and the ethereal or _tomic_ matter be inversely as the weight of the atomic matter in the same space, it follows that the product of the specific gravities and specific heats of the simple gases should be constant; or that the specific heats should be inversely as the specific gravities,--taking pound for pound in determining those specific heats. If we test the matter by the data now afforded, it is best to obey the injunction, "_In medio tutissimus ibis_." In the following table, the first column are the values obtained by Regnault; in the second, the former values; and in the third, the mean of the two.
Gases. Reg. specific heats. Former specific heats. Mean. Atmospheric air, .237 .267 .252 Oxygen, .218 .236 .227 Nitrogen, .244 .275 .260 Hydrogen, 3.405 3.294 3.350
The specific gravities of these gases, according to the best tables in our possession, are:
Specific gravities. Mean. Products. Atmospheric air, 1.0000 × .252 = .252 Oxygen, 1.1111 × .227 = .252 Nitrogen, 0.9722 × .260 = .252 Hydrogen, 0.0745 × 3.350 = .249
As might be expected, there is a greater discrepancy in the case of hydrogen.
If we test the principle by the vapor of water, we must consider that it is composed of two volumes of hydrogen and one volume of oxygen, and that one volume disappears; or that one-third of the whole atomic motion is consumed by the interference of the vibrations of the ether, necessary to unite the atoms, and form an atom of water. We must therefore form this product from its specific gravity and two-thirds of its specific heat. On no one subject in chemistry has there been so much labor expended, as in determining the specific heat of watery vapor. In relation to this, Regnault observes: "It is important to remark that an immense number of experiments have been made, to find the specific heat of steam, and that it is about one-half of what it was thought to be." He gives its value .475; but this is vitiated still, by the non-recognition of the specific heat of the ether. Former experiments give .847. Perhaps Regnault's numbers are entitled to the most weight. Instead of taking the mean, therefore, we will give double weight to his results; so that we get .600 for the specific heat of vapor, and as its specific gravity is .625, the product .400 × .625 is .250, the same as for hydrogen. Little importance, however, should be attached to such coincidences, owing to the uncertainty of the numbers. If our position be correct, the specific heat of hydrogen should be 10 times greater than of oxygen. The atomic weights are as 1 to 8, while their volumes are as 2 to 1; therefore, for equal spaces, the matter is as 1 to 16. Calling the specific heat 10 to 1, and taking the amount due to half the space, the product becomes as 8 to 16; but in the rarer gas there is _8 times_ as much ethereal momentum or matter, which, added to the atomic matter, renders the spaces equal.[3] Regnault's results give a ratio of specific heats = 1 to 3.405/.215 = 1 to 15.6.