(97.) Another law, common to all elastic fluids, and of equal importance with the former, was discovered by Mariotte. By this law it appears that every gas or vapour, so long as its temperature is unchanged, will have a pressure directly proportional to its density. If therefore, while we compress steam into half its volume, we could preserve its temperature unaltered, we should increase its pressure in a two-fold proportion; but if the process of compression should cause its temperature to increase, [Pg172] then its increase of pressure will be greater than its increase of density, since it will be due conjointly to the increase of density and to the increase of temperature. In this case the increased pressure may be deduced from the combined application of the two laws just explained; that of Mariotte will determine that increase of pressure which is due to the increase of density, and that of Dalton and Gay Lussac will determine the further increase of pressure which will be due to the increase of temperature. The full investigation of these effects, and the formulæ expressing them, will be found in the Appendix to this volume. (98.) The fixed relations which exist between the temperatures of common steam and its pressure and density, have never been discovered from any general physical principles. The pressures and the densities however, which correspond to a great variety of temperatures throughout the thermometric scale, have been ascertained by extensive series of experiments instituted by philosophers of this and other countries. From a comparison of the temperatures and pressures thus found by experiment, empirical formulæ have been constructed, which exhibit, with an approximation sufficiently close for practice, this relation; and these formulæ may accordingly be used for the computation of tables exhibiting the pressures, temperatures, and densities of common steam; and such tables will have sufficient numerical accuracy for all practical purposes. These formulæ, and the tables resulting from them, will be found in the Appendix to this volume. (99.) It has been explained, that to effect the conversion of water into steam, it is only necessary to impart to it as much heat as, added to the temperature which it has, would, if it continued in the liquid form, raise it to the temperature of 1212°. This condition is necessary, and sufficient to effect the transition of water into vapour. If, for example, as much heat were imparted to the water evaporated, as would maintain it in the liquid state to 1300°, then the steam so produced would be superheated steam, having 80° of heat more than is necessary to maintain it in the vaporous form. From such steam, therefore, 80° of heat may be abstracted without producing any condensation. [Pg173]