Another important result of equation (B), as applied to the liquid and vapour phases of a substance, is the information which it gives as to the density of the saturated vapour. When the two phases coexist the pressure is a function of the temperature only. Hence if the relation of pressure to temperature is known, dp⧸dT can be calculated, or obtained graphically from a curve; and the volume v₂ per unit mass of the vapour will be given in terms of dp⧸dT, the temperature T, and the volume v per unit mass of the liquid. The density of saturated steam at different temperatures is very difficult to measure experimentally with any approach of accuracy: but so far as experiment goes equation (B) is confirmed. The theory here given is fully confirmed by other results, and equation (B) is available for the calculation of v₂ for any substance for which the relation between p and T is known. It is thus that the density of saturated steam can best be found. We can obtain another important result for the case of the working substance in two phases from equation (B). The relation is ∂L⧸∂T + c － h = L⧸T ... (C) where c and h are the specific heats of the substance in the two phases respectively, and L is the latent heat of the second phase at absolute temperature T. We shall obtain the relation in another way, which will illustrate another mode of dealing with a cycle of operations which Thomson employed. Any small step of change of a substance may be regarded as made up of a step of volume, say, followed by a step of temperature, that is, by an isothermal step followed by an adiabatic step. In this way any cycle of operations whatever may be regarded as made up of a series of Carnot cycles. But without regarding any cycle of a more general kind than Carnot's as thus compounded, we can draw conclusions from it by the dynamical theory provided only it is reversible. Suppose a gramme, say, of the substance to be taken at a specified temperature T in the lower phase, and to be changed to the other phase at that temperature. The heat taken in will be L and the expansion will be v₂ － v₁. Next, keeping the substance in the second phase, and in equilibrium with the first phase (that is, for example, if the second phase is saturated vapour, the saturation is to continue in the further change), let the substance be lowered in temperature by dT. The heat given out by the substance will be hdT, where h is the specific heat of the substance in the second phase. Now at the new temperature T － dT let the substance be wholly brought back to the second phase; the heat given out will be L － ∂L⧸∂T.dT. Finally, let the substance, now again all in the first phase, be brought to the original temperature: the heat taken in will be cdt, where c is the specific heat in the first phase. Thus the net excess of heat taken in over heat given out in the cycle is (∂L⧸∂T + c － h)dT. This must, in the indicator diagram for the