Owing to the restricted range of the observations available for CO2, Clausius also applied his method to steam, for which Regnault's values of the saturation pressures were above sus picion, and extended over a much wider range. Having succeeded in representing the observed steam-pressures over the range o° to 23o° C by means of an equation similar to (io), but with a somewhat more complicated expression for A as a function of the temperature, Clausius was able to calculate the values of the critical temperature and pressure from the critical relations, which were very similar in form to (8). These gave the values, t = 332° C, and p= 134 atmos., and should have afforded a good test of the theory, but no satisfactory observations were avail able for comparison. The old estimate, C, made by de La Tour, for a solution of soda, might not apply to pure water, and the temperature was somewhat doubtful. The values given by Clausius brought the properties of steam more nearly into correspondence with those of CO2, and the theory of the continu ity of state was by that time so firmly established that everyone assumed that all the other properties of the fluid must fall naturally into line if the saturation pressures were correct. The value of the constant b" was adjusted, as in the case of CO2, to make the calculated value of v correct at 20° C, but the value given by the equation was nearly i00% too large at 300° C. This was regarded as unimportant, because engineers at that time were in the habit of neglecting the volume of the liquid, but the dis crepancy would necessarily make a corresponding error in the calculated values of the latent heat according to van der Waals' theory. Some ten years later Cailletet and Colardeau succeeded in measuring the saturation pressures of steam up to the critical point, which they estimated as 365° C, confirming the old value given by de La Tour. They found the critical pressure at this point to be nearly 200 atmospheres, which greatly exceeded the value given by Clausius. Meanwhile more and more complicated equations on the lines of van der Waals' theory, were still being evolved by mathematicians, who were strongly attracted by the conception of an internal pressure applying equally to the gaseous and liquid states, but were not greatly concerned with the prac tical question of agreement with actuality. The qualitative agree ment with the properties of the vapour were sufficiently striking to arrest attention, while the discrepancies with regard to the properties of the liquid and the latent heat entirely escaped notice owing to the extraordinary difficulties involved in the experimental measurement.
on the equilibrium of heterogeneous substances. That a simple substance like water might possibly contain molecules of differ ent types, was first suggested by Rowland as an explanation of the remarkable variation of the specific heat of water near the freezing point, which he attributed to the presence of a small proportion of ice molecules. The measurement of the specific heat of water up to ioo° C by the continuous electric method (see CALORIMETRY) suggested that the variation at higher tem peratures could be explained by supposing that water contained its own volume v of saturated steam, which would contribute the fraction v/(V-v) of the latent heat of vaporization L to the total heat It of the water. This gave the very simple and convenient expression for h (Phil. Trans. 19o2) h=st-FvL/(V-v)=std-avT(dp/dt) (II) which appeared to be capable of taking account of the variation of specific heat of the liquid at higher temperatures, and at the same time fitted perfectly with Clapeyron's equation, (2), and with all the properties of the liquid in relation to the vapour. Thus if we add L to both sides of (I I) we obtain, H = st -1-VL/(V-v) = st aVT (dp/dt) (12) which gives the corresponding relation for the total heat H of the saturated vapour at the same temperature. Moreover it gives equally simple and exact expressions for the entropy of the liquid and vapour in equilibrium, namely, IP= slog, (T/T.) vL/T (V-v) (13) cf.= sloge VL/T(V-v) (i4) From (I I) and (12) we obtain a very useful relation between the volumes and total heats of the liquid and vapour at saturation, v/V= (h-st)/(H-st) (15) and from (r I) and (13) we obtain a simple expression for the Gibbs' function, G = TO„,—h, which has the same value for water at saturation as for wet steam of any quality at the same tern perature and pressure, namely, One of the chief advantages of (I I) is that it completely solves the problem of finding the theoretical equation of saturation pres sure so far as the liquid is concerned. As indicated above, Rankine had to neglect v entirely and to assume that s was con stant. Whereas in (I I) s denotes the constant minimum specific heat of the liquid, and the second term takes complete account of the variation of h in terms of the volume v. This term is exactly eliminated by adding the expression for L from Clapey . ron's equation, leaving (12) as the equation to be integrated, from which the troublesome terms representing the volume of the liquid, and the variation of its specific heat, have both automati cally disappeared. We have only to find consistent expressions for H and V, and the equation must be the exact differential of the corresponding equation of saturation pressure. The equa tion for the liquid was verified indirectly by the fact that this method gave correct values of the saturation pressures of steam up to 200° C, when the defect of H from Rankine's ideal value was determined by the differential throttling method. The corre sponding values of V, as given by the Joule Thomson equation (6), were verified up to the same limit by the subsequent obser vations of Knoblauch (19o5).