DAVIS. CERTAIN THERMAL PROPERTIES OF STEAM. 289 



than one atmosphere. If these are all " reduced " to one atmosphere 

 by means of Clausius' equation, using Linde's best characteristic equa- 

 tion to represent the volume measurements, the results, plotted in 

 Figure 9, show deviations from a common curve that increase with the 

 pressure. The same is more strikingly true in Thomas' case. If his 

 results, so recomputed 37 as to partly eliminate the wet steam error 

 already mentioned (see page 271), are similarly reduced to one atmos- 

 phere by means of Clausius' thermodynamic equation and Linde's 

 best characteristic equation, the progressive departure with increasing 

 pressure from the probable curve for one atmosphere is very marked, 

 the 500 lb. and 600 lb. values disappearing beyond the bottom of the 

 diagram altogether. That is, although Linde's second best equation 

 gave no variation of C P with pressure at all, his best one gives alto- 

 gether too much. The experimental evidence is thus wholly against 

 the reliability of any C p values obtained by means of Clausius' equation 

 from any volume measurements as yet available. 



Be. The Joule-Thomson effect. — There are three ways in which 

 C p can be connected with the Joule-Thomson coefficient ft. The first of 

 these was suggested almost simultaneously by Linde and by Planck. 38 

 It is thermodynamically rigorous, except for the assumption of the 

 form of an analytical expression for /ias a function of t. The one 

 they used, namely, 



Const. 



A* = /7T2 » 



was proposed by Joule and Thomson in their original memoir on air, 

 and is not at all accurate, especially for steam. If it is replaced by a 

 more complicated expression, the integration of the partial differential 

 equation, to which the reasoning of Linde and Planck leads, is 

 impossible. 



A second equation connecting C p with /m is used by Griessmann 39 

 in the discussion of his throttling experiments. It is not a thermody- 

 namic equation in the true sense because it does not involve either 

 of the two laws of thermodynamics ; it is merely a manipulative 

 identity that can be proved by the laws of partial differentiation — 

 that is a truism. It says that at any point in any thermodynamic 

 plane 



37 Davis Proc. Am. Soc. Mech. Engs., 1908, 30, 1433. 



38 Linde, Sitzungsber, bays. Akad., Math. KL, 1897; Planck, "Vorlesungen 

 iiber Thermodynamic," 1897, 117; Eng. ed., 1903, 124. 



39 Forschungsarb., 1904, 13, 7 and 46. 

 vol. xlv. — 19 



