June i6, 1921] 



NATURE 



483 



In this respect it differs from characteristic equa- 

 tions such as those of Van der Waals or Clausius. 

 But within the range of its application it gives 

 results the agreement of which with the results of 

 direct observation is as close as the agreement of 

 one set of observations with another. 



Prof. Callendar treats steam as a gas the devia- 

 tions of which from perfection may be expressed 

 by writing the characteristic equation in the form 



V = RT/P-c + b, 



where RT/P is the ideal volume of a perfect gas, 

 h is the " co-volume," or volume occupied by the 

 molecules — a volume which is not reducible by 

 lowering the temperature — and c is what he calls 

 the " coaggregation volume," which is the volume 

 lost by the interlinking or pairing of molecules. 

 He treats c as a function of the temperature only, 

 within the range of temperature and density to 

 which the equation applies, making c vary as 

 i/T". He makes the further assumption that 

 when the pressure is indefinitely reduced the speci- 

 fic heat of the gas is not altered by changes of 

 temperature within that range. These assumptions 

 not only accord with the results of experiment; 

 they also have the great practical advantage of 

 yielding expressions that are easily integrable for 

 all the properties of steam with which the engineer 

 is concerned, such as the total heat, the 

 internal energy, the entropy, the specific heat, the 

 Joule-Thomson cooling effect, and the thermo- 

 dynamic potentials of Willard Gibbs. Prof. 

 Callendar shows that, by help of his equa- 

 tion and of the assumption which has been 

 stated, expressions for all these quantities are 

 readily obtained by applying the usual thermo- 

 dynamic relations, and, being so derived, the result- 

 ing numerical values, which he calculates for his 

 tables, are necessarily consistent amongst them- 

 selves. It was the absence of mutual consistency 

 that was perhaps the gravest defect in earlier 

 tables of the properties of steam. 



The range through which the Callendar 

 characteristic equation is applicable may conveni- 

 ently be described as the range through which 

 the Amagat isothermals (of PV and P) are sensibly 

 straight lines. The slope of these lines depends 

 on the values of the quantities h and c in the 

 characteristic equation : it is, in fact, equal to b — c. 

 But to determine the constants of the equation 

 Prof. Callendar relies mainly on experiments of the 

 porous-plug type, which measure the cooling effect 

 produced by forcing the gas through a constricted 

 orifice. In his own experiments of this kind he 

 employed an ingenious differential device which, 

 with his platinum thermometers, went far to elimi- 

 nate sources of error that affected the somewhat 

 NO. 2694, VOL. 107] 



discordant results obtained by other observers. 

 When a gas passes a throttling orifice of any 

 kind, under conditions which prevent loss or gain 

 of heat by conduction, there is one function of its 

 state that undergoes no change, namely, the 

 function which Willard Gibbs represented by the 

 symbol x- This function is equal to the internal 

 energy plus the thermal equivalent of the product 

 PV. It is now usually called the "total heat" — 

 a name first applied to it by Prof. Callendar 

 himself. Its value in technical thermodynamics 

 was emphasised by Prof. MoUier, who introduced 

 charts exhibiting the total heat in relation to other 

 functions of the state, notably the entropy. The 

 " heat-drop," or loss of total heat which the 

 working fluid undergoes in passing through a 

 turbine or engine of any type, is the basic quan- 

 tity in all calculations of thermodynamic perform- 

 ance. It is equally useful as a means of analys- 

 ing the reversed thermal cycle that is gone through 

 by a refrigerating machine, for which purpose 

 tables or charts are needed of the total heat of 

 such working substances as carbonic acid and 

 ammonia. 



Besides his detailed tables of all the pro- 

 perties of steam, saturated or superheated, 

 within the usual working range. Prof. Cal- 

 lendar gives in this volume an empirical table 

 of the properties of saturated steam up to the 

 critical point, to " serve as a guide for future 

 -work." In the extended table the critical tem- 

 perature is taken as 374° C, in accordance with 

 the results of Traube and Teichner, and the latent 

 heat is calculated by a formula of the Thiesen 

 type, which makes it vanish at the critical point. 

 The critical volume becomes 325 c.c. per 

 gram. The critical state lies, of course, far 

 outside the region within which Prof. Callendar 's 

 characteristic equation is applicable. He deals 

 with it in a separate chapter, which includes an 

 interesting discussion of recent experiments on 

 carbonic acid by Jenkin and Pye. 



Another section of the book deals with the 

 theory of flow through nozzles and of the steam 

 turbine. In this field also Prof. Callendar's work 

 has been of fundamental importance by showing 

 that the conditions of adiabatic flow are not, in 

 general, equilibrium conditions, but involve com- 

 plications due to supersaturation. By taking 

 account of the effects of supersaturation he has 

 brought the theory of steam-jets into harmony 

 with the results of observation, removing what 

 had been a puzzling discrepancy and explaining 

 why it is that the measured discharge from a 

 nozzle is actually greater than the limit which, 

 according to the older theory, would be found 

 even under frictionless conditions. The same 



