496 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



Von Bez ^ld called attention to the fact that this law bears a strik- 

 ing resemblance to the well-known theorem of Clausius, now com- 

 monly known as the second law. of thermodynamics, viz: "that 

 the entropy strives towards a maximum;" but, he says, "it is not 

 identical with it." 



The purpose of this paper is to examine into the precise relation- 

 ship between the two functions "potential temperature" and 

 "entropy" and to see whether any use can be made advantage- 

 ously of the former in the treatment of certain thermodynamic prob- 

 lems as well as to ascertain wherein the potential temperature law 

 fails to give full expression of the second law of thermodynamics. 

 To my knowledge no application has as yet been made of the new 

 term in treatises on thermodynamics. The substance of this paper 

 was communicated to the American Association for the Advance- 

 ment of Science at the Springfield meeting in 1895, but publication 

 pending opportunity for further elaboration was deferred. 



The ''potential temperature" of a body is defined as the absolute 

 temperature assumed when the body is brought adiabatically to standard 

 pressure. 



Defining the thermodynamic state per unit of mass of a body by 

 the three variables, T, the absolute temperature, v, the volume per 

 unit of mass, p, the pressure supposed uniform, the following char- 

 acteristic equation subsists between them: T = f (v, p). 



If the body be brought now adiabatically to standard pressure 

 p , then the temperature assumed at the end of the process is the 

 so-called potential temperature as above defined and is designated 

 by the symbol d. Hence, 



= f {v, Po) 0) 



For a perfect gas, since kT = pv, k being a constant for any par- 

 ticular gas, 



d=t*. v = k .v (2) 



k 



or the potential temperature for any particular gas is directly propor- 

 tional to the volume and, hence, as von Bezold showed, the potential 

 temperature readily admits of a graphical representation on the 

 usual pv diagram, being simply proportional to the v abscissae of 

 points of intersection of the line of standard pressure, p = p , with 

 the adiabats. 



Hence, were it possible to express the entropy function for perlect 

 gases directly in terms of potential temperature, we should likewise 



