28o Thermodynamic Theorems of Carnot 



to say that in the sciences making up theoretical physics we have construction 

 followed by deduction. Turning now to consider the evolution of any of 

 these sciences, we are not surprised to find that the early stages are given over 

 largely to construction and that, as the science matures, deduction becomes 

 increasingly important and eventually predominates. In some cases there has 

 been reached a relatively final stage of high perfection, characterized by 

 expositions from which constructive argument is entirely omitted and the 

 general principles are treated solely as axioms sufficiently verified by their 

 consequences; examples are the exposition of classical mechanics starting 

 from Hamilton's principle and that of thermodynamics starting from the 

 axioms of Carathcodory.* In such cases the constructive arguments have, 

 however, not been banished completely, but have simply been relegated to 

 the elementary textbooks. 



Within this general evolutionary pattern the position of Carnot is now 

 clear: he stands at the beginning of thermodynamics with a constructive 

 contribution of the first magnitude, supplemented by a deductive achieve- 

 ment noteworthy for its prescience. 



IV. Significance for Thermodynamics at Present 



Needless to say, of the forgotten theorems of Carnot the true ones— those 

 belonging to classes A and B— have not been forgotten in the sense that 

 their content has become unfamiliar. What has been forgotten is the exist- 

 ence of knowledge deducible from Carnot's theorem on reversible engines 

 without the help of the first low of thermodynamics. Carnot's theorems of 

 class A are examples of such knowledge and therefore have a special sig- 

 nificance which is permanent, though neglected by contemporary authors. 

 In order fully to reveal this significance we shall give below a summary 

 of the consequences deducible from Carnot's theorem without benefit of 

 the first law. 



The existence of such consequences was well known to the pioneers of 

 thermodynamics, and most of the formulas in our summary can be found, 

 more or less mingled with consequences of the caloric theory or of the 

 first law of thermodynamics, in the writings of Clapeyron, Clausius, and 

 above all William Thomson. We shall, however, be able to make only 

 passing reference to the history of some of the individual formulas. 



The neglect of results of the type here summarized has probably been 

 due to haste to obtain the more inclusive results that follow from the first 

 and second laws combined, or, in the case of perfect gases, from the first 

 law alone. But the need for such haste is now long past and a time has 

 arrived in which writers on thermodynamics might profit from an aware- 

 ness of the consequences that follow from Carnot's theorem without the 

 first law. 



* See A. Lande: "Axiomatische Begriindung der Thermodynamik durch Cai atheodorv," in 

 Handbuch der Physik, ed. by H. Geiger and K. Scheel, IX (Berlin: 1926), 281. 



