F. O. Koenig 279 



1, 3, 4, 7. (3) Scrutiny of Carnot's proofs in the light of our present knowledge 

 reveals the fact that the distribution of the theorems among the three neces- 

 sary classes mentioned above is as follows: 



Class A: theorems 1, 3 Class B: theorems 2, 5, 6, 7 Class C: theorem 4. 

 The proof of this distribution would of course require extensive quotation 

 from the Reflexions and must be omitted here for lack of space. 



III. Significance for the History of Science 



The forgotten theorems of Carnot are the first examples in thermodynamics 

 of special results of physical interest obtained by deduction from general 

 principles ^vhich are in turn derived from phenomena. It follows that Carnot 

 is the founder not only of the second law of thermodynamics but also of 

 thermodynamic deduction. In the former and fully recognized role Carnot 

 is the first member of the trio which includes Clausius (1850) and William 

 Thomson (1851); in the latter and at present unrecognized role he is the first 

 member of a highly ramified hierarchy which culminates in Gibbs and among 

 whose chief additional figures are: Clapeyron(i834), Helmholtz(i847, 1877!!.), 

 William Thomson (1848 ff.), Clausius (1850), Kirchhoff (1858), Guldberg 

 (1867 ff.), Massieu (1877), Boltzmann (1884), Van't Hoff (1884 ff.), Nernst 

 (1888 ff.), Lewis (1907, 1923). That in brief is the significance of the forgotten 

 theorems of Carnot for the history of science. 



This view of Carnot's role in the history of thermodynamic deduction might 

 be criticized on the grounds that a majority of the forgotten theorems, al- 

 though correct, were deduced by Carnot from the erroneous caloric theory 

 (class B). The answer to this criticism is that the famous theorem on reversible 

 engines was likewise so deduced by Carnot, and that therefore, as long as we 

 regard Carnot as the founder of the second law of thermodynamics, we can 

 hardly escape from regarding him also as the founder of thermodynamic 

 deduction. 



The implications of this duality become clearer in the light of some familiar 

 facts concerning the structure of theoretical physics. Any of the major sub- 

 divisions of theoretical physics— for example, classical mechanics, relativity 

 theorv, statistical mechanics, thermodynamics, etc.— has two parts: the first 

 consists of the erection of general principles through expeditious discussion 

 of selected phenomena; the second, of the systematic deductive exploitation 

 of these general principles. This is often expressed by the statement that in 

 theoretical physics we have induction followed by deduction. Actually, how- 

 ever, the arguments leading to the general principles are more complex than 

 mere induction in the strict sense: they seem to consist in general of expedient 

 combinations of induction, deduction, and plausible assumption. Thus the 

 argument leading to the second law of thermodynamics in the form Q^TdS 

 contains all three of these elements, and in any system of statistical mechanics 

 there is always at least one general principle, for instance, that of equal 

 a priori probabilities, which is frankly an assuinption. We therefore prefer 



