I30 THOMSON'S GENERAL FOUNDATION. 



was thus forestalled by Rankine in the results to be 

 obtained by the development of the mathematical theory 

 of heat, and by Clausius in showing that Carnot's 

 theorem was reconcilable with Joule's discovery. Owing, 

 however, to the hypotheses involved in both Rankine's 

 and Clausius' theories, it was left to Sir William Thomson to 

 clear these hypotheses away, and show that Joule's discovery 

 of the equivalence and convertibility of heat and "work," 

 together with Carnot's theorem (re-founded on the axiom 

 first discovered by Clausius) constituted, alone, a sufficient 

 foundation for a complete theory of thermodynamics, ex- 

 plaining all the known physical phenomena and their quanti- 

 tative relations. This Sir William Thomson immediately 

 did. In March, 185 1, a paper "On the Dynamical 

 Theory of Heat, with Numerical Results from Mr. Joule's 

 Equivalent of a Thermal Unit, and M. Regnault's 

 Observations on Steam," by Sir William Thomson, was 

 read to the Royal Society of Edinburgh. In this paper, 

 which, in virtue of the absolute generality of his foundation, 

 and the pre-eminence of his powers in mathematical 

 analysis and sympathetic expression, easily placed the 

 author in front of his two contemporaries as an exponent 

 of Thermodynamics, Sir William Thomson gives all 

 credit to Rankine and Clausius, and expresses himself 

 with enthusiasm as to their work ; while the paper is one 

 continuous eulogy of the work of Joule, not only in dis- 

 covering the mechanical equivalent but throughout its entire 

 range. He makes reference to and gives quotations from all 

 Joule's papers, from the first presented to the Royal 

 Society in 1840, "On the Production of Heat by Voltaic 

 Electricity," continually expressing his admiration for 

 the conclusiveness of Joule's proofs and the philosophical 



