128 TRUE FORM OF CARXOT'S FUNCTION. 



from this foundation was of the greatest advantage in its 

 own mathematical development as well as in its application ; 

 and that this development and application were of the 

 greatest use in directing the development of the Theory of 

 Thermo-dynamics founded on the perfectly general laws of 

 Joule and Carnot, which followed immediately after. But 

 Rankine was not alone in affording such assistance. In 

 1848, Joule had, from the development of his own theory 

 and its application to bring Carnot's principle into accord 

 with his experiments on air, been led to the discovery of 

 the true form of the relation discovered but not defined by 

 Carnot, between the proportion of heat converted into work 

 and the initial and final temperatures at which the heat 

 existed. All Carnot had been able to show was that the 

 work done was dependent on these temperatures only,, 

 in a form that was expressible by C (Ti - T 2 ) where C 

 might depend in any unknown way on the temperatures. 

 In a letter, dated December 9th, 1848, to Sir William 

 Thomson, Joule suggested that the value of C (Carnot's 

 function) was the quotient of the heat received at the tem- 

 perature Ti divided by the temperature at which the heat 

 was received measured from the absolute zero as discovered 

 by Joule. 



In February, 1850, there was read to the Berlin Academy 

 of Sciences, a paper on " The Mechanical Action of Heat," 

 by Rudolf Julius E. Clausius. This paper, read almost 

 simultaneously with Rankine's, contained almost an iden- 

 tical theory, and its almost identical application. Clausius' 

 theory had a somewhat different foundation however. It 

 was primarily founded on Joule's law, and a general 

 hypothesis as to the dynamical constitution of gas, from 

 which Clausius, like Joule before him, obtained the absolute 



