TAIT'S " THERMODYNAMICS." 667 



energy. He has always been most careful to point out the exact extent of 

 the assumptions and experimental observations on which each of his statements 

 is based, and he avoids the introduction of quantities which are not capable 

 of experimental measurement. It is therefore greatly to be regretted that his 

 memoirs on the dynamical theory of heat have not been collected and reprinted 

 in an accessible form, and completed by a formal treatise, in which his method 

 of building up the science should be exhibited in the light of his present 

 knowledge. 



The touchstone of a treatise on thermodynamics is what is called the second 

 law. 



Rankine, as we have seen, founds it on statements which may or may not 

 be true, but which cannot be considered as established in the present state 

 of science. 



The second law is introduced by Clausius and Thomson as an axiom on which 

 to found Carnot's theorem that the efficiency of a reversible engine is at least as 

 great as that of any other engine working between the same limits of temperature. 



If an engine of greater efficiency exists, then, by coupling this engine with 

 Carnot's engine reversed, it is possible to restore to the hot body as much heat 

 as is taken from it, and at the same tune to do a certain amount of work. 



If with Carnot we suppose heat to be a substance, then this work would 

 be performed in direct violation of the first law the principle of the conser- 

 vation of energy. But if we regard heat as a form of energy, we cannot apply 

 this method of reductio ad absurdum, for the work may. be derived from the 

 heat taken from the colder body. 



Clausius supposes all the work gained by the first engine to be expended 

 in driving the second. There is then no loss or gain of heat on the whole, 

 but heat is taken from the cold body, and an equal quantity communicated to 

 the hot body, and this process might be carried on to an indefinite extent. 



In order to assert the impossibility of such a process in a form of words 

 having sufficient verisimilitude to be received as an axiom, Clausius, in his 

 first memoir, simply says that this process "contradicts the general deportment 

 of heat, which everywhere exhibits the tendency to equalize differences of 

 temperature, and therefore to pass from the warmer to the colder body *." 



* Und das widerspricht dem sonstigen Verhalten der Warme, indem sie uberall das Bestreben 

 zeigt, vorkommende Temperaturdifferensen auszugleichen und also aus den warmeren Korpern in die 

 kalteren uberzugehen. 



842 



