THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 113 



The most important attempts in this direction have been 

 reviewed by Professor G. H. Bryan in an important report 

 " On our Knowledge of Thermodynamics, with particular 

 reference to the Second Law."* 



There are three conditions which must be satisfied by any 

 dynamical analogue of temperature. It must play the part 

 which temperature plays of determining the changes in the 

 system (when it is brought into contact with another system) 

 which result in " thermal equilibrium " ; it must be shown 

 that, with the dynamical analogue, systems which are "at the 

 same temperature " as a third system, are in " thermal 

 equilibrium " with one another ; lastly, the analogue must exhibit 

 the property known sometimes as Clausius' Theorem, sometimes 

 as the Second Law of Thermodynamics. This law states that, 

 for all reversible transformations which a body undergoes, 

 if the energy supplied in the form of heat be divided by 

 the absolute temperature at which it enters the body the 

 quotient will be a "perfect differential." This expression 

 implies that whenever the body undergoes a series of changes 

 of pressure, volume, and temperature, the integral! of the 

 quotient in question throughout the series defines an 

 unambiguous change in the body called a change of entropy, 

 which is independent (if the condition of reversibility is 

 maintained) of the route by which the body passes from its 

 initial to its final state. If we concern ourselves only with the 

 quantity of heat given and make no reference to the absolute 

 temperature at which it passes into the body, we do not possess 

 the data for determining unambiguously the final state of the 

 body. Hence the absolute temperature (which converts the 



* B. A. Report, 1891, pp. 85 et seq. 



t Suppose the series of changes to be broken up into any number of 

 sections. Also suppose the heat received during each section to be 

 divided by the absolute temperature at the beginning of that section, and 

 the sum of the quotients to be taken. As the number of sections is 

 increased the sum will approach a limit (p. 103). This limit is the 

 integral. 



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