116 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



next succeeds in showing* that one of the products just 

 mentioned can always be found which is an. integrating divisor 

 of the energy of the compound cyclical system built up by 

 coupling any two given monocyclic systems together. This 

 result is easily interpreted as the analogue of the common 

 temperature at which two bodies are in thermal equilibrium.! 

 Finally, the investigation proves that these systems possess the 

 third property of temperature that if two of them can each 

 be coupled with a third, they can be equally well coupled with 

 one another. J- 



In this way Helmholtz has shown that all the thermo- 

 dynamical properties of matter can be represented dynamically 

 by means of monocyclic systems which are capable of being 

 coupled together. But owing to the somewhat arbitrary 

 nature of the assumptions which the argument makes, it cannot 

 be said that he has proved a dynamical origin for temperature 

 even in the modified sense that he has established other 

 Objective facts of a dynamical order which constantly accom- 

 pany it. Moreover, the investigation has only attempted to 

 cover reversible heat phenomena, and appears to be incapable 

 of" including the cases of irreversible phenomena, to which 

 actual experience practically confines us.|| "We may conclude, 

 then, that even the most complete and successful attempt that 

 has been made to reduce temperature to a dynamical pheno- 

 menon, not only reaches its end by inspired assumptions instead 

 of by the road of inevitable deductions, but also fails to consider 

 the enormous bulk of the primary facts in question. It does 

 not, therefore, escape the condemnation which Professor Bryan 



* Bryan, op. cit., p. 102. 



t As a simple instance of such dynamical analogues, Helmholtz gives 

 the case of two revolving wheels which may be coupled together by 

 joining their axles if their angular velocities are equal. (Bryan, op. cit^ 

 p. 101.) 



| Bryan, op. cit., p. 103. 



Op. cit., p. 104. 



|| Op. cit., p. 108. 



