114 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



increment of heat into a perfect differential) may be called an 

 integrating divisor. The third property of (absolute) tempera- 

 ture may be expressed, then, by saying that it must be an 

 integrating divisor of the energy which is given to the system 

 as heat. 



64 



Almost the only writer who has attempted to devise kinetic 

 analogues which shall satisfy at once all these conditions is 

 Helmholtz,* whose u monocyclic systems " can be shown to do 

 so if certain assumptions are allowed. 



In view of the account which we have already given of the 

 part which Helmholtz played in the derivation of the principle 

 of the conservation of energy as an extension of principles 

 founded on the postulate that dynamical transactions can 

 be reduced to attracting and repelling forces between mass- 

 particles,f it is interesting to find that he has attempted 

 a dynamical interpretation of temperature by a method that 

 avoids the postulation of the existence of an infinitely large 

 number of molecules. This can be done by means of assump- 

 tions which express the kinetic and potential energies of the 

 system in terms of the amounts and variations of a number of 

 co-ordinates a term which, by a usage introduced by Lagrange, 

 may be extended from its simple geometrical significance to 

 any quantity which can be used to fix the spatial configuration 

 of a system.^ 



But the whole difficulty of the present case is the faqt that 

 we are ignorant of the " co-ordinate " which describes the 

 configuration of the molecules vhen a body is at a definite 

 temperature. The molecules are, in fact, " concealed masses," 

 "whose position still remains unknown when the co-ordinates 

 accessible to observation have been completely specified." 



* Bryan, loc. cit., p. 104. 

 t Supra, 50. 

 I Bryan, loc. cit., p. 96. 

 Hertz, Mechanics, p. 223. 



