Laio of Molecular Force. 313 



or the temperature rate of variation of the translatory kinetic 

 energy of a molecule, is the same for all molecules when com- 

 pared as the constituents of liquids at low constant pressure. 



This is an important result in molecular dynamics ; its 

 similarity to the law of Dulong and Petit as to the constancy 

 of the molecular heats of the elements is obvious and imme- 

 diately suggestive, while its bearing on the physical meaning 

 of temperature is worth noting. It must not be confused 

 w'ith the assumption made by many continental writers on 

 thermodynamics and molecular physics, that the absolute 

 temperature of a mass is a measure of the kinetic energy of 

 translation of each molecule in the mass, no matter what the 

 state of the mass be ; this assumption gives mE ocT, and 

 therefore d{^lW)ldt is constant for all substances and for all 

 states of each substance. But the result given above holds 

 only when the external virial is negligible in comparison with 

 the internal ; in fact the difference between the two views 

 may be shown thus : — According to the arguments of this 

 paper, we can write d{mEi)ldt'=V when the external virial is 

 negligible, while d{m^)/dt^Q, when the internal virial is 

 negligible, P and Q having possibly different values ; while, 

 according to the assumption mentioned above, P is considered 

 equal to Q. Again integrating, we get 



mE = \V dt + M. for the first case, 

 and 



mE = J Q ^^ + N for the second case, 



the constants of integration being possibly different ; while, 

 according to the above assumption, the two constants are 

 assumed to be the same, seeing that the translator}^ kinetic 

 energy of a molecule, both of a hquid and of a vapour at the 

 same temperature, is assumed to be the same and to be 

 proportional to the absolute temperature. 



Before proceeding to the determination of the values of A 

 from Schiff's experimental results, it maybe as well to discuss 

 a certain old-standing difficulty in capillarity, namely the 

 rapid rate at which capillary height and surface-tension 

 diminish with rising temperature. According to the expres- 

 sion found above, the tension for a given substance varies as 

 the I power of the average density of the film, a QCp^. Now 

 G. Schall has shown {Berichte der deutsch. chem. Gesell. xiv. 

 p. 555) that approximately the surface-tension for several 

 Jiquids varies as the f power of the density ; although the 

 theoretical arguments by which he endeavours to establish 

 this relation as a consequence of the Newtonian law are not 



