312 Mr. W. Sutherland on the 



This equation contains two important consequences : — 



First. The parameter of molecular force varies inversely as 

 the product of molecular weight and modulus of dilatation. 

 [MendelejefF calls dpfdi the modulus of dilatation, and shows 

 that, for a given liquid, it is approximately independent of 

 temperature when measured at low pressures (one atmo- 

 sphere).] 



Second. The rate of variation of the translatory kinetic 

 energy of the molecules of most liquids with temperature is 

 the same, if that rate is measured at a constant low pressure, 

 such as that of one atmosphere. This second consequence 

 flows from the above equation in the following manner. It 

 is shown in my previous paper (Phil. Mag. July 1887) that 

 the virial of the mutual attractions of the molecules in unit 

 mass of a body, according to the law of the inverse fourth 

 power, is TrAp log L/a ; where L is a sensible length such as 

 the cube root of the volume of the unit mass, and a is a length 

 approximately proportional to the cube root of the molecular 

 domain (usually called molecular volume). L/a is so large a 

 number that log L/a may be regarded as constant within the 

 limits of present experimental possibility in the variation of 

 L and a. 



Now Clausius' equation of the virial applied to gases is 



fpu + internal virial = translatory kinetic energy. 



In the case of liquids under a small constant pressure, pu is 

 negligible in comparison with the other terms of the equation ; 

 so that for liquids at low pressures the equation assumes the 

 simple form 



internal virial =^ translatory kinetic energy ; 



while for gases at low pressures, the internal virial being 

 negligible, it assumes the form 



^pv or external virial = translatory kinetic energy. 



In the equation for liquids let us replace the internal virial 

 by its value SttA/d log hja, and denote the kinetic energy of 

 translation of the molecules in unit mass by E ; then 



Stt A/3 log L/a =E, 



„ . 1 Jj dp diniEt) 

 ^ a dt dt 



But Am J- is the same for most liquids, 



^(mE) * 



•*• dt ' 



