and the Partition of Thermal Energy. 677 



10" 1 '. The error in neglecting it is therefore small. Its 

 effect is felt at the boundary where it gives rise to a powerful 

 surface pressure. 



We neglect, therefore, the change in the potential energy 

 and take the velocity as constant throughout the motion. 

 Also we neglect the duration of the impact in comparison 

 with the period of vibration. If t x be the time from one 

 extreme position to the other, and t 2 the duration of the 

 impact, t 2 will be neglected in comparison with t 1 *. 



6. Heat Relations. 



To consider the heat relations of a body it is necessary to 

 formulate a relation between the molecular kinetic energy 

 and the temperature of the body. It may be pointed out 

 that the equation 



iMV 2 = «0 



for gases does not follow from dynamical considerations, but 

 is a direct consequence of Boyle and Charles' law. As a 

 matter of fact, we may take it as the definition of temper- 

 ature. For a solid we take 



Q = the average external kinetic energy of a molecule 

 = iMV 2 . 



P = the internal kinetic energy per molecule, i. e. the 

 energy of motion relative to the centre. These 

 are, of course, additive in the ordinary way. 



If Q be an analytic function of vanishing with it, we 

 may take 



We shall follow the usage of the Gas-theory and suppose 

 that the temperature is determined by the average external 

 kinetic energy of the molecule, taking 



7. Partition of Energy. 



When the temperature of a solid is raised by 1° C, the 

 quantity of energy absorbed per unit volume is D s J, s being 

 the specific heat and J = 4'18xl0 7 ergs. Now Dulong and 

 Petit's law states that W s is approximately constant for all 

 elements. Energy imparted to every molecule 



DsJ Ws T 



JN e 



* Cf. J. J. Thomson, ' Corpuscular Theory of Matter,' p. 93. 



