﻿536 Mr. S. B. McLaren on Emission and Absorption 



§9. Radiation aud Mechanics. 



It seems to be almost certain that dynamics leads to 

 a distribution o£ energy in which f varies as e~ and there 



is equipartition of energy. It is perfectly certain that in 

 nature the consequence is avoided. There are three courses, 

 and three only, open to those who would resolve this 

 antinomy : — 



(1) They may deny, and this is the most obvious course, 

 that the reasoning of the kinetic theory is sound. 



(2) They may assert that the actual distribution of energy 

 is not a temperature distribution. (See Jeans' ' Theory of 



Gases 0- 



(3) They may resign their belief in dynamics. Those 

 who haye gone beyond M. Planck and founded an atomic 

 theory of energy have made even this sacrifice. 



The difficulties of kinetic theory lie in the use it is 

 compelled to make of the rules of probability. And this 

 is of its essence. Where the senses present to us a body 

 whose properties have been through a longer or shorter 

 time unchanged, the kinetic hypothesis sees myriads of atoms 

 or molecules in rapid and always varying motion. The 

 observed absence of change is nothing but a gross or 

 average effect due to the enormous number of the changing 

 parts. It is only by counting chances and reckoning- 

 averages that the irreversible movement of heat is reconciled 

 with reversible laws of motion. Those who of our three 

 alternatives choose the first will certainly suggest that the 

 paradoxes in which the theory is landed are due to the use 

 it makes of the science of probabilities, and not to any 

 inadequacy in the science of mechanics to explain the facts 

 of heat and radiation. 



A material system which is so enclosed that it cannot lose 

 heat by radiation or conduction will in the end come to a 

 state in which the temperature is steady and the same at 

 every point. That is the great fact to be explained by mere 

 dynamics. ISo matter what the initial conditions, it is to be 

 shown that the laws of motion are always adequate to 

 produce the observed result. These laws are expressed most 

 generally by Hamilton's equations of motion deduced from 

 the principle of least action. Starting from any initial 

 values of the coordinates, the q's and p , s, we are compelled 

 to assert that on the average the system will have the 

 properties, whatever they may be, of a body in temperature 

 equilibrium. As in (2) write 



dV 2 a =dq 1 , dq 2 ... dq n , dp x , dp 2 ... dp n . 



