248 Prof. J. H. Jeans on Temperature-Radiation 



1. lie Rate of Approach to the "Normal State." 



22. The " normal state " may be thought of as a sort of 

 composite photograph o£ all possible states. Airy features 

 common to all states (or to all except an infinitesimal fraction 

 of the whole), must be features of the normal state, and 

 conversely. From this it follows (§ 10) that if there are any 

 properties which a system tends to acquire, independently of 

 the particular state from which the system starts, then these 

 must be properties of the normal state. But it has not been 

 proved, and cannot be proved, that a system will, in every 

 case, tend to pass into the "normal state." 



To take a well-known instance, the " normal state " of a 

 gas inside a rectangular vessel is given by Maxwell's law, 

 but if the system is started in such a way that the molecules 

 all move on parallel paths perpendicular to one pair of faces, 

 the system will not pass into the normal state at all. 



23. Again, the energy of a non-dissipative medium, or 

 conservative dynamical system capable of executing isochro- 

 nous vibrations, can be expressed in the form 



2T =* 1 1 2 + a 2 (£ 2 2 + ...'1 



(33) 



where <j>i, (j> 2 , ... are the coordinates of the separate free 

 vibrations. In the " normal state," we have 



i«ifc*+A*i a = i« 2 02 2 + /3 2 <£ 2 2 = ... =RT. 



But in any free motion of the system, the quantities 



£(»i0i 8 + /W), i(cc 2 ^ + M 2 '),&c, . . (34) 



retain through all time exactly those values with which they 

 started. There is no tendency towards equalization of the 

 values of these quantities, and therefore no tendency for the 

 system to pass into the normal state. 



For instance, in the system of § 17 (a string of particles) 

 the motion consists of the propagation of trains of waves, 

 without change of type or interchange of energy. As regards 

 the practical problem of finding the final partition of energy, 

 the existence of the " normal state " is of no account at all : 

 the whole problem turns on the initial state of the system. 



As regards the system of §§ 18-20 (the tube of air), we 

 know that as a matter of fact the system does tend to assume 

 the " normal state," which, as we have seen, is a state of 

 random motion of the gas-molecules. The reason why this 

 case differs from the last is that it is not permissible to 



