116 Lord Rayleigh on the Law of 



is uniform in space except near the boundary. For if g x 

 denote the ^-coordinate of a particular molecule, and if we 

 effect the integration with respect to all the coordinates of 

 other molecules as well as the other coordinates of the par- 

 ticular molecule, we must arrive at a result independent of x, 

 provided x relate to a point well in the interior. That is to 

 say in the various systems contemplated the particular mole- 

 cule is uniformly distributed with respect to x. The same 

 is true of y and z, and thus the whole spaeial distribution is 

 uniform. If the single system constituting the gas has 

 uniform statistics, it will follow that the distribution in it of 

 molecules similar to the particular molecule is uniform. 



The uniformity of the distribution is disturbed if an external 

 force acts. In illustration of this we may consider the case 

 of gravity. From (52) the distribution with respect to the 

 coordinates of the particular molecule will be 



e -gz 2K C J X ty tf-^ 



and the same formula gives the density of molecules similar 

 to the particular molecule in a single system. 



The main purpose of this paper is now accomplished ; but 

 I will take the opportunity to make a few remarks upon some 

 general aspects of a kinetic theory of matter. Many writers 

 appear to commit themselves to absolute statements, but 

 Kelvin* and Boltzmann and Maxwell fully recognize that 

 conclusions can never be more than prohable. The second 

 law of thermodynamics itself is in this predicament. Indeed 

 it might seem at first sight as if the case were even worse than 

 this. Mr. Culverwell has emphasized a difficulty, which must 

 have been pretty generally felt, arising out of the reversibility 

 of a dynamical system. If during one motion of a system 

 energy is dissipated, restoration must occur when the motion 

 is reversed. How then is one process more probable than the 

 other? Prof. Boltzmann has replied to this objection, upon 

 the whole I think satisfactorily, in a very interesting letter f. 

 The available (internal) energy of a system tends to zero, or 



* Witness the following remarkable passage : — " It is a strange but 

 nevertheless a true conception of the old well-known law of the conduction 

 of heat to say that it is very improbable that in the course of 1000 years 

 one-half the bar of iron shall of itself become warmer by a degree than 

 the other half: and that the probability of this happening before 1,000,000 

 years pass is 1000 times as great as that it will happen in the course of 1000 

 years, and that it certainly will happen in the course of some verv long 

 time."— (' Nature,' vol. ix. p. 443, 1874.) 



t ' Nature/ vol. li. p. 413 (1895). 



