712 Mr. S. H. Burbury on 



large. That of Jupiter from the actions of his satellites is an 



example of it. For these range from — r— ; for the earlier to 



1 . l3 '° . 1 



'TkT* for the later values ; while the flattening observed is ykTq.' 



Thus theory helps us to a determination of the distribution 

 of the matter composing a planet, which, since we cannot get 

 inside it, would otherwise remain unknown. 



Boston, Mass. 

 January 15, 1910. 



LXXY. Boltzmanns Law of Probability e *. 

 By S. H. Burbury, F.R.S* 



GIVEN a system of molecules between which mutual 

 forces of attraction or repulsion act, such forces 

 having a potential %, the chance, or comparative frequency, 

 of the molecules being in a configuration in which the 

 potential of the mutual forces is ^, is proportional to e~ x , h 

 being defined as follows : t, the mean kinetic energy of a 



molecule, =-5jr- This is Boltzmann's law of probability, 



proved by him to hold for gas molecules. May it not be 

 extended to any material system. in stationary motion ? 



Assuming this law to hold, the second law of thermo- 

 dynamics can be deduced from it. (See a paper of mine in 

 Phil. Mag. for January 1876 ; also Watson's ' Kinetic Theory 

 of Gases.') It seems to me now that there are strong reasons 

 for holding that the converse is also true, namely, that 

 assuming the second law to hold, the truth of Boltzmann's 

 law can be deduced therefrom. 



For, the system of n molecules being in stationary motion, 

 Clausius' equation must be true, namely, 



in which t is the kinetic energy of a molecule, Xt the sum of 

 the kinetic energies of all the molecules, p is the external 

 pressure on the vessel of volume v in which the system is 

 moving. Also, R is the repulsive force, r the distance, 

 between a pair of molecules, and the double summation 

 includes every pair. Now we may suppose v to become v + Bi% 

 while t and also p remains constant, and every r is increased 



* Communicated bv the Author. 



