On Boltzmanns Law of Distribution e~ 2hx , fyc. 403 



tube for a longer interval than under any easily producible 

 conditions which I have found. The fleeting nuclei from 

 ammonium polysulphide seem therefore much more stable 

 when preserved out of contact with an oxydizing medium 

 like air, and the same is true of sulphuric acid in a measure, 

 and for sulphur itself. 



It should be noticed that coal-gas bearing the condensa- 

 tionally active sulphide nuclei stated, is just as inert 

 electrically as air. 



I conclude, therefore, that neither Kelvin's nuclei nor 

 Aitken's " dust " particles have yet been downed by the wily 

 ion. I admit that an electric field may sometimes stress ions 

 out of them, leaving the nuclei to do the condensation. 



Brown University, Providence, U.S.A. 



XLI. Boltzmanns Law of Distribution e~ 2hx , and 

 van der WaaW Theorem. By S. H. Bujrbury *. 



1. A SYSTEM of molecules is in stationary motion within 

 _XJL a space bounded by elastic walls impermeable to ]?eat 

 the mean kinetic energy being for each molecule 3/4/i. Then 

 the above law asserts that the time during which on the 

 average of any very long time their coordinates will lie 

 within the limits x 1 . . . x 1 -j-d.v l &c, or, as we may otherwise 

 express it, the chance of their being in that configuration, is 

 proportional to 6~ 2hx da } in which x i s the potential of all the 

 forces acting on the molecules in that configuration, h is 

 constant, and do- is the continued product of the differentials 

 dx i dy x . . . dz n . 



2. I follow in substance the proof given in Boltzmann's 

 Vorlesunqen ilber Gas Theorie, Part i. p. 134. It is assumed 

 that the chance of the molecules having their coordinates 

 within the limits aforesaid, and their velocities within the 

 limits Ui . . . u 1 + dn i iv n . . . iv n + du: n is 



Ae~ hQ d<i'i . . . dz n dui . . . dic n , 



where A is, omitting numerical factors, a function of the 

 coordinates only, and Q =€ -*2j»(it2+*2+«>2) a function of the 

 masses and the velocities only. Further, the summation 

 includes all molecules. Our placing the coordinatis and 

 velocities in separate factors follows from, indeed expresses, 

 Boltzinann's fundamental assumption of the independence of 

 the molecular velocities, which I have elsewhere called 

 assumption A. It is not essential to the proof, as we shall 

 see later (art. 17). 



* Communicated by the Author. 



