THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES 



SEPTEMBER 1 



XXIX. On the Application of Probabilities to the Movement 

 of Gas-Molecules. By Professor F. Y. Edgeworth, 

 F.B.A* 



rpHE following is an attempt to vary, in the hope of 

 JL elucidating, some arguments which the kinetic theory 

 of gases derives from the Calculus of Probahilities. 



A. Beginning with the simplest case, imagine an immense 

 number of short perfectly elastic smooth cylindrical pistons 

 of equal size but two varieties of densit}-, the two sets equally 

 numerous, moving in a perfectly smooth long straight hori- 

 zontally placed groove, terminated at each extremity by a 

 perfectly elastic barrier. The pistons are capable of passing- 

 each other. They may be conceived as side-tracked from 

 time to time — say, each one after suffering a collision — and 

 guided by smooth devious paths to be replaced without loss 

 of Telocity at random at some new point on the main line f. 

 The instances in which more than two come together at once 

 are so rare that they may be neglected. Negligible also is 

 the length of the pistons in comparison with the average 



* Communicated by the Author. 



t If the pistons are not capable of passing each other, their movements 

 might still be sufficiently independent to generate the normal law by 

 repeated collisions. The conception of corpuscles thus tethered may 

 have some relevance to the vibrations of molecules within a solid. 



Phil. Mag. S. 6. Vol. 40. No. 237. Sept. 1920. S 



