THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL C® SCIENCfE 



rsixT 



FEBRUARY 1922. 



XXV. On the Application of Probabilities to the Movement of 

 Gas-Molecules. By Prof. F. Y. Edgeworth, F.B.A* ' 



THIS is a sequel to the paper bearing the same title in 

 the Philosophical Magazine for September 1920. 

 The three arguments there employed to determine the 

 distribution of velocities in a molecular medley are here 

 reinforced. 



I. Laplace's Theory of Error. 



The first argument was based on the leading property of 

 the law of error first staged by Laplace. The enunciation 

 was facilitated by the fiction of molecular movement in one 

 dimension. Two sets of perfectly elastic piston-shaped 

 particles were supposed to be moving in one and the. same 

 right line under stated conditions (loc. cit. p. 249). 



1. The form of the frequency -junction. — It was shown that, 

 whatever the initial distribution of the velocities U and u 

 pertaining to particles of mass M and m respectively, the 

 system would through repeated collisions be ultimately 

 distributed according to the normal error function 



(NyA«/7r) exp -(AU 2 -rW). . . . (1) 



That is, presuming that the two sets of velocities fluctuate 

 independently. Otherwise the ultimate distribution can be 

 written 



(Nv/Aa/TT Vl^ 72 )exp-(AU 2 -2r i/A^+au*)/(l -r 2 ). (2) 



* Communicated by the Author. 

 Phil. Mag. S. 6. Vol. 43. No. 251. Feb. .1922. U 



