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LXVI. The Foundations of the Kinetic Theory of Gases, Note 

 on Professor Tait's paper (No. 131, p. 343). By S. H. 



BUEBURT*. 



I THINK Professor Tait (p. 345, A, B, and C) has postu- 

 lated rather more than is necessary. There may, as it 

 appears to me, be a set of spheres which never collide with 

 each other, and one other sphere which collides with the first 

 set, and it will be found that this single sphere will knock the 

 others into "the special state." I prove it as follows : — 



Let there be a number of elastic spheres moving in any 

 space, each of mass P, but of infinitely small radius, so that 

 they never collide with each other. Into this system intro- 

 duce one elastic sphere of mass Q, and of considerable radius, 

 so that collisions will occur between it and the P spheres. 



Assume Maxwell's distribution to exist ; that is, that the 

 number of P spheres whose component velocity in given 

 direction lies between x and % + dx is proportional to €~ hPx2 dx, 

 and the time during which, on the average of any long time, 

 the sphere Q has component velocity between x and x 4 dx is 

 proportional to e~ hQx2 dx. When the sphere Q collides with 

 one of the P spheres, let V, represented by pOq in the figure, 

 be the relative velocity of the two spheres, and V', represented 

 in the figure by 0, be the velocity of their common centre 

 of gravity. 



Let qO " P 



Consider all the collisions which take place in unit time in 

 which V and V' have these values before collision. The 



* Communicated by the Author 



