on the Physical Properties of Gases. 407 



where 



7 a } 11 a P 



h = —s — r- 9 - and. Y = -9 — 7v>* 

 The second integral 



I +co -— /— 



= 1 (u + h)e y 2 c??j = hviry ■ 



c/— QO 



2 + /3 2 )' 

 Hence the whole integral 



& 



__ 1 (r* — c /2 W "*+pdr 



(** + /?)* J* 



Let - be the common mean kinetic energy of molecules in 

 each system. Then 



*> ni a 



m 1 ot- = m 2 li —v; 



also 



g2+/3 „ = mi +», 2 



, ???! + v7? 2 



lm^m 2 v 



Hence the number of blows > c in a unit of volume per unit 

 of time between molecules of the first and second kinds respec- 

 tively is 



zv 7rJNJNV\/ — L_ £ V&? 4w 1 »« 2 a. 



V m^m^ 



The law of variation of the number for the same pair of gases 

 is of the form 



AppWte t, 



where p, p' are the densities of the two gases, t is the absolute 

 temperature, and A and t are constants. It is probable that 

 c or t will vary with the amount of internal energy of the mo- 

 lecules, and will diminish as the temperature increases. 



Putting c = 0, we find the whole number of collisions to be 



V i7i 1 m 2 

 as has been shown by Maxwell*. Hence the number of colli- 



* Phil. Mas?. January 1860 



