164 PHENOMENA DEPENDENT ON MOLECULAR PATHS 70 



where L r is the value of the free path as deduced in 67 on 

 this assumption, viz. 



L' = fX 3 / 2 , 

 and where 



as in 27. Thus between these two values there is the ratio 

 T 1 : T = V3 : \/TT 



[or very nearly as 43 : 44] ; the interval between successive 

 collisions is thus somewhat smaller, and the collision- 

 frequency a little larger on Clausius' theory than on 

 Maxwell's. 



71. Relations of the Free Path to the Pressure 

 and Temperature 



According to the theoretical formula we have found, 

 the value of the molecular free path depends only on the 

 volume X 3 of the elemental cube and the area Trs 2 of the 

 central section of the molecular sphere of action ; the 

 molecular speed H, by which the value of the temperature 

 of the gas is determined, does not, however, occur in the 

 formula. 



Of these two magnitudes the elemental cube denotes 

 the small volume in which, on the average, each single 

 molecule only is contained. The size of this space is not 

 altered by mere addition of heat, but can only be altered 

 by the volume of the gas becoming greater or less ; it is 

 proportional to this volume, and therefore varies inversely 

 as the density, but is independent of the temperature of 

 the gas. 



If now the size of the sphere of action were not variable 

 with either the pressure or the temperature of the gas, it 

 would follow that the molecular free path cannot depend on 

 the temperature, but only on the density of the gas ; and, 

 indeed, must decrease or increase inversely proportionally 

 to the density, and therefore, if the temperature remains 

 constant, inversely proportionally to the pressure, by reason 

 of Boyle's law. 



