71 MOLECULAR FREE PATHS 169- 



for while the factor O increases with , the newly added 

 factor diminishes as increases. 



The value L of the molecular free path is altered for the 

 same reason in inverse ratio to the collision-frequency. It 

 must be represented by the improved formula 



in which L denotes the value that holds at the temperature 

 of melting ice, and therefore at = I/a = 272'5 degrees 

 above absolute zero, a being the coefficient of expansion of 

 the gas. According to this formula, the free path L in- 

 creases with the temperature . 



The extent of increase to be expected from this theory 

 may be easily judged by considering the two possible limit- 

 ing cases. If there were no cohesion, there would be no 

 increase of L with the temperature ; if the cohesion is so 

 great that the numerical value of is small in regard to (7, 

 the factor 



+ (7/0) = 0/(C + 0) 



approximates to proportionality with , and the more so the 

 greater C. The free path therefore increases with rise of 

 temperature at most as greatly as the temperature estimated 

 from absolute zero, and consequently in a slighter ratio in 

 general. (Compare 87.) 



72. On the Absolute Value of the Free Path 



The absolute magnitude of the number of collisions of a 

 molecule that occur in unit time a second, for instance 

 can be determined from the above formulae just as little 

 as the value of the mean free path in absolute measure- 

 millimetres, for instance. For the latter depends on two 

 unknown magnitudes, viz. the mean distance of molecular 

 separation X and the radius of the sphere of action s. 

 With respect to these we only know, as has already been 

 mentioned in 65, that X must be very much larger than $, 

 and therefore L very much larger than X. 



Although, therefore, a molecule passes by many mole- 



