11 PRESSURE OF GASES 21 



The number of impacts on one of these faces in the 

 time-unit is found from the consideration that between 

 every two successive impacts by one and the same molecule 

 there elapses the interval during which the molecule passes 

 to and fro between the faces, that is, the interval in which 

 it traverses the path 7 with the speed G. The number of 

 impacts, therefore, which a single particle makes on the face 

 in a unit of time is the ratio of the path G traversed in the 

 time-unit to the length 2^ of the path to and fro, and is thus 

 G/Zy; hence the number of impacts on a face a/3 in the 

 unit of time made by all the particles is 



The product of this number into the impulse 2mG, 

 which is in the mean exerted at each impact, gives for the 

 whole impulse exerted on the face a/3 in the unit of time, 

 that is, for the total force exerted on it, 



pa/3 = NmG*a/3, 



p being the pressure ; so that the pressure on the surface is 

 given by 



p = pTmG 2 . 



This formula confirms what has been 'deduced before, 

 viz. that the pressure p is directly proportional both to the 

 square of the speed ( 9) and also to N, the number of 

 molecules in unit of volume, and therefore to the density of 

 the gas ; it is consequently inversely proportional to the 

 volume ( 6). 



12. Another Calculation of the Pressure 



I do not wish, however, to be content with this one 

 calculation of the pressure, as it suffers from the defect of 

 containing an unproved and unprovable hypothesis which 

 it would have been easy to avoid I mean the hypothesis 

 that the laws of elastic impact hold for the collisions of 

 molecules, even if only to a limited extent. We do not 

 need this hypothesis if we investigate the pressure in the 

 interior of the gas in place of that on the walls ; and this 



