70 MOLECULAR MOTION AND ITS ENERGY 35 



to repeat a proof which has been given by Clausius, 1 by 

 which also the rise of pressure already described in the 

 direction of the flow is better explained. 



For this we start, as in the consideration ( 12) of the 

 state of equilibrium, from Joule's assumption, 2 which even 

 in this case is admissible, that the pressure caused by the 

 motion of the gaseous molecules so operates as if a third 

 part of the molecules move to and fro along the normal to 

 a stressed surface, while the other two-thirds move parallel 

 to this surface. Of the first third one-half will at every 

 moment have a molecular velocity G in the same direction 

 as the velocity of flow a, while the other half has a mole- 

 cular velocity in the opposite direction. Therefore, of the 

 N molecules contained in unit volume, j?N move with a 

 resultant velocity G + a in the direction of the flow, and 

 simultaneously the same number ^N move in the opposite 

 direction with the resultant velocity G a. 



The difference G a we may take to be positive, since 

 the mean molecular velocity G is very great, while the ob- 

 served speeds of flow are for the most part considerably less. 

 The greatest velocity which the wind attains that, for 

 instance, of the most fearful storm may be taken at about 

 only one-tenth of that with which the molecules move 

 about. But if, indeed, it should happen that a were greater 

 than G, the argument would not be invalidated. 



If, now, one- sixth of all the molecules move with the 

 velocity G -f a in the line of flow, the number which pass 

 through a surface F in unit time in this direction is 



iNF(G + a), 

 and they carry with them momentum equal to 



NmF(G + a) 2 . 



In the backward direction there pass 



*NF(G - a) 



1 Bulletin de VAcad. de Belgiqiw [3] xi. 1886, p. 180 ; Mech. Warmetheorie, 

 2. Aufl. iii. p. 248. 



2 The calculation is carried out independently of this assumption, and 

 purely on the basis of Maxwell's law, in 7* and 43* of the Mathematical 

 Appendices. 



