524- Frof. Clauslus on the Conduction of Heat by Gases. 



powers of e, we thus obtain for the mean value of 8 the quantity 

 qiie. Introducing this value in equation (X.), we obtain 



- N , 3 



and accordingly equation (46) becomes 



,, 1 N 2 f+V 2 \ , 



and performing the integration, we get 



M= iv (48) 



The total positive momentum of the molecules which strike 

 each other within the stratum during a unit of time may be 

 arrived at in a corresponding manner. The positive momentum 

 of a molecule whose velocity is V and whose cosine is jjl, is rn/nY, 

 and hence we have to make use of the product m/nYa, instead of 

 the quantity a ; but here again we have to determine the mean 

 value of Ya, just as previously we had to determine the mean 

 value of a. The expression for the momentum sought is there- 

 fore 



1 f +1 — 



- cfomN j lYapdfi, 



If, as before, we substitute their values for I and Ya in this 

 expression, it becomes 



2 dxm JH \ Y + 5 ^ 6 )M"> 



whence we get, by performing the integration, 



1 , W 

 - dxm ^r- uq, 

 i\ 



for which, by applying equation (48), we may also write 

 ^dxmMqe. 



§ 22. This last expression may serve us for the determination 

 of the constant quantity q. 



The molecules which impinge within the stratum are also those 

 which, after impact, are emitted from the stratum, and the col- 

 lective momentum which these molecules possessed before im- 

 pinging must remain the same afterwards. Now the positive 

 momentum of the molecules emitted from the stratum can be 

 easily expressed according to the method of representation pre- 

 viously adopted. For we have seen that the motions of these 

 molecules may be expressed by assuming at first motions taking 



