12 PKESSURE OF GASES 23 



Since each of these molecules, being of mass m and 

 moving with speed G from left to right, carries over into 

 the right half the momentum mG, the molecular momentum 

 of this half from left to right will have been increased by the 

 passage of molecules over this unit area in the unit of time 

 by the amount 



x mG = 



while simultaneously the same number of molecules cross 

 the area from right to left, diminishing thereby the oppo- 

 sitely directed from right to left momentum of the right 

 half by the same amount ; and therefore there is produced 

 in the right half an excess of the left-to-right molecular 

 momentum over that from right to left of twice this amount, 

 or of jjNmG 2 . This excess acts continuously during the 

 given time viz. the time-unit as a force from left to right 

 on the right half of the medium, and it is nothing else than 

 the pressure 



p = NmG 2 , 



which is balanced by the oppositely directed pressure of the 

 other half. 



This formula is the same as that found before, and thus 

 proves that its validity is not bound up with the assumption 

 before made, which assimilated the problem to that of elastic 

 collision. 



13. Absolute Value of the Molecular Speed 



The product Nm in the last formula, of the mass of a 

 molecule m into the number N of the molecules contained 

 in unit volume, has a simple meaning, for it obviously repre- 

 sents the mass of gas in the unit of volume ; but this may 

 be shortly called the density of the gas, the density of 

 water of which the mass-unit, one kilogram, occupies the 

 volume-unit, one litre being the unit density. This defini- 

 tion of the density p gives 



Nm = p. 



Consequently the formula may be written 



P = 





