SECT, ii.] PROPERTIES OF STEAM. 85 



Experience proves that these gases would gradually mix together till they 

 became completely intermixed. It further shows that during this operation heat 

 is neither evolved nor absorbed ; so that after a certain time the mixture is per- 

 fectly homogeneous, the two gases holding the same proportion in every part, and 

 the temperature and pressure being t and p. From these facts, established by 

 observation, we may deduce another equally well verified by experience. 



123. If two gases, or a gas and vapour, mixed together at the temperature t, 

 fill a volume v ; and if p and f denote the pressures they would separately exert 

 when separately occupying the same volume v, at the same temperature t, the 

 pressure of the mixture will be p +f. 



In effect, let us suppose that the two gases at first are distinct, and let f be 

 greater than p ; then dilating the gas under the pressure /, until f changes to p, 

 its volume will become 



I/ 

 P 



provided the same temperature t has been preserved. Placing the two gases now 

 one on the other, their united volume is 



v + L/ or I (p+f). 

 P P 



124. These gases, according to what we have said above, will equally intermix 

 without changing their temperature or common pressure p. Now according to the 

 law of the volume being inversely as the pressure, which is true of mixed as well 

 as of simple gases, if we compress the mixture without changing its temperature 



until its volume - (p+f) becomes v, the pressure p will become p+f, the same 



as we had to prove. 



Equally good would the principle hold with three or more gases, or with a mix- 

 ture of gases and vapour : in all cases the united pressure will be equal to the sum 

 of all the pressures which the gases or vapours would each exert, when separately 

 occupying the same volume v at the same temperature t. 



When a change of temperature takes place, either after or during the mixture, 

 the first temperature being t ; then 



= the volume at the new temperature t', and pressure p. 



125. This is compared with General Roy's experiments in the following table, 

 formed from the mean results which he obtained. 1 Commencing at zero, 1000 

 parts of air, in contact with water, and under a pressure of 32'18 inches, is 



Philosophical Transactions, vol. Ixvii. p. 653. 



