336 M. Polsson on the Caloric of Gases and Vapours. 



provided the same temperature fl has been preserved. Phicing 

 the two gases now one on the other, their united volume is 



i,_(_^!iL or - {p-\~p'). 



These gases, according to what we have said above, will equal- 

 ly intermix without changing their temperature or common 

 pressure p. Now by Marriotte's law, which is as true of 

 mixed as of simple gases, if we compress the mixture without 

 changing its temperature until its volume 



I {P+P') 



becomes v, its pressure p will become p +/>', the same as we had 

 to prove. Equally good would the princqile hold with three or 

 more gases, or with a mixture 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 singly exert, when separately 

 occupying the same volume v at the same temperature 9. It 

 may be seen in the 12th book of the Mecanique Celeste how 

 M. Laplace has deduced this principle from the hypotheses 

 he has made on the caloric and radiation of the gases ; we 

 simply propose to exhibit its connexion with another fact which 

 we first announced. 



Let n and n be the number of grammes of two different 

 gases mixed together at the temperature 9 under a pressure p 

 and filling a volume v ; and let c, c' denote the specific heats 

 of a gramme of these gases under an invariable pressure p, 

 and c" the specific heat of a gramme of the mixture under the 

 same pressure. Then will 



(?? + «') c" = n c+n c (11) 



For if we suppose the two gases instead of being mixed merely 

 superposed, so that under the temperature 9 and pressure p of 

 the mixture they occupy separate portions u and ii of the total 

 volume V ; then, by what we have said above, the quantity of 

 heat will be the same in the two gases thus placed as in the 

 perfect mixture of them. This equality will moreover subsist 

 if we augment by one degree the temperatures of the mixture 

 and of the gases. Now to make this augmentation we must 

 communicate a new quantity (w + n') c" of heat to the mixture, 

 and the quantities n c, n' c to the two gases. The first there- 

 fore must be equal to the sum of the other two, which is equa- 

 tion (11) — an equation that may be easily extended to the 

 mixture of any number whatever of gases and vapours. It will 

 give the specific neat of any mixture when that of each of the 

 component gases or vapours is known ; and reciprocally we 

 may employ it to find the specific heat of either of the com- 

 ponent gases when those of the others and of the mixture are 



known. 



