1821.] P/n£7iom€na of Heat, Gases, Gravitation, ^c, 345 



in one medium arises from the action of the particles of the first 

 stratum alone, so it does also in the other medium ; and if it- 

 arises from the action of the particles of the two first, three first, * 

 or n first strata in one medium, the same holds true with the-^ 

 elasticity in the other medium. But the number of particles of^ 

 any one stratum that strike against a given portion of the con^ >. 

 taining surface of one medium, is to the number of particles o£ 

 the corresponding stratum that strike against an equal and simi- 

 lar portion of the other medium, in the duplisubtriplicate ratio of 

 the numeratoms directly ; that is, in the duplisubtriphcate ratio- - 

 of the spaces occupied by equal portions of the gases inversely;.'; 

 Therefore as the whole elastic forces of these corresponding^ 

 strata are in a ratio compounded of the ratios of the numbers of^^ 

 particles that strike against equal portions of the sides of the 

 containing bodies, and of the numbers of returns which they 

 make to the sides in a given time, that ratio must be equal to 

 one compounded of the inverse duplisubtriplicate and of the 

 inverse subtriplicate ratios of the spaces occupied by the two ' 

 gases ; it must, therefore, be equal to the simple inverse ratio of 

 the spaces occupied. And since the same number of strata 

 affects the elasticity of the one gas as of the other ; and since 

 the inverse ratio of the spaces is the ratio of the elastic force of 

 any two corresponding strata, it is consequently the ratio of the 

 united elastic forces of all the strata that affect the elasticity ; 

 and is, therefore, the ratio of the elastic forces of the two gases» 

 Cor. — Because the numeratoms are reciprocally proportional 

 to the spaces occupied, it follows that the elasticities are, under 

 equal temperatures, directly as the numeratoms. 



Scholium. 



We have in the two preceding theorems and their corollaries 

 supposed the atoms, or particles, to be perfectly hard ; but the 

 same consequences would follow if they were either perfectly or 

 imperfectly elastic, and the containing vessel either elastic or 

 hard. For the temperature being invariable, the intensity of 

 the collisions, and consequently of the reflections, would remain 

 the same in a rare as in a denser medium. The law, therefore,, 

 that the elasticities and compressions are proportional, under 

 equal temperatures, is true not only in permanent airs or gases, 

 but in all kinds of vapours, which is conformable to experience. 



Prop. VIII. 



The same things remaining, the elasticity of a gas under a 

 variable temperature and compression, is proportional to it»-- 

 numeratom and the square of its temperature conjointly ; or the 

 elasticity varies as the square of the temperature directly, and 

 the simple of the space inversely. 



If we first suppose in two portions of the same gas the nume- 

 ratoms to be equal, the elasticities of those portions will have the<: 



