1821.] Phfcnomena of Heat y Gases, Gravitation f^c, 349 



only a striking instance of the coincidence of our theory of the 

 constitution of gases with pheenomena, but also a fine corrobora- 

 tion of our theory of collision. 



In ccr. 2, I have generalized this law, by which means we 

 have an opportunity of comparing the theory with phaenomena 

 on a more extensive and varied scale. For if we suppress the 

 ratio of the temperatures, by making it the ratio of equality, this 

 cor. will, in a variety of ways, become comparable with obser- 

 vation. By taking portions of any two gases, and measuring 

 their elasticities and volumes at any common temperature, we 

 ought by this cor. to find, that if we raise or diminish the tem- 

 peratures equally, and make the ratios of the first and second 

 volumes equal, the ratios of the first and second elasticities ought 

 to be equal. Again, if the two temperatures be equal, and we 

 any how change the temperature, elasticity, and volume of one 

 of the gases ; and if we make the second elasticities and volumes 

 to hold respectively the same ratios as the first ; then ought the 

 second temperature of the one gas to be equal to the second 

 temperature of the other. 



Prop. X. 



If the ratio of the elasticities of any two gases be that of e to 

 1, the ratio of their volumes that of i) to 1, and of their tempera- 

 tures that of ^ to 1 ; and if the elasticities, volumes, and tem- 

 peratures of these gases be any how varied, so that the ratios of 

 the second elasticities, volumes, and temperatures, be respectively 

 those of e^ to 1, i?i to 1, and t^ to 1 then will the ratio of e^ to 1 

 be equal to that of e t^H to f^ v^. 



For let us call V, V the first volumes ; E, E the first elastici- 

 ties ; and T, T the first temperatures of the gases ; and let F,, Vj 

 in like manner denote their second volumes : E^, Ei their second 

 elasticities; and T,, T^ their second temperatures. Then by 

 hypothesis, we have 



F : V :: -y : 1 and F, : V^ :: v, : 1 

 jB : E :: e : 1 £, : E, :: e, : 1 



r : T :: ^ : 1 T, : T, :: ^, : 1 



But by prop. 8, 



E, : E :: T,^ V : T' V\ and 

 E : E, :: T^ V, : T,°- V, and 

 E : E :: e : 1. 



Therefore compounding these ratios, we shall get E, : Ej or e, 

 : 1 :: 2^ T^ F V^ e : T^ T,^ V, V; and consequently e, : 1 :: 

 et^^v : f^v,. 



Cor. 1. — From this theorem it appears, that if the ratio of the 

 first temperatures be a ratio of equality ; and if the same be the 

 case with the ratio of the second temperatures, no matter what 

 be the ratio of the first and second temperatures ; and if the 



