346 Mr. Htrapath on the Causes, Laws, and principal [May, 



same ratio as the elasticities arising from the actions of corre- 

 sponding particles in the two media ; for the change of tempera- 

 ture does not alter the manner in which the corresponding 

 particles act in the media, but only the intensity of action. 

 This being the case, the elasticities due to the actions of corre- 

 sponding particles are to one another as their momenta and the 

 number of their revolutions or returns in a given time; that is, 

 ^s their temperatures and velocities. But the masses of the 

 corresponding particles being the same, the velocities are as the 

 temperatures ; therefore, the elasticities due to corresponding 

 particles, and consequently the elasticities of the media, are as 

 the squares of the temperatures. And by the cor. to the preced- 

 ing prop, the temperatures being the same, the elasticities areas 

 the numeratoms. Whence, if neither the temperatures, nor the 

 immeratoms are the same, the elasticities are in a ratio com- 

 pounded of the ratio of the numeratoms, and that of the squares 

 of the temperatures, or, which is the same, in a ratio compounded 

 of the inverse ratio of the volumes and the duplicate direct of 

 the temperatures. 



Cor. 1. — Hence the elasticities are also in a ratio which is 

 ■equal to that compounded of the simple ratio of the numeratoms, 

 and the duplicate of the velocities. 



Cor. 2. — And hence also the elasticities are in a ratio com- 

 pounded of these three simple ratios ; namely, the ratio of the 

 numeratoms, the ratio of the temperatures, and the ratio of the 

 velocities. 



Prop. IX. 



The spaces occupied by equal portions of the same gas, under 

 equal elasticities, are directly proportional to the squares of the 

 temperatures. 



For by the preceding proposition, the elasticity varies as the 

 numeratom and the squai e of the temperature conjointly ; there- 

 fore, the elasticity being constant, the numeratom is inversely 

 as the square of the ten:»peratures. But the quantity of gas 

 being the same, the space occupied is reciprocally as the nume- 

 ratom; consequently the space, or volume, is directly as the 

 square of the temperature. 



Cor. 1. — Because this is true of any gas, it follows that equal 

 volumes of any gases whatever, under equal pressures and tem- 

 peratures, will be equally augmented by equal augmentations of 

 temperature. 



Cor. 2. — Or more generally, if the elasticities ofany two gases 

 have an invariable ratio, and if their temperatures also have an 

 invai'iable ratio, their volumes will have an invariable ratio. 



Cor. 3. — It has been found by MM. Dalton and Gay-Lussac, 

 and lately confirmed by the further experiments of MM. Dulong 

 and Petit, that the volume of a given portion of gas at the tem- 

 perature of water freezing is to its volume under an equal pres- 



