348 Mr. Het'apathoji the Causes, Laws, and princip<il [May, 



are, therefore, equally applicable to all gases, simple, or com- 

 pound, supposing, however, their particles to be indefinitely 

 small, or their diameters to have no sensible proportion to the 

 lines they describe. 



One of the longest known laws of gaseous bodies is, that of 

 the volume being reciprocally proportional to the elasticity. 

 This law is demonstrated in prop. 7, and is one that I have been 

 careful to establish by a clear and explicit proof, as well on 

 account of its own importance, as of its being the foundation of 

 most of ray other deductions on the properties of gaseous bodies. 

 I have, however, shov('n, in the schoHum to prop. 7, that the 

 same law would result from the supposition of the particles being 

 either perfectly or imperfectly elastic. But though this is true 

 in the present instance, it is not so universally. For if we sup- 

 pose a medium to be composed of elastic particles, and to be 

 kept in a gaseous state by the actions of its particles on one 

 another, and on the particles of the containing body ; and if we 

 also suppose the temperature to be equal to the momenta 

 which these gaseous particles impress on the particles of the 

 other bodies, then we find that, in order to preserve the temper- 

 ature of the containing body, the gaseous particles must have 

 such motions as will repel the particles of the containing body, 

 with momenta equal to the momenta which they had previous 

 to the contact. But to do this, the particles of the gas, if they 

 and the particles of the containing body are unequal, will have 

 different motions before and after the collision, which is 

 evidently absurd. And if the gas should be transferred into a 

 different body, whose particles are larger or smaller than the 

 particles of the other body, the temperature and elasticity of the 

 gas will be changed, though both the capacity and temperature 

 of the two containing bodies should be the same. Besides, the 

 temperatures of the gas and of the containing bodies would never 

 be the same, if their particles were unequal. Nor could a gas, 

 constituted of elastic particles, follow the laws of either of the 

 other propositions. 



If any method were known of experimentally determining the 

 ratio of the temperatures of two bodies, we might easily devise 

 ways enough of putting our theory to the test of observation; but 

 since this is not the case, independent of theorems drawn from 

 our principles, we are obliged to search for such consequences 

 as are not under the controul of the ratio, or of the quantity of 

 temperature. The inference drawn in the first cor. to prop. 9 is 

 precisely of this kind, and presents us with a law th^t is easily 

 examined by experiment. Indeed this law was discovered 

 several years ago by MM. Dalton and Gay-Lussac, and has 

 been established by many experiments. It is one of the most 

 important laws, relative to the expansion and contraction of 

 gaseous bodies, that has yet been discovered ; and affords not 



