344 Mr, Herapaih on the Cause$, Laws, and principal [May, 



this being the same, the motion is the same.' But the motion, 

 quantity of gas, and capacity, being the same, the elasticity must 

 be the same. 



Scholium, 



This theorem and its cor. agree with the opinion of philoso- 

 phers respecting the elasticity of gaseous bodies, though I am 

 not aware that they have ever been made the subject of direct 

 experiment. Indeed it seems to have been taken for granted 

 that wherever the temperatures, spaces occupied, gases, and 

 quantities of gas, were the same, the elasticities were the same ; 

 but it would be worth while to be more certain of it. An expe- 

 riment to settle this point, taking every circumstance into consi- 

 deration, would, perhaps, require as much care and skill as 

 almost any of those that have been made on gases. 



Prop. VII. 



If a given portion of a fluid gas, composed of particles 

 mutually impinging on one another and the sides of the contain- 

 ing body, in the manner that has been described, has its temper- 

 ature the same ; and if the particles be indefinitely small, its 

 elastic force, under different compressions, is reciprocally projpor- 

 tional to the space it occupies. 



Let us suppose that equal portions of the same gas be enclosed 

 in two vessels of unequal capacity. Then, by the last Prop, it 

 is immaterial whether these vessels be of the same or of different 

 figures ; the difference of figures would have no influence upon 

 the ratio of the elasticities ; but, for the sake of simplicity, we 

 will suppose the two figures similar. Now because the only 

 change that is supposed to take place is in the space which the 

 gas occupies, the motions and coUisions of a particle in the one 

 will be similar to those of a corresponding particle in the other ; 

 and the temperature, that is, in this case, the velocity being the 

 same in each, the numbers of revolutions that two corresponding 

 particles in the two media make in a given time must be 

 inversely proportional to the paths the particles describe; that is, 

 these paths being alike and described with equal velocities in 

 the inverse subtriplicate ratio of the spaces occupied by the 

 equal portions of gases. But because the elasticity of a gas is 

 proportional to the action of its particles against a given portion 

 of the surface of the containing body, the ratio of the elastic 

 forces, arising from the repeated actions of equal numbers of cor- 

 responding particles in the two media, will likewise, their 

 velocities being the same in both media, be inversely as the 

 subtriplicate of the spaces occupied. And if we conceive the 

 two gases to be divided into strata, parallel to the sides of the 

 bodies on which the elastic forces are measured, and of one, two, 

 or any number of particles thick, it is manifest, since the motions 

 of the particles are alike in each medium, that if the elasticity 



