ILLUSTRATIONS OF THE DYNAMICAL THEORY OF GASES. 409 



three axes is the same in all the systems, and equal to the average vis viva 

 of rotation about each of the three principal axes of each particle. 



Adding the -vires vivce with respect to the other axes, we find that the 

 whole vis viva of translation is equal to that of rotation in each system of 

 particles, and is also the same for different systems, as was proved in Prop. VI. 



This result (which is true, however nearly the bodies approach the spherical 

 form, provided the motion of rotation is at all affected by the collisions) seems 

 decisive against the unqualified acceptation of the hypothesis that gases are such 

 systems of hard elastic particles. For the ascertained fact that y, the ratio of 

 the specific heat at constant pressure to that at constant volume, is equal to 

 T408, requires that the ratio of the whole vis viva to the vis viva of translation 

 should be 





whereas, according to our hypothesis, ^8 = 2. 



We have now followed the mathematical theory of the collisions of hard 

 elastic particles through various cases, in which there seems to be an analogy 

 with the phenomena of gases. We have deduced, as others have done already, 

 the relations of pressure, temperature, and density of a single gas. We have 

 also proved that when two different gases act freely on each other (that is, when 

 at the same temperature), the mass of the single particles of each is inversely 

 proportional to the square of the molecular velocity ; and therefore, at equal 

 temperature and pressure, the number of particles in unit of volume is the same. 



We then offered an explanation of the internal friction of gases, and deduced 

 from experiments a value of the mean length of path of a particle between 

 successive collisions. 



We have applied the theory to the law of diffusion of gases, and, from an 

 experiment on olefiant gas, we have deduced a value of the length of path not 

 very different from that deduced from experiments on friction. 



Using this value of the length of path between collisions, we found that the 

 resistance of air to the conduction of heat is 10,000,000 times that of copper, a 

 result in accordance with experience. 



Finally, by establishing a necessary relation between the motions of trans- 

 lation and rotation of all particles not spherical, we proved that a system of 

 such particles could not possibly satisfy the known relation between the two 

 specific heats of all gases. 



VOL. I. 52 



