378 ILLUSTRATIONS OF THE DYNAMICAL THEORY OF GASE& 



If the properties of such a system of bodies are found to correspond to 

 those of gases, an important physical analogy will be established, which may 

 lead to more accurate knowledge of the properties of matter. If experiments 

 on gases are inconsistent with the hypothesis of these propositions, then our 

 theory, though consistent with itself, is proved to be incapable of explaining 

 the phenomena of gases. In either case it is necessary to follow out the 

 consequences of the hypothesis. 



Instead of saying that the particles are hard, spherical, and elastic, we may 

 if we please say that the particles are centres of force, of which the action is 

 insensible except at a certain small distance, when it suddenly appears as a 

 repulsive force of very great intensity. It is evident that either assumption 

 will lead to the same results. For the sake of avoiding the repetition of a. 

 long phrase about these repulsive forces, I shall proceed upon the assumption 

 of perfectly elastic spherical bodies. If we suppose those aggregate molecules 

 which move together to have a bounding surface which is not spherical, then 

 the rotatory motion of the system will store up a certain proportion of the 

 whole via viva, as has been shewn by Clausius, and in this way we may 

 account for the value of the specific heat being greater than on the more 

 simple hypothesis. 



On the Motion and Collision of Perfectly Elastic Spheres. 



Prop. I. Two spheres moving in opposite directions with velocities inversely 

 as their masses strike one another ; to determine their motions after impact. 



Let P and Q be the position of the centres at 

 impact ; AP, BQ the directions and magnitudes of 

 the velocities before impact ; Pa, Qb the same after 

 impact ; then, resolving the velocities parallel and per- 

 pendicular to PQ the line of centres, we find that 

 the velocities parallel to the line of centres are exactly 

 reversed, while those perpendicular to that line are 



unchanged. Compounding these velocities again, we find that the velocity of 

 each ball is the same before and after impact, and that the directions before 

 and after impact lie in the same plane with the line of centres, and make equal 

 angles with it. 



