

Mr. J. C. Maxwell on the Dynamical Theory of Gases. 139 



When, after their mutual action and deflection, the molecules 

 have again reached a distance such that there is no sensible action 

 between them, each will be moving with the same velocity rela- 

 tive to the centre of gravity that it had before the mutual action, 

 but the direction of this relative velocity will be turned through 

 an angle 20 in the plane of the orbit. 



The angle 6 is a function of the relative velocity of the mole- 

 cules and of by the form of the function depending on the nature 

 of the action between the molecules. 



If we suppose the molecules to be bodies, or systems of bodies, 

 capable of rotation, internal vibration, or any form of energy 

 other than simple motion of translation, these results will be 

 modified. The value of 6 and the final velocities of the mole- 

 cules will depend on the amount of internal energy in each 

 molecule before the encounter, and on the particular form of 

 that energy at every instant during the mutual action. We 

 have no means of determining such intricate actions in the pre- 

 sent state of our knowledge of molecules ; so that we must con- 

 tent ourselves with the assumption that the value of 6 is, on an 

 average, the same as for pure centres of force, and that the final 

 velocities differ from the initial velocities only by quantities 

 which may in each collision be neglected, although in a great 

 many encounters the energy of translation and the internal 

 energy of the molecules arrive, by repeated small exchanges, at 

 a final ratio, which we shall suppose to be that of 1 to /3 — 1. 



We may now determine the final velocity of Mj after it has 

 passed beyond the sphere of mutual action between itself and M 2 . 



Let V be the velocity of M 2 relative to M 2 , then the compo- 

 nents of V are 



. . . . fi—& vi-vv 6— &• 



The plane of the orbit is that containing V and b. Let this 

 plane be inclined <£ to a plane containing V and parallel to the 

 axis of x; then, since the direction of V is turned round an 

 angle 20 in the plane of the orbit, while its magnitude remains 

 the same, we may find the value of f, after the encounter. Call- 

 ing it fj, 



^^ + l|W sW I . . (i) 



There will be similar expressions for the components of the 

 final velocity of Mj in the other coordinate directions. 



If we know the initial positions and velocities of M x and M 2 , 

 we can determine V the velocity of Mj relative to M 2 , b the 

 shortest distance between Mj and M 2 if they had continued to 



