36 THE DYNAMICAL THEORY OF OASES. 



ilicular will be b, and the plane including b and the direction of relative motion 

 will bo the plane of the orbits about the centre of gravity. 



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 relative 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 is a function of the relative velocity of the molecules and of 

 It, 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 

 rutation, 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 

 <>t' the molecules 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 present state of our knowledge of molecules, so that we must 

 content ourselves with the assumption that the value of 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 ft 1. 



We may now determine the final velocity of M, after it has passed beyond 

 the sphere of mutual action between itself and M t . 



Let V be the velocity of J/, relative to M t , then the components of V are 



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. Calling it ',, 



~ sn * cos 



