1891.] Doctrine regarding Distribution of Energy. 83 



8. If we try to answer this question synthetically, we find a com- 

 plex and troublesome problem in the details of all but the very simplest 

 case of collision which can occur, which is direct collision between two 

 not previously vibrating doublets, or any collision of one not previously 

 vibrating doublet against a fixed plane. In this case, if the masses 

 of globule and shell are equal, a complete collision consists of two 

 impacts at an interval of time equal to half the period of free vibration 

 of the doublet, and after the second impact there is separation without 

 vibration, just as if we had had single spheres instead of the doublets. 

 But in oblique collision between two not previously vibrating doublets, 

 even if the masses of shell and globule are equal, we have a somewhat 

 troublesome problem to find the interval between the two impacts, 

 when there are two, and to find the final resulting vibration. When 

 the component relative motion parallel to the tangent plane of the first 

 impact exceeds a certain value depending on the radius of the outer 

 surface of the shell, the period of free vibration of the doublets, and 

 the relative velocity of approach ; there is no second impact, and the 

 doublets separate with no relative velocity perpendicular to the tangent 

 plane, but each with the energy of that component of its previous motion 

 converted into vibrational energy. When the mass of the shell is much 

 smaller than the mass of the interior globule, almost every collision 

 will consist of a large number of impacts. It seems exceedingly 

 difficult to find how to calculate true statistics of these chattering 

 collisions, and arrive at sound conclusions as to the ultimate distribu- 

 tion of energy in any of the very simplest cases other than 

 Maxwell's original case of 3860; bnt, if the Boltzmann-Maxwell 

 generalised doctrine is true, we ought to be able to see its truth as 

 essential, with special clearness in the simplest cases, even without 

 going through the full problem presented by the details. T can find 

 nothing in Maxwell's latest article on the subject (' Camb. Phil. 

 Trans.,' May 6, 1878), or in any of his previous papers, proving an 

 affirmative answer to the question of 7. 



9. Going back to 6, let the globules be initially distributed as 

 nearly as may be homogeneously through the hollow ; let each globule 

 be connected with neighbours by massless springs; and let all the 

 globules which are near the inner surface of the shell be connected 

 with it also by massless springs. Or let any number of smaller 

 shells be enclosed within our outer shell, and connected by massless 

 springs as represented by the accompanying diagram, taken from a 

 reprint of my Baltimore lectures now in progress. Let two such 

 outer shells, given at rest with their systems of globules in equi- 

 librium within them, be connected by massless springs, and be started 

 in motion, as were the shells of 6. There will not now be the , 

 great loss of energy from the vibration of the shells which there was 

 in 6. On the contrary, the ultimate average kinetic energy of the 



G 2 



