82 Sir W. Thomson. On the Maxwell-Boltzmann [June 11, 



to the vihration excited in it by the vibration of the shell, until nearly 

 all the initial energy of the tuning fork is thus spent. 



7. Going back to the double molecules of 5, suppose the internal 

 globule to be so connected by massless springs with the shell that the 

 globule is urged towards the centre of the shell with a force simply 

 proportional to the distance between the centres of the two. This 

 arrangement, which I gave in my Baltimore Lectures, in 1884, as an 

 illustration for vibratory molecules embedded in ether, would be 

 equivalent to two masses connected by a massless spring, if we had 

 only motions in one line to consider; but it has the advantage of 

 being perfectly isotropic, and giving for all motions parallel to any 

 fixed line exactly the same result as if there were no motion perpen- 

 dicular to it. When a pair of masses connected by a spring strikes a 

 fixed obstacle or a movable body, with the line of their centres not 

 exactly perpendicular to the tangent plane of contact, it is caused to 

 rotate. No such complication affects our isotropic doublet. An 

 assemblage of such doublets being given moving about within a 

 rigid enclosing surface, will the ultimate statistics be, for each 

 doublet,* equal average kinetic energies of motion of centre of inertia, 

 and of relative motion of the two constituents ? 



* This implies equal average kinetic energies of the two constituents ; and, con- 

 versely, equal average kinetic energies of the two constituents, except in the case of 

 their masses being equal, implies the equality stated in the text. Let u, u' be abso- 

 lute component velocities of two masses, m, m', perpendicular to a fixed plane ; 

 II the corresponding component velocity of their centre of inertia; and r that 

 of their mutual relative motion. We have 



.hence 



(2) . 



Now suppose the time-average of Ur to be zero. In every case in which this is 

 so we have, by (2), 



Time-av. tmtf-mW = (m-m f ) x Time-av. {u 2 - . mm ' r<2 1 . . . (3) 



I (m + m') 2 J 



Hence in any case in which 



Time-av. mu? = Time-av. m'u' 2 (4) 



we have (m-m 1 ) x Time-av. |u 2 --r^-^| = o (5), 



and therefore, except when m = m', we must have 



Time-av. (m + m') U 2 = Time-av. mm ' r \ ( 6 ) , 



m + m 



which proves the proposition, because, as we readily see from (1), % mm' r* I (m + m') 

 is, in every case, the kinetic energy of the relative motions, -U, and U-'. 







