Kinetic Theory of Gas. 371 



is 3/5 of the whole of that energy of the mechanical model 

 which comes under the notice of the theorem. The rotations 

 (o 2 and 6) 3 are Ba events, and their energy } viz. : — 



Average value of 2JB(o> 2 9 + ^>3 2 ) 



is 2/5 of the energy dealt with by the theorem. The rotation 

 cji is a Be event, which can be kept outside the theorem. In 

 it, accordingly, any amount of energy may reside. 



Another instructive mechanical illustration is constructed 

 by considering each molecule as a rigid ellipsoid of one 

 uniform density surrounded by a rigid envelope of another 

 uniform density, extending from the surface of the ellipsoid 

 to the smooth surface of an outer concentric sphere (see 

 Bryan, loc. cit.). Such a complex molecule may represent a 

 diatomic molecule with only three of its degrees of freedom 

 operated upon during collisions. Here the energy of the 

 molecule is 



T=^[M^ 2 + v 2 + io 2 )+A< + Bft» 2 2 + Cftj 3 2 ], 



whereas the part concerned in the theorem is only 



T'=|M(m 2 + ^+«; 2 ), 



since the external surface being a smooth rigid sphere round 

 the centre of inertia, the collisions cannot set up rotations. 



In this case u, v, and id are A events ; and, on the average, 

 divide equally among themselves the share of energy coming 

 to this molecule under the theorem. At the same time the 

 rotations a> l9 a> 2 , oi B are Be events, and may be going forward, 

 subject only to the equations of the rotation of a rigid body 

 round its centre of inertia, viz. : — 



T'^KA^ + B^ + C^), 

 G =A 2 o> 1 2 + BW + CW. 



Their energy T" may, accordingly, be of any amount in 

 each molecule separately. 



We have hitherto had only A, Ba, and Be motions in our 

 illustrative models. Be events are of little practical interest ; 

 whereas the study of B£ events is of much use, since they are 

 probably present in large amount in actual gases. It is easy 

 to modify our mechanical illustration so as to introduce events 

 of this class. It may be done in either of the models we have 

 employed by imagining the surface to be roughened (either 

 by a small amount of friction or in the sense of being covered 

 with slight frictionless elevations and depressions), and by 



2 C2 



