92 The Law of Distribution [CH. v 



uncertainty may be represented by an infinitesimally small probability of 

 error: it may, in the terminology previously used, be "infinitely probable" 

 that the result is true. 



We have found that the^ assumption of molecular chaos, on the other 

 hand, leads to a definite certain result, and not merely to one which is 

 infinitely probable. Incidentally, this circumstance enables us to trace out 

 some of the inner significance of this assumption. We see at once that the 

 assumption rests on the supposition that the systems with which it deals 

 have at every instant a definite statistical specification. It therefore just 

 excludes those systems, an infinitesimal fraction of the whole, which wander 

 away from the statistical specification obeyed by the majority. In other 

 words, it implies that any system under discussion has the statistical 

 specification of the majority, and therefore naturally leads to a certain result 

 instead of leading merely to one of infinite probability. 



As regards Maxwell's treatment of equipartition, enough has perhaps been 

 said to shew that in dealing statistically with a gas, we can never arrive at 

 absolute certainty : it is therefore impossible to reach any definite result 

 unless a loophole of escape from absolute certainty has been introduced into 

 the premises on which we work. 



MECHANICAL ILLUSTRATION OF EQUIPARTITION. 



105. It may be useful to illustrate the abstract results which have been 

 obtained in this chapter by a concrete mechanical example. 



Let us again suppose, as in Chapter II., that the molecules of a gas are 

 hard, rigid spheres ; but, in order to get more than the three degrees of freedom 

 represented by the motion of translation of a molecule, let us also suppose 

 that the centre of gravity of these spheres does not coincide with their 

 geometricaljcentre, so_that rotations are set upjby collisions. 



Each molecule possesses an axis of symmetry, namely, the line joining 

 the centre of gravity to the centre of figure. Let us take any two other 

 axes, fixed in the molecule in the plane perpendicular to the axis of 

 symmetry, and let us denote the components of angular velocity about these 

 two axes by TI, or 2 , and that about the axis of symmetry by iy 3 . If the 

 corresponding radii of gyration are k, k, k', the kinetic energy L will be 

 given by 



2L = ra (w 2 + v 2 + w 2 ) + mk 2 (^ + w 2 2 ) + raA/ 2 r 3 2 . 



It is clear at the outset that the velocity -sr 3 is peculiar in that its value 

 cannot be changed by collisions. It follows, then, that the system, as at 

 present specified, does not satisfy Maxwell's condition of continuity of path. 

 Or, again, there are other constants besides the energy, namely, the w 8 co- 

 ordinates of the various molecules, which remain constant throughout the 



