88 REPORT— 1894. 



above in Section I., gives a long and laborious investigation relating to a, 

 free system of particles with constant linear and angular momenta ; ' bub 

 the formulae, which are very long and complicated, do not appear to be 

 applicable to the present problem, since they take no account of collisions 

 between the various systems. 



Case III. — When each molecule has an axis of symmetry the angular 

 velocity Cl^ or W3 about this axis is constant and unaltered by collisions, 

 provided the molecules be regarded as perfectly smooth. Hence the law 

 of distribution is independent of O3 and W3, and these angular velocities 

 may be distributed according to any law. This is not inconsistent with 

 general conditions, for the collision formuhe Vl^'=-Vl^ and w.^=zu)^ show 

 that Yf-=Y'f' is satisfied by any functions whatever of W3, ^3. 



This case has already been alluded to in § 37 as furnisliing an exception 

 to the law obtained for lop-sided spheres. But its chief interest lies in 

 the fact, pointed out by Boltzmann,^ that since partition of energy only 

 takes place among live of its six degrees of freedom, tlie ratio of the 

 two specific heats 



l+-=l + -^ = l-4 .... (39) 

 m b 



agreeing closely with the value found for air and most gases. 



46. Except in the above cases and the still simpler case of smooth 

 elastic spheres whose cm. is at the centre, it will, I think, be found 

 impossible to devise any form of riyld bodies in which the conditions 

 of permanency are satisfied for all geometrically possible collisions other- 

 wise than by the Boltzmann-Maxwell distribution. For example, the 

 alternative distributions for non-colliding rigid bodies worked out in 

 Appendix A cannot remain permanent unless the surfaces of the bodies 

 are spherical, so that the line of collision always passes through their 

 CM. [This I have roughly verified by a process of ' exhaustion,' the 

 details of which are uninteresting.] 



In his aforementioned paper on the nature of gas molecules, Boltz- 

 mann considers the number of degrees of freedom of molecules generally 

 in relation to the ratio of their specific heats, and arrives at the following: 

 conclusion : tliat ' the entire aggregate which forms a single gas molecule, 

 and which can consist, not only of ponderable atoms, but also of ether 

 atoms bound with them, probably behaves in its progressive motion and 

 its collisions with other molecules neai'ly like a rigid body.' 



The case of a polyatomic molecule, whose atoms are capable of vibrating 

 relative to one another, affords an interesting field for investigation and 

 speculation. Is the Boltzmann-Maxwell distribution still unique, or do 

 other permanent distributions exist in which tlie kinetic energy is unequally 

 divided between the momentoids 1 



Steady States under Permanent Disturbing Influence. 



47. The important and highly interesting applications of the Kinetic 

 Theory to disturbed states of a gas in which, by the action of external forces, 

 a steady state differing from the Boltzmann-Maxwell distribution is main- 

 tained fall outside the scope of this Report. These include the problems 



' Camb. Phil. Trans., 1879. 



^ ' Deber die Natuv der Gasmolekiile,' Sitzh. der h. Wiener Akad., Ixxiv. (ii..), 

 1876. He mentions this also in liis paper translated in the Phil. Mag., March 1893. 



