34 Lord Kelvin on the 



Single particle bounding from corrugated floor (semicircular 

 hollows), 143 flights : — 



V — U f= +'197 for isochronous sinusoidal flights. 

 y_j_XJ L = + '136 for gravitational parabolic „ 



Rotator of two equal masses, 110 flights : — 



V — R f = — *179 for isochronous sinusoidal flights. 

 y _}_ R [_ = — *150 for gravitational parabolic „ 



Biassed ball, 400 flights :— 



V-R f= + *025 for isochronous sinusoidal flights. 



5/ 



V + R L = "~ 'Q14: for gravitational parabolic „ 



The smallness of the deviation of the last two results from 

 what the Boltzmann-Maxwell doctrine makes them, is very 

 remarkable when we compare it with the 15 per cent, which 

 we have found (§ 43 above) for the biassed ball bounding free 

 from force, to and fro between two parallel planes. 



§ 50. The last case of partition of energy which we have 

 worked out statistically, relates to an impactual problem 

 belonging partly to Class I., § 28, and partly to Class II. 

 It was designed as a nearer approach to practical application 

 in thermodynamics than any of those hitherto described. It 

 is, in fact, a one-dimensional illustration of the kinetic theory 

 of gases. Suppose a row of a vast number of atoms, of equal 

 masses, to be allowed freedom to move only in a straight line 

 between fixed bounding planes L and K. Let P the atom 

 next K be caged between it and a parallel plane C, at a 

 distance from it very small in comparison with the average 

 of the free paths of the other particles ; and let Q, the atom 

 next to P, be perfectly free to cross the cage-front C, without 

 experiencing force from it. Thus, while Q gets freely into 

 the cage to strike P, P cannot follow it out beyond the cage- 

 front. The atoms being all equal, every simple impact would 

 produce merely an interchange of velocities between the 

 colliding atoms, and no new velocity could be introduced, if 

 the atoms were perfectly hard (§16 above), because this 

 implies that no three can be in collision at the same time. 

 I do not, however, limit the present investigation to perfectly 

 hard atoms. But, to simplify our calculations, we shall 

 suppose P and Q to be infinitely hard. All the other 

 atoms we shall suppose to have the property defined in § 21 

 above. They may pass through one another in a simple 

 collision, and go asunder each with its previous velocity 

 unaltered, if the differential velocity be sufficiently great ; 



