1895-96.] Prof. Tait on Clerk-Maxwell's Lav: of Distribution. 127 
solution, for it is easy to see that collisions do not alter it* There- 
fore it is the solution. 
5. M. Bertrand treats the above result of Clerk- Maxwell’s to the 
following sweeping condemnation : — 
“ II y aurait indulgence a reprocher a cette formule trop peu de 
rigueur : les habitudes de la Geometrie autorisent a la declarer tout 
simplement absurde.” 
Comment on this would be superfluous. 
But it is easy to see how M. Bertrand has been led into this 
position. The following is, according to his information, the 
problem as proposed, and solved, by Maxwell : — 
“ Les molecules d’une masse gazeuse, fitant en nombre immense 
et considere comme infini, sont animees de vitesses inconnues. On 
ne sait rien sur les conditions initiales et sur les actions perturba- 
trices qui s’exercent entre elles et sur elles. 
Determiner le rapport du nombre total des molecules au nombre 
des celles dont la vitesse est comprise entre des limites donnees. 
On n’admet rien de plus, sinon que, par l’absence de toute ordon- 
nance reguliere, tout est pareil dans toutes les directions.” 
No wonder M. Bertrand says that this reminds one of the question 
of finding the age of the captain from the size of his vessel ! 
The real cause for wonder is that M. Bertrand, who must be 
perfectly aware that strong common-sense was as prominent a 
characteristic of Maxwell’s intellect as was brilliant, and often 
daring, originality, could believe him capable of propounding such 
manifest nonsense. 
6. What Maxwell did propose, and solve, was a very different 
problem indeed. Here are his words (Pliil. Mag. xix. (1860), 
p. 22) : — 
“ Prop. IV. To find the average number of particles whose 
velocities lie between given limits, after a great number of col- 
lisions among a great number of equal particles.” 
He had already pointed out that the particles are regarded as 
spherical and perfectly elastic ; and that, though collisions are 
* With this particular form of f{x) not only is f{x)f(y)f{z) an Invariant in 
the usual sense of being independent of the rectangular system of axes em- 
ployed ; but its separate factors are unaltered by a collision if one of these 
axes be taken parallel to the line of centres at impact. 
