78 PROFESSOR TAIT ON THE 



features, besides too great conciseness, in respect of which it seems objec- 

 tionable, are : — 



((/) He assumes that the transference of energy from one system to the other 

 can be calculated from the results of a single impact between particles, one 

 from each system, each having the average translational energy of its system. 



Thus (so far as this step is concerned) the distribution of energy in each 

 system may be any whatever. 



(b) In this typical impact the velocities of the impinging spheres are taken 

 as at right angles to one another, so that the relative speed may be that of 

 mean square as between the particles of the two systems. The result obtained 

 is fallacious, because in general the directions of motion after impact are found 

 not to be at right angles to one another, as they would certainly be (on account 

 of the perfect reversibility of the motions) were this really a typical impact. 



(c) Clerk-Maxwell proceeds as if every particle of one system impinged 

 upon one of the other system at each stage of the process — i.e., he calculates 

 the transference of energy as if each pair of particles, one from each system, 

 had simultaneously a typical impact. This neglect of the immensely greater 

 number of particles which either had no impact, or impinged on others of their 

 own group, makes the calculated rate of equalisation far too rapid. 



(d) Attention is not called to the fact that impacts between particles are 

 numerous in proportion to their relative speed, nor is this consideration intro- 

 duced in the calculations. 



(e) Throughout the investigation each step of the process of averaging is 

 performed (as a rule) before the expressions are ripe for it. 



18. In seeking for a proof of Maxwell's Theorem it seems to be absolutely 

 essential to the application of the statistical method to premise : — 



(A) That the particles of the two systems are thoroughly mixed. 



(B) That in any region containing a very large number of particles, the 

 particles of each kind separately acquire and maintain the error-law distribu- 

 tion of speeds — i.e., each set will ultimately be in the " special " state. The 

 disturbances of this arrangement produced in either system by impacts on 

 members of the other are regarded as being promptly repaired by means of the 

 internal collisions in the system itself. This is the sole task assigned to these 

 internal collisions. We assume that they accomplish it, so we need not further 

 allude to them. 



[The warrant for these assumptions is to be sought as in § 4 ; and in the 

 fact that only a small fraction of the whole particles are at any instant in 

 collision; i.e., that each particle advances, on the average, through a consider- 

 able multiple of its diameter before it encounters another.] 



(C) That there is perfectly free access for collision between each pair of 

 particles, whether of the same or of different systems ; and that, in the mixture, 



