11* MAXWELL'S LAW 373 



11*. Mechanical Conditions 



The correctness of the conclusion that all the states of distri- / 

 bution considered occur with equal probability we see still more 

 clearly when we remember that a change of condition does not 

 occur as a consequence of chance, but that each alteration of the 

 molecular motions takes place in accordance with fixed and 

 invariable mechanical laws. Each distribution of speed that at any 

 moment exists was the necessary consequence of that which 

 ceded it, and from it in its turn necessarily arises a new state 

 with a distribution that is by no means arbitrary, but completely 

 determined. 



Before, therefore, the final state, which seems to the observer 

 one of equilibrium, that does not alter with the time, is arrived at 

 in a mass of gas left to itself, the function which expresses the 

 probability of a given value of the~speecl continual}/ changes its 

 nature according to the fixed laws of mechanics./ But when the 

 final state is attained the form of this function remains always the 

 same ; only the arguments the values of the components then 

 alter at each encounter, this alteration also being subject to the 

 general laws of mechanics. Each system of simultaneous values 

 of the speeds appears therefore as often as that from which 

 arises and as that which results from it ; in other words, the pro- 

 bability of occurrence of all these systems is the same. 



The laws from which this conclusion is the necessary con- 

 sequence are contained in the theorems which deal with the 

 mechanicsjoLsy stems of free particles in motion. For our prob- 

 lem, the establishment of the law of distribution of the energy 

 and speed, only those theorems come into consideration which - 

 contain and determine these magnitudes alone. These theorems 

 are 



1. The principle of the conservation of energy ; ^~ 



2. The principle of the conservation of the motion of the 

 centroid. 



Further hypotheses are not needed for the present ; indeed both ( 

 these theorems depend on a single common basis, ifwe may assume 

 that the action exerted by one particle on another is equal to the 

 reaction which at each moment it experiences itself from the other 

 in the reverse direction. 



In respect to the application of these theorems to our proof, 



