280 G. H. BRYAN. 



and frora tins it is reqiiired to investigate the distribution of velocities 

 in ovder tliat, the state of the sjstem may be stationary. 



The pi'obability that the coordinates of the molécules of a body shall 

 lie betweeu given liraits is of course a function of the coutrollable 

 coordinates, such as the volume of the body, and further dépends on 

 the state of the body, its chemical composition, crystalline structure, 

 and so forth. The distribution of coordinates at any instant is not theo- 

 retically really independent of the distribution of velocities at that 

 instant, and we may imagine that with the aid of Ma.xvvell's „demons" 

 it would be possible to utilise the relation betweeu the two distributions 

 to obtain perpétuai availability. As however it is physically impossible 

 to control or observe the motions of individual molécules, we may 

 assume that the proper measure of the probable distribution of coordi- 

 nates, estimated according to the best of our knowledge of the state of 

 a body is one which does not dépend on the motions of tlie molécules 

 and remains independent of the time so long as the energy and coutrol- 

 lable coordinates of the system are constant. This assumption is couve- 

 nieut for matheraatical calculation but the properties of Systems in 

 which it does not to hold good are also capable of theoretical investi- 

 gation and discussion. 



The method which it is now proposed to apply to this problem cou- 

 sists in obtaining expressions for the .srcoNfl differential coefficients with 

 respect to the time of squares and products of velocities such as enter 

 into the expression for the kinetic energy of the system. I propose to 

 call thèse second differential coefficients the accélérations of the energy 

 components in question from their analogy with the accélérations repre- 

 sented by the second dilferential coefficients of the coordinates. This 

 nomenclature;, I find, makes it casier to think clearly of the effects under 

 considération. From the expressions thus obtained, équations of energy 

 equilibrium are found, as well as conditions of stability for the statio- 

 nary state, and thèse bave so close au analogy with the température 

 condition of thermodynamies as to suggest that they may possibly 

 afford the true due to the partition of energy problem, while the limi- 

 tations re(|uired by thèse conditions may not improbably explain the 

 failure of Maxwell's .Law of Partition of Energy to account for many 

 physical phenomeua. The method has the further advantage of sugges- 

 ting a dynamical basis for the phenomeua of Irréversibilité/ , which is 

 not incompatible with the assumption that any motion of the sys- 



