294 G. H. BRYAN. ENERGY ACCELERATIONS, A STUDY, &C. 



Lagrange's équations it is always tlieofeticaUy possible to write clown 

 expressions for tlie accélérations of the squares and products of tlie 

 generalised velocities, or moraenta, or both. 



If tlien the etlier be assumed to be amenable to tlie fuudaraental 

 équations of dynamics tlie doctrine of energy accélérations enables us 

 tlieoretically to discuss tlie partition of energy and corrélation existing 

 in a stationary state between tlie molécules and tlie etlier. 



(8) If we pass from tlie case of finite intermolecular forces to the 

 case of a system of colliding molécules modifications will hâve to be 

 niade in the équations similar to tliose made in ordinary dynamics in 

 passing from a system of finite forces to the limiting case of impulsive 

 forces. Tliis will bring us back to the ordinary methods of the Kinetic 

 Theory of Gases. 



The theory put forward in the présent paper is of course of a so- 

 mewhat tentative character, and it must be left for future investigation 

 to deal with its applications to more complicated Systems approaching 

 more nearly to the Systems with wliicli we hâve to deal in molecular 

 physics. But I cannot help thinking that the présent method niay help 

 to clear up many of the difiiculties associated with dynamical inter- 

 prétations of thermal phenomena. 



If Personal opinions are of any use in such discussions_, I can only 

 say that for some years jjast the problem of accouuting for irréversible 

 phenomena on dynamical principles lias seemed to me to be of in- 

 superable diificultyj now the main difficulty appears practically removed 

 and I find it perfectly easy to foriii a clear mental conception of a 

 dynamical system reproducing the irréversible lieat properties of matter. 



The study of energy accélérations cannot fail to lead to interesting 

 results in connection with any attempts that may be made to formulate 

 kinetic théories of solids and liquids corresponding to the Kinetic 

 Theory of Gases, or to account for divergences from Maxwell's Law 

 of Partition of Energy between the degrees of freedom of a polyatomic 

 ffas or between the molécules of a a;as and the ether. 



&' 



Bangor, August. 1900. 



