ENERC4Y ACCELEIlATIONSj A STIIDY IN ENERGY, &C. 393 



(5) We have seen tliat tlie law of distribution of coordinates must 

 be siKîli that certain conditions are satisiied in order that a stationary 

 distribution of squares and products of velocities may be possible, 

 Moreover certain other conditions, which raay or may not be identical 

 with thèse, must be satisfied in order that the distribution may be stable. 

 Thèse properties naturally suggest a physical interprétation in tlie 

 phenomena of change of state. 



If a distribution of energy is unstable, and a slight disturbance be 

 given to the System, which causes one portion of it to have slightly less 

 tlian its equilibrium share of energy and another portion slightly more, 

 then from the gênerai properties of unstable equilibrium we should 

 iufer that energy will be accelerated from the parts with lesser to the 

 parts with greater energy, thus increasing the unequiil distribution of 

 the energy. jMow tliis is very like what happens in the phenomena of 

 liquéfaction of a gas or solidification of a liquid, when energy in the 

 form of latent beat passes from the portion of the substance in the lower 

 state to that in the higher state. lustability may also lead to an iu- 

 crease in the mean kinetic energy of the system at the expense of the 

 potential energy or vice verset and this may possibly find an interpré- 

 tation in certain cheraical phenomena, 



(6) In the simple examples already considered Ave have been led to 

 a study of the mean values of products of velocity components which 

 do not enter into the expression for the kinetic energy, and we have 

 found that thèse mean products do not necessarily vanish. This resuit 

 is practically identical with that put forward by Mr. Burbury in many 

 récent papers, and in particular in his treatise on the Kinetic Theory 

 of Gases, in which lie iinds that the velocities of neighbouring molécules 

 become correlated. In the most gênerai case of 7i particles each having 

 tliree degrees of freedom, there will be 3?^ velocity components, and if 

 the corrélation is of the most gênerai character possible we shall have 

 to examine the mean values of the \ 3// (3;/ -{-1) squares and j^roducts 

 of velocities; the number ^ 3;^ (3;; -|- 1) will therefore represent the 

 number of rows and columns which will enter into the déterminants 

 required for the investigation. Trom this will be readily realised the 

 difficulty of a gênerai investigation, or indeed of the investigation of 

 any but the simplest cases. 



(7) On the other hand even if we pass from the case of a system of 

 particles to a dvnamical system of the most gênerai character satisfyiiig 



