of the Phenomena of Dissociation in Gases. 25 



and not because Maxwell's law makes them equal, (ii.) The 

 energy, of the molecules formed may, on the contrary, be 

 different from that of the free atoms, and then, according to 

 Maxwell's law, an interchange of energy will take place 

 between the molecules and atoms ; every molecule will tend 

 to regulate its velocity according to Maxwell's law. This 

 phenomenon happens during the collisions of the molecule ; 

 after a few collisions the molecule will approximately fulfil 

 the conditions of Maxwell's law. If the molecule does not 

 last longer than the time requisite for this process of equaliza- 

 tion of energy, or if it lasts a shorter time, the equalization 

 can only take place in part, and only a part of the difference 

 of energy will be equalized. A stationary condition may 

 therefore arise, in which the ratio of the molecular and atomic 

 energies has a value which is intermediate between unity and 

 the value obtained from the energy of the molecules formed 

 and that of the atoms. 



Now I hope to be able to prove that the case (i.) corre- 

 sponds to the hypothesis (/3) of § 3, while case (ii.) corresponds 

 to the hypothesis (a) of the same section. Let us assume that 

 a is the most probable velocity of the atoms, so that J ma 2 =E l . 

 The velocity of the progressive movement of a molecule, 

 which is formed oat of two colliding atoms, being Y, let us 

 choose V as one of the independent variables in the collision 

 of two atoms. According to the rules laid down in § 3 of my 

 paper " On the Kinetic Theory of Imperfect Gases " (loc. cit.) 7 

 there will occur in unit time, 



^l^e-^\{ X ,y,...)d\TcUdy (1) 



collisions between atoms, in which the velocity of the centre 

 of gravity of each lies between V and Y + dV; and the 

 remaining variables also lie between certain infinitely close 

 limits, which we do not need to specify. In (1) N, is, 

 as before, the number of atoms, v the volume, R x the charac- 

 teristic distance determining whether a collision will or will not 

 ensue between two atoms. We shall assume that in every 

 collision of class (i.) a molecule is formed. (According to 

 hypothesis (/3) this is always the case ; but on the (a) hypothesis 

 the variables sc } y, . . . must satisfy certain conditions.) There 

 exist, then, at any time, 



^^ t W 2V2 / a2 % 0r, y,...)dYdxdy... . (2) 



molecules of the class considered, whose duration is t. The 



