of the Phenomena of Dissociation in Gases. 21 



then we can say that in unit time otZ molecules are created, 

 and -or is the ratio of the number of associating collisions to 

 the total number. Now let us suppose that the gas has 

 reached a state of equilibrium as regards dissociation. During 

 time t, 



tZ<£ (x,y,...) dxdy (7) 



molecules of class (2) will be formed, and they will each last 

 for a time equal to t, or differing from it by an infinitely 

 small quantity. Therefore there will exist at any time as 

 many molecules of class (2) as are given by (7) *. 

 Hence the total number N 2 of existing molecules is 



N 2 = zf l y\..r4>(x,y-...)da!dt,... 

 • T<f>(x,y...)dxdy... 



> (8) 



= OT Z<^» 



it 



=^zs, 



. . . <p (x, y, . . . ) dx dy . . . 



'So Jvo 



where S denotes the mean value of the interval during which 

 a molecule remains intact. 



The conditions which are necessary in order that a molecule 

 should be formed when two atoms collide are very different, 

 according to the assumptions made respecting the mutual 

 actions of the atoms. As hypothesis (a) we shall designate 

 every assumption, according to which, as the result of a col- 

 lision of two atoms, two opposite cases arise : either the 

 collision is "associating," the motion of the atom becoming a 

 stationary one, and a molecule is formed ; or else " normal/' 

 in which case the atoms rebound immediately and of their 

 own accord, as happens in the collision of molecules in 

 common gases. With this hypothesis (a) we must also 

 assume at the same time, that a molecule which has once been 

 formed cannot be decomposed of itself, but only by the action 

 of external force. As hypothesis (/3) we shall, on the con- 

 trary, designate any assumption in which the above distinction 

 is wanting : two colliding atoms will sooner or later leave 

 each other ; only the interval during which they form a 

 system can, according to the circumstances of the collision, 

 be different in different cases. There is then no sharp dis- 



* The proposition made use of here, that " there exist at any time as 

 many molecules, belonging- to a given class, as are formed during the time 

 of existence of a molecule (in case all molecules of that class exist for an 

 equal time),'' is often made use of in the kinetic theory. Cf, Wied, Ann. 

 xxxiii. p. 683 (1888). 



