20 Ladislaus Natauson on the Kinetic Theory 



2)(28 — d) 2 l(d — & t ), where 8 t may be greater or less than S, 

 and denotes a new isothermal constant*. Whether these 

 critical values of the density of N0 2 are similar to the critical 

 densities of chlorine and bromine gases (which, however, were 

 found, not fov p = 0, but at atmospheric pressure), as Ostwald 

 supposes f; or whether the proved deviations from Gibbs's 

 formula are attributable wholly or partly to the imperfect 

 nature of the gas ± — these appear to me difficult questions to 

 decide, inasmuch as there exists no firm basis to work upon. 

 It suffices us, for what follows, to know that Gribbs's equation, 

 with/(/) left undetermined, is always in general agreement 

 with experiment. 



§ 3. Two atoms collide and form a molecule, which lasts 

 for a time t. It is required to know how often this happens 

 during unit time in a given quantity of gas. The interval r 

 may depend on certain variables x, y, . , . , which we need not 

 specify, and in unit time 



Z<f>(x,y y ...)dxdy (1) 



collisions take place between the atoms, in such a manner that 

 the variables lie between the limits 



«# and # + <&e ; y and y + dy ; (2) 



Let us assume that as, ?/,... in general have values lying 

 between the limits 



os Q and x x ; y and y 1 : (3) 



and that Z is the total number of collisions between the atoms 

 during unit time, so that 



JT-- 



4>{x,y,...)dxdy...=l. . . (1) 



Let us further assume that a collision of two atoms which 

 is included in class (2) is followed by the formation of a mole- 

 cule in case #, y, . . . lie between 



£ and fx ; % and ^ j (5) 



(Each of these classes can also be subdivided into further 

 simple ones.) Let us write 



fT'. 



•'Co "lo 



${x,y,...)dxdy...=*r i ... (6) 



* Cf. p. 617 of tlie second paper. 



t Ostwald, Lehrbuch der dig. Chemie, ii. p. 699 (1887). 



t Ostwald, op. cit. ii. p. 734 ; Planck, TVied. Ann. xxxii. p. 484 (1887) ; 

 J. J. Thomson. 'Applications of Dynamics to Physics and Chemistry,' 

 p. 200. * J 



