22 Ladislaus Natanson on the Kinetic Theory 



tinction between a collision and the formation of a molecule ; 

 during the time of collision the atoms form a molecule. 

 Every collision is then an " associating " one, every molecule 

 nrnst"exist for a certain time and then decompose of itself. 



In order to bring calculation to bear on both assumptions, 

 let us consider a new mean value of t, namely 0, which we 

 define in the following manner : — 



£)-< Jx Jy . . (9) 



\ \ ...<j>(x,y,-..)dxdy... 



= <BT$ (10) 



Equation (1.0) will be found on remembering the definition 

 of tsr and also equation (4), and considering the condition that 

 r vanishes outside the limits f an( i f u ^o an d Vu & c - 1 so that 



j y y \..T<b{x,y,...)dxdy... = \ 't \.. 



4>(x 9 y,...)dxdy. 



From (10) it follows that 



N 2 = Z.6> (12) 



According to the (/?) hypothesis, 6 = § and ot = 1 ; according 

 to the (a) hypothesis, < ■&, because in the formation of S all 

 the molecules really formed must be taken into account ; but 

 in that of every collision, associating and normal, must be 

 reckoned ; and the latter contribute nothing to the sum of r. 

 Let the mean number of impacts of an atom against other 

 atoms be C per unit of time. If we write CT=1, T is 

 approximately the mean time which elapses between two 



Cj 



successive collisions*. On the other hand, Z = N 1 -^, and 



* In the space v let there be N equal molecules, whose velocities are 

 distributed according to Maxwell's law (with modulus a). If R is the 

 smallest distance within which two molecules can approach each other 

 without colliding, and if a molecule moving with a given velocity expe- 

 riences B impacts per unit of time, the mean value of the time between 

 successive impacts is 



I __ 0-6505 y =0 . 2071 v 

 B 77 NR 2 « NR 2 « 



while 



1 v =0-1995 : v 



C~ B ~2V2ttNR 2 * NB/V 



Cf. Tait, Trans. R. S* E. xxxiii. p. 74 (1886). 



