Statistical mechanics 



Calculating the numerical values of h{x) we obtain the following table: 



57 



X 



h(x) 



X 



h{x) 



0.01 



+ 0.0362 



0.6 



+ 0.2135 



0.1 



-f 0.14S9 



0.7 



+ 0.2098 



0.2 



+ 0.1717 



0,8 



+ 0.2044 



0.3 



+ 0.2091 



0.9 



+ 0.1988 



0.4 



+ 0.2154 



1.0 



+ 0.1931 



0.5 



+ 0.2161 



2.0 



-j- 0.1443 







10.0 



+ 0.044 



whence it follows that h{x) has a maximum value for x = 0.5 (appr.) and is 0 for 

 X = 0 and x = -\- cc . 



0.3- 



h{x) 



0.2 



0.1 



1.0 



2.0 



3.0 



-io 

 Fig. 6. 



5.0 



6.0 



7.0 8.0 



X 



(124) 



43. Integration regarding the velocities. 



We consider the equation 



V200 = I f + + '''^ ^-^^ 



The integration is to be performed over all values of the absolute coordinates 

 Mj, Vj, u^i v^, tv^. We remark that u, v, w, are the relative velocities {u = ti2 — %, 

 etc.) and that I is dependent on w = ]/^ ■+ + I'^f^i' executing the integration 

 we make a change of variables. It would be possible to use tl>e variables of § 25 

 but we prefer to put 



1 



(125) 



1/2 

 1 



]/ 2 



K2 

 1 



w„ = 



1/2 

 I 



1/2 



= ( ^1+ V,), 

 {W,+W,). 



Lands Universitets Årsskrift. N. F. Avd. 2. Bd 28. 



