Statistical mechanics 



81 



According to the formulae (86) and (69) we have {L = M — 0) 





^ A 



Ij: -^200 



~ (^200 



7 2) A 



(195) 



LH ^020 



~ (^020 



<^-') ^000 





^002 



~ (^002 



^000 



where, as usual, v,j7,. are relative moments. 

 As furthermore 



020 : 



"■'002 — ^f,. 



where a„, Oj,, O;,, denote the mean component velocity of 11, v, iv, so is 



l_2 Aoo = K — ^-'l^ooo. 

 (195*) |2^,,,, = (a2-a2)J„„,, 



We have just found that ^200 ' -^020' ^002 increasing t approach to the 



same limit a^. The above formulae show that a^^ , a^, 0^^^ also approach to the same 

 Hmit, which we may call a^. Hence the theorem: 



The mean component velocity of the stars approaches, with increasing t, to the 

 value 0^ in all directions. 



Which is the theorem of Maxwell. 



If a, which is arbitrary, is put = a, so is the limiting value of ^200' ^0201 ^002 

 vanishing. 



The velocity, with which these parameters converge against zero, depends on 

 the coefficient v. 



50. Numerical computation of the time of relaxation. We first com- 

 pute the dimensions, regarding lengtli and time, of the constant T. We start from 

 the formula (156*) 



00 1 _^ 



0 0 



Let the notation 



a -Hf I'" 



denote that a quantity a has the dimension m regarding length and n regarding time. 



As Z) is a length, Ü and a (= 0) a velocity and the quotient of two lengths, 

 we have 



D^l. 



(196) Q, # It-' , 



h,^l\ 



Lunds Uuiversitets Årsskrift. N. F. Avd. 2. Bd 28. 11 



