statistical mechanics 



83 



As to the large values of x we have given before a series for '^{x), from 



which we get 



(200) 



T 2. 5 [3 4.7[5^6.9|7 



x° 



For very large values of x, we may confine ourselves to the first term of the 

 right member. For moderately large values we have to take into consideration 

 also the following terms in the series till the terras begin to increase. The error 

 of the value of T thus computed is smaller than the first neglected term. 



51. Stars. For the numerical computation of the time of relaxation we 

 have to use the following formulae 



(201) 



7C 



3v = 3 J 



(1 



Vk 



47) 



,2 ' 



000 



Moreover is a = 0 = mean component velocity of the stars. 



We use planetary units (Compare Meddel. N:o 70). We then have 



^ = 271 



and 



-\- = 2 . 



Further we have, according to Medd. N:o 70 



Z) = 1.611 X10^ a = a = 5.624, 



which give 



6234, 

 1/7?= 78.96, 



^ = 0.3874 X 10-^ 



The value of q is so small that it is permissible to use the formula 



T 



K, 



= — 2 log^ 



which gives 



We further have 



K, =■- 1318.7 

 T = 38940 

 T:a.^ = 3 8 92 . 



