Statistical mechanics 33 



For reducing J., we put 



and get 



where the integral has the value 2. 

 We thus finally get 



(52) jtf„ = !!£?l£;St±^,. 



For = m., = 1 we obtain 

 (52*) iJfH = --^ 



and the number of collisions is now, according to (51*), 



(53) 4|/i d^n'^a 



which is the formula of Maxwell. This is the analytical expression for the total 

 number of collisions of all stars in a sir^ per stellar year. 



Here a denotes the mean component velocity. If the mean velocity il is in- 

 troduced (Meddel 70 (12)) 



^ 2l/"2 

 .J _ J , 



] / 7Ü 



so is the expression for tlie number of collisions 



V2 % d' n' Q 



agreeing with Meddel. 70, where, however, the number of collisions for otie star is 

 given. 



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



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