166 Prof. Ludwig Boltzinanii on the 



the velocities. Figs. 1 and 2 show the configurations before 

 and after an impact respectively, while figs. 3 and 4 give the 



Fur. 1. 



Fio-. 2. 





configurations before and after the corresponding " opposite " 

 impact respectively. Arrows numbered alike have always 

 equal lengths and make the same angle with the line of centres. 

 For all collisions which are " opposite " to those previously 

 considered, the velocity-components of the impinging shell at 

 the commencement of the impact lie between the limits 



u 1 and v! + du 1 , v' and v' + dv\ io' and w 1 -f did 

 and at the end of the impact they lie between 



u and u + du, v and v -+- dv, w and w 4- dw. 



The same holds good for the impinging single atom in 

 which the motion of the centre of gravity, the magnitude of 

 the relative velocity and its inclination to the line of centres 

 have the same values for the opposite impact as for that 

 originally considered. In each opposite impact a shell loses 



-elocity-components u', 



and a single 



'i? 



i, £#!'; on the other hand, a shell gains 



atom 

 v 



loses 



Wj and a 



single atom w 1? v u w^. If dn' is the number of collisions per 

 unit volume in time 8t which are opposite to those previously 

 considered, the term 2 log F + % log/ is increased by them to 

 the extent of 



dn' (log F + log/! -log F-log/i'). 



The total increase in the value of this expression due to the 

 specified and opposite impacts together is 



(log F + log/i - log F' - log/J)(dn - dn') . 



If we integrate this expression for all values of the variables 

 whose differentials are contained in da and du 1 , we obtain 



