1265 



The same particles which form (ogetlier a group with the same 

 A, will not all have the same A'. This circumstance does not detract 

 from the validity of (6) and (7), nor from the use made of it. 



Remark II. At a cursory view equation (4) : 



t 







looks rather strange. It seems to be quite in contradiction with 



A' = bt. For when we take the square and when we average, a 



term x^^t^ appears which is by no means small com[)ared with the 



other terras. When we, however, choose the group particles that 



have a definite velocity x^ at the moment ^ = 0, we may write for 

 this group that: 



j IV {0) dd 







For at the moment t they will be distributed over all the velocity 

 groups, and they will have a mean velocity zero. At least this will 

 be so when / is not taken too small. When t is of the order of 

 1 sec, this is amply sufficient. Hence the terms: 



t t 



f ( ( to {0) dÓj -\-2.':c^. i ^o {&) dO f' 







will neutralize each other in the expression for A"^. A direct 

 discussion of the way in which the remaining terms depend on t 

 will be very diflicult. But in this way it is at least seen that the 

 striking appearance of terms with f is only apparent. The form of 

 (4) is, accordingly, more or less misleading, which, however, is no 

 objection to the use made of it above. That (4) is really compatible 

 with A* = hi, follows from the reduction via equations (5) to (10). 



Remark III. We have assumed on p. 1258 that : 



MrA<0 



This can be demonstrated in different ways. In the first place we 

 might start from the relation A' = 6/, proved on p. 1257 which after 

 a double differentiation, yields: 



fdL\ 



^l A = — m — 

 \dt) 



