1262 



mx 



first term — /)'.r with p* = =^=:. 1 call the function of t that is 



left, q ; it has the property that q,v = 0, provided I average over 



dS\ (Px 



all the particles. When I write — = m — , (C) becomes a ditfe- 



dt dt' 



rential equation, which can be integrated. And afterwards mean 

 values can be taken over the different particles. What objections 

 Ornstein and Zermke have to this way of procedure, is not 

 clear. It is entirely incomprehensible why they assert that (6) 

 w^ould not be a differential equation. Their statement that (C) 

 would not hold at any moment, is clearer. But it is not valid. 

 (A), {B), (f), (Z)), and (E) hold of course at any moment, because 

 the different moments are equivalent for a stationary movement. 

 Strictly speaking Ornstein and Zernike do not mean that these 

 equations would not always be valid, but they assert this about 

 other equations which are obtained when ail the averages are 

 not taken over all the particles, but over a v-group. They 

 understand by this a group comprising all the particles that 

 possessed the same velocity x, at the moment tf,. When we now 

 average over this group, equation {B) does not even hold at the 

 moment /",, wheieas (.4) and (E) do hold at the moment t„, but 

 not at another moment'). When we write the equations with such 

 group means : 



r " 



^ .r — {A bis) etc. 



Ornstein and Zernike are undoubtedly right in their assertion that 

 {A bis) . . . . {E bis) are not always valid. But it is equally certain 

 that they are wrong when they assert that the validity of these 

 equations has been assumed by Miss Snethi,age or me, or has been 

 used in our reductions. We have always concerned ourselves with 

 averages over all the particles, never with such averages of a 

 v-group. 



When, therefore, accessory misunderstandings are left out of 

 account, it seems to me that Ornstein and Zernike's objection might 

 be defined like this: that they think (hat we ought to have made 

 use of averages over a v-group, and that we wioiigly failed to do 



') The authors calculate this more at length. Qualitatively this is, however, 



easy to see. For such a group x^ is not constant. At t^ we have, namely, x^ — x^(f 



- RT 

 and after not too short a time x'^ = -r^- • 



Nm , 



