1264 



quanlitj q is statistically quite independent of x. This statement 



involves g-j; = O, but it comprises more. From it follows e.g. q^ = 

 independent of the value of x for which the .r-group ') has been 



taken, which cannot be derived from the simple fact that qx^=0. 



Tlie derivation given here justifies at the same time the derivation 

 of the above given equations (6) and (7) from (5a). These equations 

 give, however, occasion to the following remarks. In the first place 

 the constancy of r" is to be demonstrated. It follows directly from 

 (8). We might also have started from (5), viz. A . iü{t) <^ Ü without 

 dividing by t first. 



Then we might have put: 



w {t) — — r"" A + s' ...... . (6a) 



Multiplication by A and subsequent averaging would have yielded : 

 L.w{t) = - r" A7i= — Q 

 so that r" had not become constant. For this reason I have preferred 



to divide (5) first by t, and to put: 



A 



to {t) = — r^ 1- » 



with y' = constant. Besides the idea of "measurable velocity" can 



A 

 now be applied to , which may lead to the application of Stokes's 



formula. 



Another remark in connection with formula (6) is the following. 



When we consider the deviations A, A', A" etc., obtained in the 



times t, t', t", etc., which have been chosen so that they all finish 



at the moment t^, hence begin at different moments t^, t\, t'\ etc., 



the quantities iü{t^) are of course the same: the accelerations of the 



particles at the moment t^. They are, however, divided into two 



Q 

 terms in different ways. When we put again r* = — we may write : 



h 



A 



to (<,) = — r' h s with s A = 



A' , 



but also : "' («,) = — r' y s' withs' A' = 



A" 



or w (O — — r' h s" withs" A " = etc. 



t 



1) By a i-group we simply mean the group of the particles for which x has a 

 definite value. Accordingly it is something different from a "v-group of Ornstein 

 and Zernike", which contains the particles which at the moment t^ had a definite 

 value V, but which have very different velocities at the moment at which we 

 consider the group. 



