1270 



the considered particle is equally probably positive as negative. 



Hence it is very probable that we may also divide the force of 



A 



friction into a term — 6 .t S « , and an irregular term k. As /t . A=0, 



we may insert k in s, so that we may write: 



A 



w {t)z=: — 6 rr 5 a -- + « With s Li = 



t 



as we did on p. 1258. 



Remark V. In conclusion 1 want still to make a remark in con- 

 nection with a derivation given by Oknstein ') of the formula ^v.«=:0. 

 In this he starts from equatioji (3j, wiiich he writes: 



du 



^-^u^F (3a) 



at 



and he proves that when F is a function of t, which is [)rescribed 

 without taking u into account, and which further fultils certain 

 conditions"), the solution of the differential equation (3a) yields such 



— J- du 



a value for u that Fu = i3u^, so that 7C — = 0. 



dt 



This result is in perfect agreement with the thesis |)ronounced by 

 Miss Snkthlage and me that i\n:=(), and in coullict with the thesis 

 from which Einstein and Hopf, Langkvin and others start, viz. that 

 R=z 0. 



Remarkable is the conclusion drawn by Ornstein out of this. It 

 runs, namely, that there is no objection to accepting equation (3a) 

 with Fu = 0. It is astonishing that Ornstein has not noticed this 

 contradiction.. In reality he nowhere introduces the supposition Fu = () 

 into his calculation. He simply integrates equation (3a), and then 

 demonstrates that Fu is ?iot zero, but equal to /:?«'. 



It follows from Fu = iiu"" that we may represent F by: 

 F =^u + F' in which l^u — , 

 so that ^z=z — iiu -\- F= —^u 4- i? w 4- F' — F' with Fu = 0. 



In so far this derivation teaches nothing new. Yet it is interesting 



') L. S Ornstein, Zittingsverslag Dec. 1917, p. 1011 

 , *) F is a continuous function, which, however, repeatedly changes its sign, and 

 which has another value for every particle. F' taken over all the particles, and 

 also the mean squares of the first and higher time derivatives of F are constant 

 in the time. Also the mean value of F^ for a single particle taken over a suffi- 

 ciently long time is constant in the time and constant for the different particles. 



