1061 



and if we combine the i-esult with (7) it follows that (6) holds for 

 every value of t, when the value of (5) is assigned to the constant 

 p, which had been left undetermined at first. 



Whereas (4) does not teach us anything, and must only betaken 

 as a definition of q, (5) and (6) are a direct conse(|ueiice of 70" = 

 = constant. And if (). and B. should succeed in proving (as they 

 pretend they do) that it follows from the complex (4) (5) and (6) 

 that u* cannot be constant, they would have done no less than 

 proving that the mathematics used are in conflict with the principium 

 contradictionis. When their proof is examined, we arrive at another 

 conclusion, in the first place tliey substitute again another equation 

 for ours, and write q =z (for given //„ and u^) '), which must no 



doubt mean that u^qit) = and u^q{t) = 0, instead of u{t)q{t) = 0, 

 as we derived. When averaging the square of u they accordingly 



erroneously omit the terms: 



t 



2u, cos {[/p .OX- \ q i») sin \ j/p {t— /J)\d i> and 

 PJ 

 



t 



«n 1 r 



2 — ^ sin {\/p.t)X' qii)) »m { Vp {t — V) | rf/> 

 \/p PJ 







They further expand q{t) into a series of Fourikk and subject the 

 coefficients of this series to the same suppositions as Planck intro- 

 duced for radiation, though it is xQvy much the question whether 

 these suppositions hold here. For though it is true that the two 

 curves in a certain sense are dependent on quantities determined 

 by chance, yet there are correlations between the q'^ at different 

 moments, which have intluence on the mean values of the Fourikr- 

 coetïicients, which intluence 0. and B. have not examined. 



I will not enter into other objections of Messrs. 0. and B. I think 

 that they were already beforehand sufficiently refuted by what I 

 wrote loc. cit. In particular this refers to the objection 0. and B. 

 advance loc. cit. p. 923 to the (apparent) occurrence of a term witli 

 f in A", for which compare Remark II of my article loc. cit. p. 1265. 



Zkrnike have, however, rightly proved that the complex of the equations (4), (5), 

 and (6) is not valid, when the means are extended over a group of particles which 

 at the moment t = have a definite velocity u (o) — and this is easy to see for 

 w2 is not constant for such a group — but this cannot be a reason why we 

 should not be allowed to use the complex with means over all particles, in which 

 case they are valid. 



1) in consequence of a difference in notation they write iv = 0, p. 928 loc. cit. 



