1257 



and tlie value ot" wliicl» is stdtistically in.dependeiit of .r. By the aid 

 of kinetic considerations we derived from this form u hi a formula for 

 A* which had the form : 



^^ = ^< (16) 



a 



(' i-epresents a constant the value of which we can leave undeter- 

 mined foi' the j)resent. When we com|)are this value with Einstein's 

 value (equation (i^/,)), we see that they wmy both be represented hy : 



/A"- = ht (1) 



wilh h = constant, i.e. that I he mean deviation is proportional lo J/^. 

 This is ilothing but the well-known result of the calculus of probability 

 for the sum of a great number of terms when the mathematical 

 expectation for that sum is zero. 1 shall assume in the future that A' 

 will certainly be represented by an equation of the form (1) '). Then 

 it only remains the question to calculate h. The ditfei-ence between 

 {\a) and (Ih) is that this quantity, is in inverse ratio to a according 

 to (1^), and to n^ according to (l/>). The experiments carried out by 

 Miss Snkthlagk '), have demonstrated that equation (l/>) can certainly 

 not be accurate, which is the more remarkable, because also other 

 kinetic dei'ivations of A"^ had yielded equations of this form '). 



Thus we w^ere confronted by the difticulty that, experiment pro- 

 nounced in favour of e(puUion (Id), whereas the derivation of {ih), 

 though doubt as to its \alidity is not excluded, seemed nevertheless 

 much less assailable to me than the introduction of a force of viscosity 

 against the thermal mo\ement, which was the foundation on which (la) 

 was based. I have had an opportunity to discuss the derivation of 

 the two formulae with seveial physicists as Lohentz, Einstein, 

 Ehrenfest, Ornstkin, and Zkrnike, and it is partly owing to their 

 remarks that 1 think that I am noAV able to give a method of 

 calculation of A% which without starting from the supposition of a 

 friction against the thermal velocity, leads to the accurate result, 

 [la), at least as far as the dependence of a is concerned. 



For this I shall start from the simple formula: 



X -:= w {t) 



') A further proof of this supposition is found in Remark II at the end of this 

 paper. 



') A. Snethlage. Moleculair-kinetisclie verschijnselen in gassen, inzonderheid 

 de Brownsche Beweging. Acadeniiscli Proefschrift. Amsterdam 1917. B. Experi- 

 menteel gedeelte. 



'■^) VoN >Smolucho\vski. Ann. d. Pliys. 21 p. 769. Ann. 1906. 



A. Snethlage. 1. c. Hoofdstuk II. 



