1258 



which, integrated, yields: 



t 



,v=z.v^+:tJ-\- jw(0).(t-0)dO. . . . . (4)>) 







The path travelled over in the time t is .r — .i'^ == A. When this 

 equation is multiplied by 7v{t), and when the mean values for all 



the particles are taken, then .i\iv{t) becomes =0, hence: 



t 



K^vjt) = w{t) i w{6),(t-0)d0 ..... (5) 







The lefthand side is negative, it is a constant which I shall represent 

 b}- Q, i.e. it is independent of the value of t, provided this is not 

 taken too small. The proof of this I shall give in remark 111 at 

 the end of this paper. When we divide this equation by t, it appears 

 that also 



- .w{t)<CO (5a) 



in virtue of this we may j)ut: 



ro{t) = -r^j-hs (6)') 



in which 



«A =r: .......... (7) 



When this equation is multiplied by A, and averaged, we get: 



A . IV (0 = - r' — = - Q or r' =: ^ . . . . (8) 

 t 



Equation (6) may be expressed in words as follows: The force 

 that acts on a particle at a given moment, ujay be split up into a 

 force of viscosity against the measurable movement and a term that 

 is independent of the measurahle velocity. The splitting up of the 

 force into a force of viscosity and an irregular force is, therefore, 

 permitted provided loe assume that the measurable velocity, not the 

 thermal velocity, is damped by such a force. If we could compute 

 ?'' by a kinetic way, we might arrive at a complete derivation of 

 Einstein's formula for A*. The calculation of ?■' will, however, be 

 no doubt attended with great difticulties. It seems, however, not 

 very hazardous to me, to assume the value ^n^a from Stokes's 

 formula for it; possibly the value corrected by Cunningham. This 



1) Compare Remark II at the end of this paper. 

 ') Compare Remark I at the end of this paper. 



