650 

 ,1' z= ,i\ when t=:0, has at the time t an abscissa between ,»; and 



For this case (VIII) becomes : 



df dV Ö 



ot o.r' dx 



in which ƒ (f,, ^, «;) (/x' is the required probability. 



This equation, integrated with respect to x from a point B with 

 negative a; to A, gives: 



A 





a «ƒ■'"' = " 1 ItJ." IfJ. i - '* ' *-'''''>^ - <■'■"'>"■ 



0/ 



As in ^ i|> = and in /> / and — will be verj strongly zero 



O.T 



by the immense repelling force, we get: 



A 

 B 



When we now make tlie thickness of the layer in which per- 



\J'"'='iB. 



ceptible forces act, very small, | / dx disappears for every time, 



B 



because / is in this layer certainly not infinite. So we get at the 

 wall : 



(l)r«- 



How ƒ may be determined from this equation, needs not be 

 explained here. 



§ 3. The boundary-condition at a reflecting wall may be easily 

 deduced from (Vlll), and this is perhaps also possible for an ad- 

 sorbing wall in the latter case, however, it seems simpler to take 

 another way. We suppose that the adsorbing wall may detain a 

 particle that collides against it, and that such a detained particle 

 never gets free again. This property may be observed under several 

 circumstances. 



Suppose that a particle at the time t has a distance .r from the 

 wall that is situated at .v = 0. After a time t the particle may be 

 adsorbed by the wall or may still be free So it naturally suggests 

 itself to introduce in this case the two following functions: 



1) Gomp. M. V. Smoluchowski, Phys. Zeitschr. 17 p. 587, 1916. 



