653 



to the wall, so after the time t there will be adsorbed in total 



00 



n = jIq I / (x, t) dx particles. 







To comj)Lite this number it is not necessary to know ƒ. As namely 

 the beginning-condition for ƒ is less simple, we introduce a new 

 function : 



l^'{p,t) = n,(nx,p,t)cLv ^) {XV T I) 







Integrating (XIV) and (XVI) with respect to x from zero to in- 

 finity, it is easily seen that F {p, t) satisfies the same differential- 

 equation and boundary-condition as /(^i', /?, ^), considered as a function 

 of p and t. Further it follows from (XIII) and (XVII) that the 

 beginning condition is F ip,0) = n^. 



The solution of the differential-equation for F, regarding the 

 beginning and boundary-conditions, is: 



in which, 



2 . 



'u . 



(u) z=z I ^-«- d 







The number of particles, .adsorbed in the time t follows from 



(XV): 



nt—. 



"o I X (*^'0 ^^^*^ = '*u^ 1 *^^'^ I /(^,'^,t) dx = X i F {o,t) dt , 



which, after integration, gives: 



With this the problem is solved that is mentioned by 

 V. Smoluchowski ') with respect to the fact that this theory was not 

 in accordance with the experimental results of Brillouin ^). The 



^) F{p,t) is the concentration of the particles at the little t at a distance p 

 from the wall. 



~) H. Weber, Die Fart. Diff. Gl. der Math. Phys. 11, p. 95. 

 •^) M. V. Smoluchowski, Phys. Zeitschr. 17, p. 570, 1916. 

 ■*■) L. Brillouin, Ann. Chim. Phys. 27, p. 412, 1912. 



