652 



o 

 because, in consequence of the meaning of /{p,t.), this function 

 for sniali t only differs fi-om zero when p is small too. Now. while 

 the limit in the first member exists and is finite, this will also be 

 the case with the limit of the second member and is therefore: 



Lim ^ / {'p,t^) dp — Lirn dp= —~ dp— a, 



(I 



where x is a constant. 

 So it follows from (XIl"): 



^-^ = >. ƒ (..,0^) . . .... {XV) 



Now, when we integrate (XIV) with respect to p from zero to 

 infinite, we find : 



J/(^,M dp=- d' ' ^ 



In reference to (XIll) and (XV) this gives the boundary-condition: 



^(11=, = "^''=" <^^'' 



From (XIV), witlj the help of this boundary-condition and the 

 beginning-condition, we may determine ƒ. ƒ being found, ^ follows 

 from (Xlll). 



While the functions ƒ and /, used above, are probabilities, we 

 can test the obtained results only by making a very great number 

 of observations. This is easily done by bringing not 07ie but many 

 particles in the liquid. Though we cannot say then liow many 

 particles after the time t will be adsorbed by the wall, we may 

 calculate the most probable number from which the true number 

 will differ the less, as there are more particles. 



Imagine a cylindric volume, limited only at one side by the 

 wall that lies at a' = 0. In this volume are, at the time t ^= & 

 great number of particles homogeneously dispersed, so that the 

 number of those particles being at a distance from the wall between 

 .)! and .1' -j- dv, is n^ dx. Now we ask after the most probable num- 

 ber of particles, that at the time t will be adsorbed by the wall. 



Of the ?Z(, dx particles at a distance from the wall between x and 

 X -\- dx there will probably, after the time t, n^ / {x,t) dx adhere 



