651 



1''' . The probability that the particle meiitioiied has at the time 

 t a distance from the wall between /) and (/ -\- dp : f{v, p,t)dp. 



2"*^l The probability that, at the time t, it has been adsorbed by 

 the wall : X ('^'> 0- 



Since a particle, that is not adsorbed at the time t^ -j- /,, is also 

 free at the time t^^, f will satisfy the integral-equation : 



3 



ƒ 



/(.r, />, t,)f{p, a, g djy = ƒ (.f, a, t, -\- f,) . . . (XI) 



We can- further obtain a simultaneous integral-equation for ƒ 

 and X" by remarking that the probability x C*^'' ^ + ^2) consists of 

 two parts viz. the probability that the particle was already adsorbed at 

 the time t^ and the probability, that at the time /^ it was somewhere 

 in the liquid and is adsorbed by the wall during the time t^. This 

 leads to the equation : 



00 



X (a^, t, + t;) = X (•^•> t,) + j /{■^■^ Ih t,) X ilh h) dp . . (X//) 







As, after the time t the particle must be somewhere, we finally 

 have as third equation for /' and x: 



ƒ 



/(.^,p,O^P + x(.',0 = i i^Jii) 



() 



Just as in § 2 we are able to derive from (XI) a differential- 

 equation for ƒ, with this difference however, that now in the liquid 

 the external force if? = 0. ^) 



So in the liquid ƒ(.*', p, t) satisfies the equc\tion : 



^■ = i>^' iXIV) 



However to determine / we need a boundary-condition. This 

 may be found from (XIlj, (XIll) and (XIV). 

 When viz. we write for (XII): 





 and make t^ very small, then the second member of (XII") becomes : 



1) The forces, that the wall exercises on the particle, are accounted for by the 

 function x- 



