654 



latter iias experimented with particles of gamboge in a mixture of 

 glycerine and water. Tiie number of the particles that was adsorbed 

 by the wall could be determined bv counting them on a raicrofotograph. 



Now, while Brillouin has concluded, that his observations agree 

 with theory, v. Smoluchowski has pointed out the incorrectness of 

 this method of reckoning and has substituted this by a better one. 

 Thereby he supposes however that every particle that collides 

 against the wall, sticks to it, and he further solves the problem by 

 using the very schematic image of the Brownian movement that is 

 mentioned in § 1 . The result of this computation agrees very badly 

 with the observations and v. Smoluchowski thinks that this is a 

 consequence of the fact, that a particle, colliding against the wall, 

 does not adhere at once, but on the average has to collide several 

 times before being adsorbed. So this would mean, that the boundary- 

 condition has to be altered. 



As now is demonstrated by v. Smoi,uchowski ^), we find the 

 solution of the problem as given by him, from the diffusion equation, 

 when we use F {o, t) ^=^0 as boundary condition, while (XIX) is 

 deduced with the general limiting-condition : 



c 

 So we may expect that by a suitable choice of x we get a result 



that is more in accordance with the experiments of Brillouin. 



To be able to decide in iiow far this is the case we compute from 



the data furnished by Brillouin, ^^ and D the latter with the help 



of {[ b). When we now choose a certain value of >«, we can represent 



nt graphically as a function of t. This is to be seen in fig. 1, in 



which the abscissa represents the number iii of the adsorbed particles, 



and the ordinate, in accordance with Brillouin, the square root of 



the time, expressed in hours. Further, for practical reasons, not the 



values of y. but those of a = — - have been written at the curves. 



{/D 



For X = GO (« = (X) ) we get a straight line, agreeing with the 

 theory of v. Smoluchowski. One sees that the observations of 

 Brillouin, indicated by crosses, do not at all cori-espond with them. 



Smaller values of jc or a give curves that agree better with the 

 observations, though none of the curves gives an entirely satisfying 

 result. Probably «=:0.003 (;c=rl.5 <10-^) comes nearest to the truth, 

 when we bear in mind, that the observations made after short times 



^) M. V. Smoluchowski Phys. Zeitschr. 17, p. 585, 1916. 



