364 Dr. H. J. S. Sand. The Role of Diffusion during [Nov. 22, 

 The integral obtained is 



a result which can be verified without difficulty. 



The amount of solute S removed by the sphere after the first t 

 seconds is 



_ dt when x = r 





The first member on the right side of this equation is identical with 

 the value which follows for R equal infinity from the Equation 9 we 

 previously employed. Making 2r = 5 x 10~ 5 cm, R = 10~ 5 cm 2 /sec., 

 we can calculate that the difference between this quantity and S amounts 

 to only 0*9 per cent, of S after 1 second. 



(b) A Sphere in a Large Enclosed Spherical Space. The close approxi- 

 mation of the result expressed by Equations 12 and 14 to the correct 

 value for stationary liquids, in which the radius of action of each 

 spherical particle is great compared with its own diameter, is specially 

 made clear by the full calculation of the case in which one of the 

 spherical particles is placed in the centre of a spherical vessel of large 

 diameter filled with solute. In this case we have to integrate 

 Equation 5, the limiting conditions being firstly that no solute can pass 

 through the wall of the vessel. Indicating the radius of the latter by 

 R, this means that 



FR = 0, i.e., according to Equation 4, that = 0, for x = R. 



8aj 



We have besides the limiting condition expressed by Equation 6 and 

 the condition 



c = Co between x = r and x = R, for t = 0. 



The differential equation can be integrated subject to these limits by 

 methods similar to those employed in 283 to 293 of Fourier's Analytical 

 Theory of Heat for the determination of changes of temperature in a 

 solid sphere. The following result is thus obtained : 



c = . -- [a^-'V' sin m (x - r} + a 2 e~ Kn 2*t sin n 2 (x - r) + . . . .], 



the numbers n being determined as the successive roots of the equation 



tan n (R - r) - 

 ~nT *' 



and the coefficients a by the equation 



