G50 Dr. F. Gr. Donnan on a 



de by the practically infinite mass of I. These circles corre- 

 spond in fact to the so-called " spheres of molecular action." 

 We assume that not only is r>l 3 but that also semicircle 

 PQR> semicircle LMN. 



The physical significance of these assumptions may be stated 

 as follows: — It is assumed that the molecular " adhesion " 

 between I and is greater than the molecular " cohesion " of 

 the colloid I, and that the intermolecular attractive forces fall 

 off more rapidly with increasing distance in the case of the 

 molecular cohesion of I than in the case of the adhesion 

 between I and 0„ It is easy to express these conditions in 

 a precise mathematical form by choosing a suitable law of 

 force with two constants, but considering our present want of 

 knowledge such a formulation could only serve the purposes 

 of illustration. 



With the assumptions made, it now becomes possible to 

 explain why the process of intermixture is arrested before the 

 molecular limit. Suppose that the sheets, filaments, or 

 particles have become so thin that the plane CD occupies a 

 position CD' within the semicircle PVR (see fig. 1). Then 

 it is evident that the value of r will be diminished since there 

 now exists an effective component due to acting on the left 

 of de. In fact, the resultant attraction due to bears a ratio 

 to its former value equal to the ratio of PRST to semicircle 

 PQR. At the same time, so long as the plane CD' lies within 

 the semicircle PVR but outside LMN the value of the force 

 I will not be sensibly altered. 



Accordingly there exists a critical thickness of I such that 

 the forces I and r just balance. When this state of division 

 is reached the process of disintegration ceases, and there 

 results a two-phase medium consisting of the medium I dis- 

 i ributed throughout the medium in some state of extremely 

 fine division. Such a medium corresponds on the present 

 theory to a colloidal solution. 



Fig. 2, which requires no further explanation, applies to the 

 case of spherical particles of I immersed in 0. 



If the medium be continuously removed by evaporation 

 or otherwise, or if sufficient of I be colloidally dissolved, 

 there results an interlacing network of I distributed through 

 0, and a more or less elastic jelly is produced (of. the views 

 of van Bemmelen). 



For thicknesses of I greater than the critical, the medium 

 I has a tendency to increase its common surface with O, i.e., 

 it possesses an effectively negative surface-tension. For thick- 

 nesses less than the critical, however, there will be a positive 

 surface-tension. Hence if the substance I be produced in the 



