128 C. Bcwus — Subsidence of fine Particles in Liquids. 



place. Under these conflicting conditions it is probable that 

 there is a critical shell, within which the energy solid-liquid 

 decreases less rapidly than the energy solid-solid ; and beyond 

 which shell the energy solid-liquid increases more rapidly than 

 the energy solid-solid. This critical shell, being compatible 

 with the conditions of minimum potential energy of the sub- 

 siding system as a whole, is the size of the precipitated particles : 

 for any change of the radius of a particle bounded by the criti- 

 cal shell, implies an expenditure of work, which under the 

 usual conditions of precipitation is not available. 



6. I have finally to endeavor to assign some value to the 

 radius of the critical shell for the case of the above water sus- 

 pensions. In my experiments with tripoli, rates of subsidence, 

 x, in cm (sec. X 10 6 ), varied from x = 1 -to x = 20, according 

 as higher orders of surfaces or turbidities of lower degree, were 

 chosen. Taking the more usual value, x = 3, the radius of the 

 particles subsiding was probably not less than 400 times the 

 molecular radius of water. The bole particles under analogous 

 conditions of suspension in H 2 0, were smaller, probably only 

 100 water radii. In Prof, Brewer's indefinitely suspended clays 

 the limit of comminution can not be estimated at all, except 

 perhaps from purely optical considerations.* Whether in 

 this extreme case colloidal hydration with concomitant volume 

 changes is still demonstrably absent, remains to be seen. To 

 test it, a sufiicient quantity of the extremely fine material 

 would have to be collected and dried by low temperature 

 evaporation. 



Again in Bulletin JSTo. 35 (p. 21), I point out at some 

 length that " when the particles decrease (in size) from 

 some estimable mean value indefinitely," liquid viscosity, 

 being at least partially if not largely kinetic in charac- 

 ter, can no longer be considered constant as regards time ; 

 that therefore a particle may descend, or in other words 

 the continuous and constant action of gravity produce an effect 

 even when the weight of the particle is below the mean 

 or physically measurable value of the friction encountered ; 

 that the limits of time- variation of viscosity will increase as the 

 radius of the circumscribed space decreases. In such a case the 

 particle to be stationary must weigh less than the lower limit 

 of the variable viscosity — a quantity which may be reasonably 

 conceived to approach zero very nearly. I carried these 

 inferences one step further by supposing, rationally, I think, 



* The optical properties of light reflected from particles small in comparison 

 with the wave length of light are discussed by Stokes (Phil. Trans., 1852, p. 530). 

 How large a particle may be without interfering with optical clearness, I 

 can not say. It is well to bear in mind that the suspension of corpuscles consist- 

 ing of a small number, say ten molecules per critical shell, would bear the out- 

 ward characteristics of solution. 



