122 C. Barus — Subsidence of fine Particles in Liquids. 



Art. XY. — The Subsidence of Fine Solid Particles in 

 Liquids ;* by Carl Barus. 



1. Throughout this paper the motion of the corpuscles 

 through the liquid is of the kind premised in treating capillary 

 transpiration : in both cases solid and liquid move relatively to 

 each other under conditions by which eddies are excluded, and 

 the whole kinetic energy is at once converted into molecular 

 kinetic energy, or heat. 



In my earlier work I endeavored to analyze the phenome- 

 non of sedimentation into parts such that the conditions under 

 which the subsidence is to be explained from a chemical, or 

 from a physical, point of view, may be better discernible. To 

 do this I first considered the question in its purely mechanical 

 aspects. f If P be the resistance encountered by a solid spher- 

 ule of radius r, moving through a viscous liquid at the rate a?, and 

 if h be the frictional coefficient, then P = 67zkrx\ Again, the 



effective part of the weight of the particle is P r =-7ir^{p — p')g, 



where g is the acceleration of gravity and p and p' the density 

 of solid particle and liquid, respectively. In case of uniform 



motion P=P'. Hence ^=-^if{p—p')g (1) 



In any given case of thoroughly triturated material the par- 

 ticles vary in size from a very small to a relatively large value ; 

 but by far the greater number approach' a certain mean figure 

 and dimension. An example of this condition of things may 

 be formulated. To avoid mathematical entanglement I will 



select y=Ax*e~ x ~ (2) where y is the probable occur- 

 rence of the rate of subsidence x. If now the turbidity of the 

 liquid (avoiding optical considerations) be defined as propor- 

 tional to the mass of solid material particles suspended in unit 

 of volume of liquid, then the degree of turbity which the given 



*The present article, being a continuation of Bulletin U. S. G. S., No. 36, 1886, 

 is largely based the experimental evidence there tabulated. Mr. William Dur- 

 ham (Chem. News, xxx, p. 57, 1874; id. xxxvii, p. 47, 1878) was the first to give 

 an incentive to this class of experiments. Much of our knowledge of the effect of 

 precipitants is due to him. Moreover, the theoretical views at which he ulti- 

 mately arrives may be regarded as a definite point of departure. In this country 

 Prof. T. S. Hunt (Proc. Boston Soc. Nat. Hist., Feb., 1874), Prof. W. H. Brewer 

 (National Acad. Sc, 1883; Am. Journal, (3), xxix, p. 1, 1885) and Prof. C. R. 

 Stuntz (Cincinnati Soc. Nat. Hist., Feb., 1886) have occupied themselves with 

 similar work. Prof. Stuntz's paper contains further references among others to 

 Waldie's results (Journal Asiatic Soc, of Bengal, 1873; Chem. News, 1873). 

 Meanwhile Mr. W. Hallock has made experiments on the subsidence of lamp- 

 black in connection with his work on the density of that substance (Cf. Bull. U. 

 S. G-. S., No. 42, p. 132, 1881). I may add that my own experiments were sug- 

 gested by Prof. Brewer's memoir. 



f Cf. G. Kirchhoff, Mathematische Physik, lecture 26, § 4, 1876. 



