C. Barus — Subsidence of fine Particles in Liquids. 123 



ydx particles add to the liquid is, caet. par., proportional to 

 r s yd%, where r is the mean radius. Hence the turbidity, T, at 

 the outset of the experiment (immediately after shaking) is 



T=T I r 3 ydx=T , where equations (1) and (2) have been in- 

 corporated. 



If the plane at a depth d below the surface of the liquid be 

 regarded, then at a time t after shaking the residual turbidity is 



(3) T d =T o f\^dx=T o (i-(i+ d iy *y 



The equation describes the observed occurrences fairly well. 

 In proportion as the time of subsidence is greater, the tube 

 shows opacity at the bottom, shading off gradually upward, 

 through translucency, into clearness at the top. If instead of 

 equation (2) there be introduced the condition of a more abrupt 

 maximum, if in other words the particles be very nearly of the 

 same size, then subsidence must take place in unbroken column 

 capped by a plane surface which at the time zero coincided 

 with the free surface of the liquid. Again suppose one-half of 

 the particles of this column differ in some way uniformly from 

 the other half. Then at the outset there are two continuous 

 columns coinciding, or as it were interpenetrating throughout 

 their extent. But the rate of subsidence of these two columns 

 is necessarily different, since the particles, each for each, differ 

 in density, radius and frictional qualities by given fixed amounts. 

 Hence the two surfaces of demarcation which at the time zero 

 coincided with the free surface. In general if there be n 

 groups of particles uniformly distributed, then at the time zero 

 n continuous columns interpenetrate and coincide throughout 

 their extent. At the time t, the free surface will be repre- 

 sented by n consecutive surfaces of demarcation below it, each 

 of which caps a column, the particles of which form a distinct 

 group. This phenomenon is Prof. Brewer's stratified subsi- 

 dence. In the case of particles which have undergone an 

 earlier fractionated sedimentation either in nature or in the arts, 

 the occurrence of groups possessing the distinctive character- 

 istics here discussed is not improbable. On the other hand 

 when during subsidence the surfaces of demarcation follow each 

 other in regular succession, one is tempted to look for some- 

 thing more than an adventitious cause for the phenomenon. An 

 orderly arrangement of groups of particles might for instance 

 indicate successive stages of hydration. Cf. § 6. In case of 

 stratified subsidence, it is convenient to speak of the planes of 

 demarcation as orders of surfaces, numbering them from the 

 top downward. Seven or even ten orders are not uncommon. 



