324 H. A. Baker — Loose Arenaceous Sediments. 



of any specified grain is controlled by its size, specific gravity, and 

 shape, as well as by the density and viscosity of the liquid 

 in which it is subsiding. Experimental work has shown that the 

 size or surface-area of the grains is the dominant controlling factor, 

 and is of much more account than specific gravity in the case of 

 small particles. Where the aggregation of grains consists largely of 

 variously sized fragments of the same mineral, as, for example, 

 in a quartz sand, the difference of " free-settling velocity " or 

 '■' hydraulic value " of the grains affords a convenient means of 

 classifying them according to size. Although increase of temperature 

 diminishes both the density and the viscosity of the water which is 

 sorting the grains it is possible to apply an appropriate correction 

 to counterbalance these variations. The process of elutriating by 

 means of currents of water is based upon the fundamental assumption 

 (which is justified by results) that the final velocity of subsidence 

 of a grain is that of the upward current of water which will just 

 keep it in suspension. Laborious experimental work on the relation 

 between diameter of grains and rate of free settling in water has 

 been carried out in the case of the mineral quartz, and has yielded 

 data upon which the elutriation process is based. Loose arenaceous 

 sediments, being composed very largely of quartz grains, can be 

 classified into grades down to, and below, material of "01 mm. 

 diameter, and if necessary up to about 12 mm. diameter, and in the 

 separation of any specified grade the experimenter may make the 

 minimum and maximum limits of size as narrow as he pleases. 



From the purely mathematical point of view the problem of the 

 subsidence of a small sphere in a fluid medium was investigated by 

 Sir G. G. Stokes. 



If a small particle, assumed spherical, of density />i and radius a 

 fall through a fluid of density p and viscosity ^t, and at rest, it will 

 be accelerated at first. This acceleration is not, however, constant, 

 but decreases with increasing speed, so that the particle, if afforded 

 the opportunity, eventually moves uniformly with velocity 



2 pi — p „ 



If the particle is at the bottom of an elutriator tube and it 

 encounters an upward current of water of velocity V, it will initially 

 begin to move up with the water with the same velocity. But 

 gravity will retard it, and it will suffer a negative acceleration. 

 Consequently its speed will be reduced, and it will ultimately, if 

 afforded the opportunity, move upward with velocity 



9 ;i ^ 



If F = - • -* ga'^ the particle will cease to rise after the 



steady state has been attained. 



