1915-16.] The Size of the Particles in Deep-sea Deposits. 223 
enormous number of particles which enter into the composition of even a 
comparatively small fraction of the sample. 
As the probability of a certain orientation is about the same for all the 
particles, we may assume that the average rate of fall for a large number of 
particles (which is the only quantity measured by the new method) will give 
a fairly accurate value of their mean effective radius. Also the orientation 
of the smaller particles will vary considerably during their fall, owing to an 
irregular Brownian rotation due to molecular impacts, so that the resistance 
encountered by each of these particles will undergo incessant variations. 
In cases where the shape of the particles deviates considerably from 
that of an ellipsoid of rotation, the relationship between the effective radius 
and the real dimensions of the particle remains, of course, unknown. 
However, by stating the effective radius of a particle, or rather the mean 
effective radius of not excessively heterogeneous fractions, we obviously 
define a quantity which will on the whole give a fairly accurate idea of the 
real size of the particles. 
As a further argument in favour of this reasoning and of the applica- 
bility of Stokes’s law to the process of sedimentation, I have given in Table I 
the effective radius of certain sediments (silt and clay) investigated by 
A. Atterberg,* viz. the values measured directly by him with the microscope, 
compared with those found by calculation according to Stokes’s law from 
the time required for their sedimentation.-J- 
As the Swedish soils considered are chiefly made up from practically 
unaltered fragments of feldspar, mica, and quartz, I have taken the average 
density of the particles to be 2 -7. 
Table I. 
Time of Sedimentation for Fall through 10 cm., according to Atterbera . 
£ = Time of fall through 10 cm. 
= Velocity in cm./sec. 
r = Mean effective radius calculated according to Stokes’s law. 
r p Mean radius measured with the microscope by Atterberg. 
t 
v in cm./sec. 
r 
r' 
5 seconds 
50 seconds 
7 minutes 30 seconds 
1 hour 
8 hours 
2 
0*2 
222-2. 10" 4 
27-78. 10“ 4 
3-472.10 
78/4 
24'8/x, 
8*3j u, 
2 9/4 
1 *03/x 
100/4 
30/4 
10/4 
3/4 
1/4 
* “ Die mechanische Bodenanalyse und die Klassifikation der Mineralboden Schwedens 
International Reports on Pedology , ii, 319 (1912). 
f See also A. D. Hall, Journ. of Chem. Soc. Trans., lxxxv, 959 (1904). 
