1915-16.] The Size of the Particles in Deep-sea Deposits. 229 
But according to Stokes’s law 
v = Cr 2 (la) 
Thus 
<f>(r) =0.Y(r)drr 2 t ..... (3a) 
The whole of the fraction considered will be deposited when (p(r) 
= F (r)dr, i.e. when 
F (r)dr = ^ F (r)dr rH 
or 
( 4 ) 
Now consider the situation at the end of a particular time t'. According 
to equation (4), all particles having their radii not less than 'sj ^7 w iH 
then have fallen to the bottom. The total quantity of these may be written : 
A =T F (r)dr. 
VA 
v c t> 
At the same moment a certain quantity D of particles having r< 
(which are still to some extent present in the suspension), namely, 
/. a / Jl c\/ Jl n 
D = | cr <£(»•) = j a ' j¥(r)rHdr 
will also have been deposited. The total quantity deposited on the 
bottom is therefore 
P(0 = A + D = f 
• i v Cf 
c 
F ( r)r 2 dr + 
F (r)dr 
(5) 
of which terms the first represents the smaller and the second the larger 
particles of the suspension. 
Substituting t for t', we have the same function of time, t, which is 
actually registered by the instrument. Differentiating this equation (5) 
with regard to t, we have 
A second differentiation gives 
d^(t) 1 111 1 F / /T\ 
dt 2 ~ 2A C ' t 5/2 W C t) 
(D 
