230 Proceedings of the Royal Society of Edinburgh. [Sess. 
Substituting p 
i0T ik 
and solving p from this equation, we have 
F( P ) = 
2 19 
Af h ’ dt 2 
(8 a) 
( 86 ) 
We thus have arrived at an expression for F (p) ( i.e . for the total 
quantity of particles with an effective radius p), where F is expressed in 
terms of t and of the second derivative of the experimental “ accumulation- 
curve ” P(t) taken at the same moment t. The radius itself is also 
expressed in terms of t together with constant quantities. 
The simplest way is now to plot the logarithm of the first derivative, 
dP(t) 
2 = log' 
dt 
against x 
log t. 
We can then find graphically from this 
auxiliary curve the value of 
dz 
dx 
d 2 P(t) 
dt 2 
dP(t) 
dt 
t . 
(9) 
Again, the equation (8a) 
curve 
can be written in terms of this auxiliary 
P(p)=I- 
P 
dP(t) 
dt 
dz 
dx 
(8c) 
For any given value of the radius p, we obtain from equation 8 b the 
corresponding value of t , whereas the two last factors are easily found 
from the auxiliary curve by a graphic construction. 
For further details of the technique of the necessary mathematical 
operations, reference may be made to my original paper * quoted above. 
Y. Discussion of the Results. 
As too much space would be required were my original observations 
to be reproduced in extenso, I have given at the end, in Tables II and III, as 
a typical example, only the observations and the results calculated for a 
sample of red clay from the Pacific Ocean. From 60 to 110 observations 
were taken with the other deposits, according to the character of the sample. 
In all cases the depth of the liquid was h = 20 cm. The measurements 
were made (May 5th to 25th, 1915) by my assistant, Mr Gustav Larsson, 
under my supervision and control. 
Each sample was treated in the following manner. According to the 
* International Reports on Pedology , v, 257-312 (1915). 
