238 Proceedings of the Koyal Society of Edinburgh. [Sess. 
Similarly, for the next following intervals 
p=n-r r , l 
Pr+l = 22/r+l8f + 2 V+ 
P = 2 L 
P=n—r r , 2 
^r+2 = Vr+'fit + r pVr+iM • 
Hence 
SR 
SP r+ i — P,. +2 
p=2 J 
or 
r 1 p=»- 
=^.-p, “*h+i*+i+2 
*— _p =2 
r l p=n-r J -j 
r + 2 yr t a + 2 r + p^ r+p j 
A*P\ 1 , ^ 1 
^p 
dt )r+l *^2 ?A ' +2+ 2 
P =3 
r + 2 
.yr+p 
Then by subtraction 
which may be written 
dP\ 
dt ) 
(PP\ 
dtVr 
r + 1 
/dP\ _ 1 
\dt )r r+ 
Vr + 1 
?/r+l 
r+1 (r + 1)S^ f r+1 
Now the whole deposit due to y r+l is 
1 
~i)Vr+l tr + 1 
ty_ I! 
where P is the measured deposit at the time t r+1 due to all the sets of 
particles falling together. 
If we obtain, by Sven Oden’s method of continuous weighing, the 
gradually accumulating deposit and plot this against the time, we get the 
accumulation-curve P =f(t). 
1 ,d 2 P 
From this we construct f° r successive 
given instants of time, and plotting these values against the times we get 
a distribution-curve whose ordinates represent the relative quantities of 
particles whose times of fall are the corresponding abscissae. Or we may 
use for abscissa the terminal velocity corresponding to the time of fall 
through the given height, h , of the column of liquid, namely, 
v — hjt. 
This is all that can be done without making more or less doubtful 
assumptions as to the density, form, and size of the particles. The applica- 
tion of Stokes’s formula gives what Dr Sven Oden calls the “effective 
radius,” and this may be regarded as affording a good approximation to 
