” 
64 On the Laws of Absorption of Liquids by Porous Substances. 
sented by the general formula 
T=a(6°—1) —y log (S!+p—8), 
where a, @, y, and p are constants. 
When 8=1, this formula becomes the same as equation (1) ; 
and when y=0, or very small, it becomes 
Taa(S 3), o3. 2. a 
which is the general formula applying to the second class of 
filters. 
By differentiation, we find 
1 -s 
Sa peaeatie ne a = 904 pee 
v a log, 8 B ? ( ) 
which is a general formula for the rate of descent of the liquid. 
In the foregoing experiment, a=262°3, 8=1°355, and 
= ga b855™*. kt 2g 
Towards the close of the experiment the velocity of descent 
became exceedingly small, showing that the adhesion of the hquid 
to the bottom of the filter-tube interfered with the law of velo- 
city expressed by equation (8). 
This experiment being immediately repeated, it was found 
that the rate of filtration had sensibly diminished, showing that 
the filtermg power of the paper had undergone a decided change 
during the process of filtration. This change, as will be here- 
after shown, is progressive, being in proportion (within certain 
limits) to the quantity of liquid filtered. But after the filter had 
been dried, it somewhat regained its original power. 
In this manner various experiments were made, which gave 
precisely similar results. 
Although the liquid in these experiments had been carefully 
filtered through ordinary filtermg-paper, yet it is possible that 
certain minute particles may have passed through the filter, suffi- 
cient to deteriorate the filtering power of a small filtering surface 
such as that used in the foregoing experiment. 
The following experiments were made on upward filtration. 
Experiment XXIII. 
In this experiment the filter was immersed in a jar of liquid 
to the depth of 7 units of the filter-tube. As the liquid rose in 
the tube through the filter, the liquid in the jar was maintained 
at a constant level. The filter was the unsized paper of the last 
experiment, the diameter of the plate being ;4ths of an inch. 
The liquid was a diluted solution of carbonate of soda. 
