Laws of Absorption of Liquids by Porous Substances. 117 
fully filtered through ordinary filtering-paper. The discharge 
was produced by downward filtration, the exterior portion of the 
filter being exposed to the air. The pressure on the filter, 
throughout the experiment, was produced by a column of 15 
inches of the liquid; and the temperature was carefully main- 
tained at 51° throughout the experiment. The successive inter- 
vals of time requisite for the discharge of one cubic inch of 
water were noted, and recorded in the following Table of results. 
Succession of |corresp. time in Value of T by 
cubic inches minutes for each formula 
Heehateed, puemeh; piled = 3°16 x 1497 1 
1st cub. in. 3°16 3°16 
2nd .,, 4:56 4:49 
and ,; 6°36 6°37 
Ath ,, 9:00 9-05 
BSth. 5, 13°50 12-85 
6th ,, 18:00 18°24 
Pulte 55 26:00 25°91 
Sih. ,; 33°00 36°80 
Here the near coincidence of the results in the second and 
third columns shows that, under a constant pressure on the filter 
(within certain limits), the times requisite to produce equal suc- 
cessive quantities of discharge are in geometrical progression. 
At or near to the eighth cubic inch of water discharged the 
progression seemed to have reached its limit; for the time required 
for the diseharge of the succeeding cubic inch was found to be 
nearly the same as that of the eighth cubic inch. 
The experiment, as above recorded, extended over a period of 
two hours nearly, and during that time the rate of filtration had 
changed from seth of a cubic inch per minute to s.rd of a 
cubic inch; that is, the rate of filtration had decreased eleven 
times nearly. 
I offer no hypothesis on these remarkable results, beyond the 
mere statement of the fact that during the process of filtration 
these filters undergo a progressive molecular change, causing the 
rate of filtration to decrease according to a general law expressed 
by the formula T,,_,;=a B"—1, where « and B are constants for 
each particular filter, and 'T,_, is the time required to filter the 
nth unit of water. 
At the close of the foregoing experiment, the water being dis- 
charged, the tube was filled with water by upward filtration, and 
then, this water being allowed to discharge itself by downward 
filtration, it was found that one cubic inch of water was dis- 
charged in 156 minutes, showing that by thus reversing the 
