Laws of Absorption of Liquids by Porous Substances. 59 
The near coincidence of the results im the third and fourth 
columns shows that the velocity of discharge varies digectly as the 
height of the column of liquid upon the filter. 
Let S! = the whole depth of the liquid at the commencement 
of the experiment, in umits of the divisions of the filtrometer ; 
S =the descent of the liquid in the time T; v = the corre- 
sponding velocity of descent ; «, y, p = constants ; then we have 
generally, 
T=a—ylog (S'+p—S). ... . (1) 
By differentiation, we get 
dS __ log.10,, 
7 (S’-+e—S) ; 
2°30258 
= orice e -@ . ° ° ° ° (3) 
2°30258 1 
~ 2037 
relation of time and space is expressed by the formula 
T= 415:74— 460'4 log fea cn 2s) (A) 
This experiment, upon being repeated, gave a slight diminu- 
tion in the velocity of descent of the liquid, showing that the 
- filter had undergone only a very slight change during the pro- 
cess of filtration. This observation applies to the filters used in 
the three following experiments. 
Experiment XVII. 
The filter in this experiment was coke, ;4,ths of an inch in 
thickness. The liquid was distilled water. The diameter of the 
orifice of the plate was 7/j;ths of an inch. The filter-tube was 
the same as in the last experiment, and the temperature was 57° 
throughout the experiment. 
In the foregoing experiment, p=0, 
e 
Height of Cc : Corresp. Value of v 
column of |Corresp- 4ME€! velocity of | by formula 
liquid, oo sceoude, descent, h 
h. +3 a v. v= 205. 
8 0 Pe os 
7 27 29 29 
6 59 Ba Bq 
+ 99 40 ar 
4 139 = sr 
3 195 es os 
2 279 wh zis 
1 460 
