370 TRANSACTIONS OF TIIE PHARMACEUTICAL SOCIETY. 
rate of flow until the medium is impervious. And now the pressure on the 
upper surface of the medium really is wholly hydrostatic, but the instrument is 
no longer a filter. 
Conclusion. 
We (hearers, readers, and myself) have now studied one small paragraph of 
one of the great chapters of nature’s great book. And, like true students of 
nature, we have studied her for her own sake. Yet all natural facts must have 
their application ; and so we will not be content with the pleasure we may have 
obtained from our work, but will endeavour to deduce some useful lessons from it. 
The practical applications of the truths we have been considering, are for the 
most part obvious, and already well known to all. But of what new value are 
they ? as follows:— 
Firstly, these observations and experiments give us, I think, clearer, more 
correct views of the nature of the operation of filtration, than most of us had 
before. We should, 1 think, regard filtration under any and all circumstances 
from a hydrodynamic point of view. We should regard it as the flow of a liquid 
from an orifice in the vessel containing the liquid, the flow being interfered with 
or resisted, to a greater or less degree, by a porous fabric, termed a filtering 
medium. The rate of flow we should regard as normally following that de- 
cribed in the theorem of Torricelli, namely, in proportion to the square root of 
the distance from the orifice of outflow to the surface of the filtering-liquid ; or, 
as the law may perhaps be stated for our purpose, u the rate of flow is propor¬ 
tionate to the square root of the power,” whether that power be derived from 
gravitation, muscular or mechanical force, or the elasticity of compressed air or 
steam. As the flow becomes slower and slower, the manifestation of this dynamic 
law becomes less and less evident, and the existence of a static lav/, in the in¬ 
strument, more and more evident, until, when the flow ceases altogether, a static 
pressure only exists within the apparatus: hydrostatic in the common conical 
and other simple filters, the filter-bag pressed in the various ways, and the filter 
in which there is a column of liquid above the medium ; aerostatic where the air 
is removed from below a medium or additional air, etc., forced on the filtering 
mixture from above, or where there is a column of liquid maintained below the 
medium. As a filtering medium always presents some resistance, dynamic laws 
can never apparently exclusively obtain in a filtering apparatus, though they 
nearly do so in the filtration of water on the large scale. So also, as that 
resistance can never be complete, filtration can never be a static operation, nor 
can static laws exclusively obtain in a filtering apparatus, until the latter ceases 
to be a filter, though they nearly do so when the filtered liquid is escaping drop 
by drop, as may generally be seen in an analyst’s filter. Though, however, a 
•filtering apparatus can never be the exclusive seat of either dynamic or of static 
laws, it is quite possible that the flow from the apparatus is governed purely by 
dynamic laws. The rate of flow does not appear to be a pure dynamic rate, 
probably because we can only compare it with the total amount of force applied. 
But a portion of that force is expended in producing static pressure within the 
instrument; the residue, if we could estimate it, would probably show that the flow 
from the filter is actually, though not apparently, a flow proportionate to the square 
root of the amount of force which produces it. For instance, a filter is giving a 
certain number of drops per minute, under a certain amount of force; double the 
amount of force, and we get nearly double the number of drops: in the first case, 
nearly all the force applied is expended in producing static pressure within the 
instrument, the residue being expended in producing the flow ; in the second 
case, also, nearly all the force is expended in producing static pressure within 
the instrument, but not quite twice as much as in the first case ; thus, probably, 
the residue of power is four times greater than in the first case, and hence we 
get a double flow. And so on, until, with a free orifice, there is no static pres- 
