738 
ME. HOPKINS ON THE THEOET OE THE MOTION OF OLACTEES. 
Now, manifestly, the atmospheric pressure, acting equally in all directions, can contri- 
bute nothing to this effect ; nor can there be an upward pressure on the base E F of the 
raised column of water ; for the pressure at any point of that base can only be equal to 
that at any point in the surface of the external fluid, which, neglecting the pre^re of 
the atmosphere (as we may do from what has just been stated), will be zero. Again, 
the resultant attraction of the tube on any single particle of the fluid must be in a 
direction perpendicular to the surface of the tube, and. must therefore be horizontal. 
Consequently it can produce directly no force on the particle or on the whole mass of 
the fluid column in a vertical direction. The direct effect of gravity, on the contrary, 
is to drag the whole column of water downwards, and the leading point in the problem 
of capillary action is to explain how this tendency of gravity is counteracted. 
In a question like this, which is merely subsidiary to the general problem treated on 
in this paper, it must suffice that I quote those results which are familiar to every one 
acquainted with the ordinary investigations respecting capillary action. Now it is 
shown by such investigations that the fluid column A E F B is supported (so far as regards 
any vertical action upon it) in the same manner as if it were suspended freely from an 
inflnitely thin and perfectly flexible membrane accurately coinciding with the actual 
surface A C B, the particles of the fluid being supposed to adhere to the membrane and 
to each other by virtue of the cohesion or attraction between them, -without which, in 
fact, the ordinary phenomena of capillarity could not exist. 
If the column of water in the tube were entirely supported by an upward pressure 
on its base E F, then would gravity produce a pressure on any horizontal section Q M P, 
the whole amount of which would be the weight of the portion of the column above it, 
and there would be a corresponding pressure on the inner surface of the tube at P and. 
Q, tending to push it outwards ; but if the column were supported, as above supposed, 
at its upper surface, gravity would produce a tension at the horizontal plane Q M P, the 
whole amount of which would be equal to the weight of the fluid between Q P and the 
base EF. Thus the whole column would be in a state of longitudinal tension, and 
therefore also, by the fundamental property of fluids, in a state of horizontal tension — 
i. e. the action between the fluid and the inner surface of the solid tube, instead of being 
a pressure, must be a tension, supported by the mutual attraction between the particles 
of the solid and those of the fluid, supposing the contact between them not to be broken. 
This must be the direct effect of gravity in the actual case ; and so far, therefore, its 
tendency is to contract and not to enlarge the diameter of the tube. 
There are other causes, however, by which action may be produced between the tube 
and the contained fluid. First, a pressure will necessarily arise from the mutual attrac- 
tion between the tube and the fluid ; but here we have the action of the fluid on the 
tube, and the reaction of the tube on the fluid, the one tending to pull the surface of 
the tube inwards, and the other to push it outwards. The action and reaction thus 
counteract each other, and the pressure thus produced can manifestly have no tendency 
either to expand or contract the tube. 
