pillary tube, MNP the surface of the water in 
the vessel, Iz the height of its ascent, VIZ the 
concave surface of the fluid column, and IKLM 
an indefinitely small column of fluid reaching to 
the surface at M. Now the column ML is soli- 
cited by the force of gravity which acts through 
the whole extent of the column, and by the reci- 
procal attraction of the molecule, which, though 
they act the same in all the points of the column, 
only exhibit their effect towards the extremity 
M. If any particle e is taken ata less distance 
from the surface than the distance at which the 
| attraction of the liquid generally terminates, and 
if m n is a plane parallel to MN, and at the same 
|| distance from the particle e, then this particle 
will be equally attracted by the water between 
the planes MN, mn. The water, however, below 
/m n, will attract the particle downwards, and 
| this effect will take place as far as the distance 
| where the attraction ceases. 
| on the other hand, which is in a state of equili- 
The column IK, 
brium with ML, is acted upon by the force of 
gravity through the whole extent of the column, 
also by other forces at the upper and lower ex- 
tremities of the tube. The forces exerted at the 
upper part of the column, are the attraction of 
_the tube upon the particles of water, and the 
_ reciprocal attraction of these particles; but as 
every particle is as much drawn upwards as 
downwards by the first of these forces, the con- 
sideration of it may be dropped. In order to 
estimate the other force, let a horizontal plane 
VX touch the concavity at I, a particle p, situ- 
ated infinitely near to I, is attracted by all the 
particles above VX, and by all below it whose 
sphere of activity comprehends that particle ; 
and as the particles above p are fewer than those 
| below it, the result of these forces must be a 
force acting downwards. In order to estimate 
the value of the forces which act at the lower 
end O of the tube, let us suppose that the tube 
has a prolongation to the bottom of the vessel, 
formed of matter of the same density as the 
water. Let a particle R be situated a little 
above the extremity of the tube, and another Q 
as much below that extremity, they will be 
equally acted upon by the water above that 
place, and by the water between the fictitious 
prolongation of the tube, and therefore these 
forces will destroy one another. By applying to 
the case of the particle R the same reasoning 
that was used for the particle e, it will appear, 
that the result of its attraction by the tube is an 
attraction upwards. The particle R ‘is likewise 
attracted downwards by the supposed prolonga- 
tion of the tube, and the difference between 
these is the real effect. The other particle Q is 
| also drawn upwards by the tube with the same 
{—___ 
force as R, since, by the hypothesis, it is as far 
distant from the points, D, G, as the particle R 
is from the points d, g, where, with respect to it, 
the real attraction of the tube commences. The 
particle Q is attracted also downwards, by the 
CAPILLARY ATTRACTION. 
supposed prolongation of the tube, and the dif- | 
ference of these actions is the real effect. Hence 
the double of this force is the sum of all the 
forces that act at the lower part of the tube. 
These forces, when combined with those exerted 
at the top of the tube, and with the force of 
gravity, give the total expression, which should be 
combined with that of the forces with which the 
column MUI is actuated. Clairaut then observes, 
that there is an infinitude of possible laws of 
attraction which will give a sensible quantity 
for the elevation of the fluid above the level MN 
when the diameter of the tube is very small, and 
a quantity next to nothing when the diameter 
is considerable ; and he remarks, that we may 
select the law which gives the inverse ratio be- 
tween the diameter of the tube and the height 
of the liquid, conformable to Exp. 4. 
The subject of capillary attraction was next 
taken up by Segner in 1751, who referred all the 
phenomena to the attraction of the superficial 
particles of the fluids. He deduces this prin- 
ciple from the doctrine of attraction. He sup- 
poses the attraction of the tube to be ingensible 
at sensible distances; and he has shown that the 
curvature of each part of the surface of a fluid is 
proportional to its distance from the general 
level; and without much error, he has obtained 
from experiments the magnitude of this curva- 
ture at a given height both for water and mer- 
cury. M. Monge followed Segner in ascribing the 
capillary phenomena to the cohesive attraction 
of the superficial particles of the fluids; and he 
maintains that the surfaces must be formed into 
curves of the nature of lintearize, resulting from 
the uniform tension of a surface resisting the 
pressure of a fluid, which is either uniform, or 
varies according to a given law. 
In a very ingenious paper on the cohesion of 
fluids, read by Dr. Young in the Royal Society 
in 1805, that able mathematician gave a new 
theory of capillary attraction. He reduced all 
the phenomena of cohesion to the joint operation 
of a cohesive and a repulsive force, which balance 
each other in the internal parts of a fluid, where 
the particles are brought so near that the repul- 
sion is exactly equal to the cohesive force by 
which they are attracted; and he assumed only, 
that the repulsion is more increased than the 
cohesion, by the mutual approach of the parti- 
cles. More than a year after the publication of 
Dr. Young’s paper, M. La Place published a Sup- - 
plement to the ‘ Mecanique Celeste,’ upon capil- 
lary attraction, where he proposed a theory 
which led him to several conclusions that Dr. 
Young had already obtained by a more simple 
route. la Place supposes, from Exp. 11 and,18, 
that capillary action, like the refractive force, 
and the chemical affinities, is only sensible at 
imperceptible distances; that a narrow ring of 
glass immediately above the surface of the fluid, 
exerts its force on the water ; and that this force, 
combined with the weight of the water and the 
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