576 MOSSOTTI ON CAPILLARY PHA.NOMENA. 
tension its molecules are separated; as the attractive forces are removed to a — 
greater distance, they are counteracted by the repulsive forces, but these decrease 
more rapidly than the former in proportion to the increased mutual distances 
between the molecules, and in consequence of this excess of attraction the fluid 
destroys the action that tends to separate the prism from the plane. ‘This last 
excess (of the attractive over the repulsive force) is always very small in fluids, 
since they do not offer much resistance to division ; still it exists, and various 
phenomena are known in which fluids show a sensible force of attraction before 
they are separated from the rest of the mass. 
“ From these considerations we must conclude, then, that in every fluid there 
exists between the molecules a certain space, in which the different parts of the 
fluid neither attract nor repel each other, and in which the fluid does not 
undergo any pressure or tension whatever, but is constituted in what we call 
a natural state. If this space be diminished, the parts of the fluid repel one an- 
other mutually, and sustain a pressure; vice versd if it be increased, the parts 
of the fluid attract one another mutually, and counteract a tension.” 
Nore 2. 
Formule for calculating some Phenomena of Capillary Action. 
1. The height a, to which a fluid rises between two vertical planes parallel 
and close to one another, and wetted by the fluid, is given by 
T T 
a=7-—r(i-+), 
2r 4 
2r being the distance between the planes, and x the ratio of the cireumference 
to its diameter. 
2. The depression — a of a fluid between two planes, as above, but not wet- 
ted by the fluid, is given by 
9 
iT Se 2) . 
—Aa= —r(+sin20+ 5 —* — cosa), 
r 4 2 4 
a being the angle of contact between the fluid and the planes, measured by the 
angle formed by the normal to the external surface of the fluid, and the perpen- 
dicular to the nearest plane. 
3. The height of a fluid in a small cylindrical and vertical tube is expressed 
b 2 
y pe od Sel « 
r 3 
r being the radius of a horizontal section of the tube. 
2 
A oe: : 
4. If the tube be rather wide, so that rg be a fraction, then we have 
tM AVE al cas 
os Lys 
where 
b= r +(/2—1)7. 
5. The depression in a small cylindrical vertical tube, not wetted by the 
fluid, is given by 
2 
tT COS 0 r re 2 
—¢ = = eh (cos + = sin'a— =). 
r cos? w 3 3 
as the molecules are condensed or separated from one another. That we must consider 
the molecules as separate, and employ the sums instead of the integrals, is clearly shown 
by the fact that the forces change their sign as the distances vary, as Poisson first 
observed. 
