NOTE ON A CAPILLARY PHA NOMENON, 579 
the fluid is rarefied to such a degree that the sum of repulsive 
and attractive actions of the internal molecules on a molecule 
situated in the surface is zero. If the surface of the fluid be not 
free, but there be another fluid contiguous to it, the contractile 
force diminishes, for the rarefaction of the fluid in which the 
molecular forces are more powerful is carried only to such a 
degree that the sum of the actions of the internal molecules on 
a molecule placed in the surface of contact of the two fluids shall 
be equal to the sum of the actions that are exerted on the 
same molecule by the fluid in which the molecular forces are less 
energetic. By means of this rapid decrease of density in the 
neighbourhood of the surface of contact between the two fluids 
_ the passage takes place from the more energetic state of the mo- 
lecular forces of the first fluid, to the less energetic state of those 
of the second without altering the total equilibrium of the masses. 
These results are the necessary consequences of the theory that 
we have developed in the above-named lecture to explain the 
capillary phenomena. 
3. In accordance with these principles, let us represent by T 
the constant force of tension that arises in the surface of con- 
tact between the two fluids in consequence of the above-men- 
tioned decrease in density, and let us imagine a small fluid thread 
at a perceptible distance from the sides of a small cylindrical 
tube, terminating internally at the upper surface of the upper 
fluid and externally at the free surface of the lower fluid. Divi- 
ding the internal part of the fluid thread corresponding to the 
upper fluid into two portions, we shall easily see (following the 
same reasoning that was employed in § 9 of the above-named 
lecture) that the equations for the particular equilibrium of these 
two portions will be 
1 1 
Nes -9=T(-+-5) 
g A ( ) Q Fi 
1 1 
gA(b— 2) +942, +=, (—-+ =r) 
i i 
where 4 denotes the height of the point of division between the 
two portions above the level of the external fluid, and © the 
pressure or tension to which the fluid is subject at that point. 
The other letters have the same meaning as in the above-named 
lecture, and the accents serve to denote the analogous qualities 
in the lower fluid. 
The horizontal section of the small fluid column at the height 
4 being a surface of level, since the resultant of all the forces is 
