572 MOSSOTTI ON CAPILLARY PHANOMENA. 
weight which would balance the external pressure, this will icanll 
sure the two vertical tensions, and calling o the thickness of the 
section along the length of which the tension T — © acts, we 
shall have 
P=2(T—@0)c=2T oc cosa... web ogi) 
7. The second case, in which the action of the planes on the 
liquid being greater than that of the fluid on itself, the fluid is 
compressed and rises along the planes, is easier to consider. 
The fluid stratum which covers the planes forms a continuation 
of the rest of the free surface of the fluid, which thus on either 
side becomes tangent to the planes. As that stratum has always 
a thickness greater than the inappreciable distance at which the 
molecular forces act, its external surface rapidly decreases in 
density and acquires a tension equal to that of the free surface. 
Thus on either side the free surface is acted on by a vertical 
tension which raises it up. As it rises the molecules beneath 
become rarefied, they acquire a force of tension owing to the 
rising of the free surface, and they follow its motion, which 
ceases when the weight of the raised column of fluid counteracts 
the two lateral tensions. If then we call P the weight of this 
column, we shall have 
P si? Dihos ai sis eure ee (2.) 
8. We can now, from the equations (1.) and (2.), deduce the 
experimental law which we enunciated at the beginning, that the 
elevations or depressions of the same fluid between two planes 
are in the inverse ratio of the distances between the planes; for 
let d be the distance between the planes, a the depression or ele- 
vation of the fluid between them below or above the external 
level, and since the distance d is supposed very small, and the 
weight of the fluid which would fill up the convexity or concavity 
of the upper extremity of the column may be neglected, if we 
call g the force of gravity and A the density of the fluid, the 
weight P will be expressed approximately by gy. A.o.d.a, and 
equations (1.) and (2.) will thus give 
gAcda=2(T—O0)c=2Tc cosa, 
gAcda=2Ts, 
whence we get 
ea Crane Ringe 
The coefficient of = being constant in all cases for the same 
