570 MOSSOTTI ON CAPILLARY PHA NOMENA. 
Fig. 2. action extends only to inappreciable di- 
stances, if we suppose that at any point 
M (fig. 2) of such a section, and at a 
~ sensible distance from the planes, an 
osculating circle be described, all the 
molecules which in the same section 
exert a sensible action on a thread of 
fluid normal to the surface at the point 
M may be considered as contained within 
this circle; and since the density along 
the surface at a sensible distance from 
the planes varies only by insensible de- 
grees, the resultant of the actions of all these molecules will 
be in the direction of the radius of curvature C M, that is nor- 
mal {o the surface, since everything may be supposed sym- 
metrical on either side. Hence it follows that the tension of the 
fluid along the surface, arising from the greater rarefaction of the 
molecules, will be the same at every point, and the resultant of the 
excess of the attraction above the repulsion between the parts of 
the fluid will be in the inverse ratio of the radius of curvature. 
Nor ¢an the tension be different at different surfaces of the 
same fluid, since as the molecular forces act only at insensible 
distances, the resultant of the forces corresponding to any one 
point of the surface cannot vary as long as the position of the 
fluid about that point continues the same, that is to say as long 
as the radius of curvature does not change. In order then that 
the tension may be the same for two surfaces, it will suffice that 
they meet so as to have for one of their points of intersection 
two equal radii of curvature. The tension is therefore indepen- 
dent of the nature of the surface, and is equal to that which 
we have found to exist in a plane surface. We shall call T the 
value of this tension. 
6. Now let us consider the case in which the fluid is depressed 
between the two planes. In this case the action of the substance 
of the planes on the molecules of the liquid must be less than 
that of the fluid on itself. If the substance of the planes exerted 
an equal action, the fluid in contact with them would have the 
same density as it has internally ; if their substance exerted no 
action, the fluid along the planes would be equally rarefied with 
the free surface. The action of the planes being intermediate 
between these two limits, the contiguous stratum of the fluid. 
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