equally applicable to any 
other, and hence to the whole 
: 
MOSSOTTI ON CAPILLARY PHZ NOMENA. 569 
raised column of fluid shall counteract the force of tension of 
the two lateral sheets, the motion will cease and there will be 
equilibrium. 
' The object of the capillary theory is to determine the con- 
ditions of equilibrium of a fluid in these and in other similar 
cases. 
' 5. To give some idea of the manner in which these conditions 
must be considered, we must premise some notions on the pro- 
perties of curved surfaces subject to any pressure or tension. It 
is proved in statics, that if any surface be acted on at every 
point by forces normal to it, it will suffer a constant pressure or 
tension in every part, and the force which acts at each point is 
equal to the product of this tension by the sum of the inverse 
yalues of the radii of maximum and minimum curvature, or in 
general of the radii of curvature of two sections at right angles. 
To explain this proposition by an example, suppose that on a 
solid cylindrical surface 2 piece of cloth or any flexible surface 
be kept stretched by means of forces applied at its extremities 
perpendicular to the axis and tangent to the surface. It will be 
sufficient in this case to consider the equilibrium of a single zone 
or section made perpendicu- 
larly to the axis, since what 
is said of this section will be 
Fig. 1. 
M 
cloth. Let A M B then (fig. 
1) be this section, P the tan- 
gential forces applied at Aand 
B, that keep the correspond- 
ing belt of cloth stretched: 
since this belt can exert only a normal pressure on the arc be- 
neath it, its tension must be constant along its whole length and 
equal to P, and the force of pressure which it exerts on any 
point M of the arc A M B will be in the inverse ratio of the 
radius C M of the osculating circle of the curve at the point M; 
the other radius of curvature being in this case infinite, its inverse 
value is therefore zero. 
The tension of this belt may serve to represent an image of 
_ the force of contraction of the surface of a fluid in a section con- 
tained between two solid planes parallel and very near to each 
other, and made perpendicular to them. As the molecular 
