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- The only surface of revolution having this property is the
**catenoid**formed by the revolution of a catenary about its directrix. - This
**catenoid**, however, is in stable equilibrium only when the portion considered is such that the tangents to the catenary at its extremities intersect before they reach the directrix. - Hence a
**catenoid**whose directrix coincides with the axis of revolution has at every point its principal radii of curvature equal and opposite, so that the mean curvature of the surface is zero. - Hence if a film in the form of the
**catenoid**which is nearest the axis is ever so slightly displaced from the axis it will move farther from the axis till it reaches the other**catenoid**. - Hence if a film in the form of the
**catenoid**which is nearest the axis be displaced towards the axis, it will tend to move farther towards the axis and will collapse.

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