The catenaries which lie beyond the two generate surfaces whose radius of curvature convex towards the axis in the meridian plane is greater than the radius of concave curvature.

The radius of curvature of a catenary is equal and opposite to the portion of the normal intercepted by the directrix of the catenary.

We know that the radius of curvature of a surface of revolution in the plane normal to the meridian plane is the portion of the normal intercepted by the axis of revolution.

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The catenaries which lie between the two whose direction coincides with the axis of revolution generate surfaces whose radius of curvature convex towards the axis in the meridian plane is less than the radius of concave curvature.

At any point a sounding line would hang in the line of the radius of curvature of the water surface.