The stability of a meniscus joining a vertical rod to a bath of liquid

A circular cylinder is held vertically and withdrawn from a large bath of liquid. When the horizontal end face of the cylinder rises above the mean undisturbed liquid level, an axially symmetrical meniscus is formed, which joins the cylinder at the circumference of the end. If the cylinder is further withdrawn, at a certain height the meniscus breaks. By means of the calculus of variations the condition for stability is derived in terms of the increase in height and the increase in the angle between the tangent to the meniscus and the face of the cylinder at the point where the meniscus joins it. The meniscus is unstable as long as these changes are of the same sign.