Archimedes und die Stabilität von Schiffen

Abstract

Archimedes, an outstanding mathematician, natural scientist and engineer of antiquity, is widely known for having established the hydrostatic principle of the balance between the buoyancy and displacement forces of floating bodies. Much less well-known, however, are his equally significant achievements in the development of a criterion for the hydrostatic stability of such bodies and thus of ships, comparable in a sense to the concept of a positive lever arm of the righting aspect of these forces. This lack of fame is surprising, considering that his unusual ideas on stability, demonstrated in the example of the simple form of a rotation paraboloid, appeared in the same extant treatise that contains the basic principle of hydrostatics: On Floating Bodies. Yet Archimedes’ treatises are seldom read carefully. The study at hand therefore takes a closer look at the treatises on which his contributions to the subject are based. An explanation is provided for his ability to calculate lever arms despite the fact that he did not have the methods of integral calculus at his disposal. Finally the article provides an account of the adventurous paths by which this nearly forgotten knowledge of Archimedes reached modern times, and how it contributed to the reestablishment of the stability theory, above all by Pierre Bouguer and Leonhard Euler. Within this context, light is shed upon those aspects of the knowledge of antiquity that serve as the roots for our present-day understanding of the stability of ships.