Chasles and the Ellipsoid Attraction

This chapter is divided into seven sections. The problem of the ellipsoid attraction was a subject to which many of the greatest physicists and mathematicians devoted their research, starting from Newton’s Principia onwards. Therefore, when Chasles had begun to deal with this topic the literature was already abundant. In the first section, I recall the main steps concerning the history of this subject because they are fundamental to understand the novelty of Chasles’ approach. The other sections are dedicated to his works, methods and results. Chasles campaigned for 6 years, from 1837 to 1842, to get to the bottom of the matter. His aim was methodological: he was going to determine the ellipsoid attraction by means of a synthetical approach and succeeded. The projective properties of the conics and of the transformations between conics, in particular polarity, played a crucial role in his research. Therefore, the attraction of ellipsoid is a further result that can be included within Chasles’ foundational programme.