Archimedes' Principle and Capillarity

Archimedes' principle may be used to predict when and how an object places into a bath of liquid will float. Certain inconsistencies with the predictions of the principle have been pointed out since the time of Gallileo, but have only recently been understood in something approaching a quantative manner.

I will outline previous results concerning floating objects and describe one of my own which gives some quantitative information about the shape of the liquid interface and the attitude with which a sphere may float. As an aside, I will describe the predominant reinterpretation of Archimedes' principle which likely has played a role in delaying the appearance of such results.