Edme Mariotte's legacy

During the 17th Century, Edme Mariotte observed that floating rigid bodies could attract or repel each other, and he attempted to develop a quantitative description of the phenomenon. He did not succeed, which in retrospect is not a surprise, as the behavior seems to depend on surface tension, for which there was no conceptual theory at that time. There are now elaborate surface tension theories, nevertheless very little quantitative information on the original question has appeared. I will describe some recent progress on a simplified model proposed by Laplace in 1806. This is nominally the second of two lectures, but was delayed due to unfortunate circumstances; I have reorganized it to be self-contained.