anand@utastro.UUCP (Anand Sivaramakrishnan) (12/13/84)
All this talk about battleships seems to have confused the issue a bit. I find Archimedes' principle best understood if one throws the battleship out but retains the bath water... Think of a closed surface enclosing some water. The enclosed water has a certain weight, W (a vector pointing downwards). Now integrate the hydrostatic pressure over the surface surrounding this bit of water. What must the answer be? Since the water isn't flowing anywhere, the result of the integration is a vector of magnitude W, pointing straight up. Obviously the pressure at any point on this surface is not dependent on the shape of the container (as long as it is larger than the surface of interest), so we can discard as much of the surrounding water as we wish without affecting the value of the pressure integral. As a matter of fact, we can discard the complement of the smallest open set of water that includes the surface, if one is allowed mathematical water. Furthermore, this pressure integral does not depend on the nature of the substance within the enclosed surface, so we can replace the enclosed bit of water with shoes, sealing wax, cabbages or kings. Please note that the above discussion does not involve ships of any sort.