Floating

In his 1611 experiments on floating, Galileo attempted to answer the question whether shape plays any role in floating, or whether floating is determined entirely by density. The history of the controversy was such that he was committed to upholding and defending Archimedes' Principle, that floating is determined entirely by density: anything that is denser than water sinks, anything that is less dense floats.

His opponents introduced something that was more dense than water, but nonetheless floated when it was the right shape, a chip of ebony. In their minds it was "case closed."

Galileo's approach was different. He argued ingeniously that their counterexample was not all that it seemed. He also did his own experiments, and noticed things that were a surprise to him. Perhaps most impressive, he managed to separate and control the two experimental variables, density and shape, by using soft wax, capable of assuming different shapes, and capable of assuming different densities if one worked metal filings into it.

Here are some things to try:

(1) Float a needle in a cup. Use initially dry tissue paper to help float the needle initially, then tease the paper away to leave the needle afloat. (Put the cup with your floating needle on the central table near the blackboard, and have a careful look at all the needles before you leave for the afternoon.)

(2) Try floating a chocolate chip both ways -- point down and base down. Galileo used this example in one of his typical "reversal" type arguments. It was just the opposite of what his opponents would (presumably) have said: with the point down, and thus well able to penetrate the water, it floats, but with the base down, and thus less able to penetrate the water, it sinks!

(3) Try to add density to a lump of beeswax to bring it to exactly the density of water (there will be little bits of copper wire to stick into the wax to increase its density). Galileo was interested to notice that he couldn't seem to get the densities exactly the same, and makes use of this observation in his arguments.

(4) Add density to a lump of beeswax until it is so nearly the density of water that it floats with the removal of one small bit of copper and sinks when that bit is replaced. Then change the shape to make it flatter (and more resistant to sinking?), and see if its behavior is different.

(5) Galileo claimed that on the basis of experiments like these, anyone could prove that shape was not the cause of floating. Is it really so clear cut? Textbooks sometimes say the Scientific Method is recourse to experiment: we do the experiment, and we see what is true (in this case, the effect of shape). Well, you have done the experiment. What did it tell you? Be scrupulously honest!