Thanks very much to everyone who sent in a comment - I've now published these against the original post - here - and am pleased with the responses.
Yes, this is all about things which float, starring Archimedes - a man who was famous in my schooldays as someone who made his life's greatest discovery when he broke wind in the bath.
The puzzle is set out in yesterday's post.
When the stones are in the boat, they are floating - well, technically it is the boat that is floating, but the stones will push the boat down into the pool to displace an extra volume of water equal in weight to the weight of the stones themselves. This is where Archimedes comes in.
When the stones go over the side, they sink, and will now displace their own volume of water, which - since stones are more dense than water - is less than what they displaced when they were in the boat. Thus - yes, that's right - the water level on the side of the pool will go down. The only special case would be if the stones were able to float on their own (because they were pumice, or hollow, or fake stones made of wood, or because the water was polluted to an astonishing degree), in which case, of course, they would continue to displace their own weight of water, and the level would remain the same.
Once again, thanks very much for having a go. Some excellent answers, and some very good explanations of the less correct ones. Just to put an official seal on things, I was going to attempt this experiment today, but the bird bath is too small.