[withinboredom]

Umm. I’m pretty sure if water that exists above the water line is melted into the water line, the overall water line will rise. You can directly observe this in a glass of ice that starts with no liquid water will melt into a glass of liquid water.

[nrclark]

I could be wrong about this (it's been awhile since I took chemistry), but I think the ice has to be floating for the Archimedes principle to apply.

You can fill a glass of ice-water right up to the brim, and it won't spill over as the ice melts. But only if the ice is floating in the water. It's because the ice's mass pushes down on the liquid water, displacing a fixed amount relative to the weight of the ice.

[withinboredom]

Ah. I missed the “floating” part. That makes sense.

[brilee]

This is untrue.

Ice is about 91% the density of water. If you have water at 0 height, and you put in water equivalent to +1 unit of height. If it's in liquid form, obviously height goes up by +1. If it's in ice form, there is +1.09 height worth of ice (because it expands when it freezes), but it only displaces water up to +1 unit of height in order to support its weight through buoyancy. The overall change in height is +1 unit regardless of whether it's liquid or ice