If the polar ice caps were to melt .

[SW VandeCarr]

:

When an object is floating in a liquid medium it displaces it weight in the medium. A thirteen ton boat will displace thirteen tons of water.

When that same object is totally immersed, it displaces its volume, not its weight. Since the rocks weigh more than the lake water, when totally immersed they will displace a volume that is less than the volume that they displaced by weight. The water level will be lower.

So when you throw rocks into a confined volume of water, the water level will drop?

 

[Evo]

Really? Try reading these peer reviewed papers.

http://onlinelibrary.wiley.com/doi/10.1111/j.1365-246X.2007.03472.x/abstract?systemMessage=Wiley+Online+Library+will+be+disrupted+6+Aug+from+10-12+BST+for+monthly+maintenance

http://efdl.cims.nyu.edu/publications/refereed/grl_melt_floating_ice_07.pdf (open access)

Noerdlinger demonstrates that melt water from sea ice and floating ice shelves could add 2.6% more water to the ocean than the water displaced by the ice, or the equivalent of approximately 4 centimeters (1.57 inches) of sea-level rise.

We're going to accept the above publications as the best answer, the difference being the consideration of fresh water added to salt water. If the icebergs were melting in freshwater, there would be no rise is water level.