Hole in earth - stone falling....

If it was possible to drill a hole in earth - passing center of earth. And then you dropped a stone in that hole - what would happen?

Would the stone come up in the other end - stop at highest point - and then return back. And for each turn making smaller and smaller turns, finally stopping at center of earth. Or would the stone stop at the first passage at center?

Assume that the stone don't melt or get stuck against the walls of course.

What do you think? What would happen to a stone that you drop in a hole drilled through whole earth?