Right now, the rheostat is the ONLY resistance in the circuit. If it's replaced with a short copper wire, then there's no resistance at all between the terminals of the battery.
As soon as you go to close the switch:
-- There's a big spark at the switch.
-- There's an audible "click", as the needle of the Ammeter slams into the peg at the top of its scale. (It's trying to read infinite, or very very large, current.)
-- The meter could burn out very quickly. If it doesn't, then
-- Somewhere between the battery and the Ammeter, or between the Ammeter and the switch, or between the switch and the battery, the WIRE will get very hot, and try to behave like an electric toaster. If the wire is bare, you'll see it glow red. If the wire has plastic or rubber insulation on it, the insulation will smoke.
-- The batteries will get hot, and quickly die.
