makes no diff at all. There should be three wires coming in, two of them (likely red/black) will be hot, the third will be neutral/ground. The only one that matters where it goes is the neutral/ground; the other two are interchangeable as they are both 120VAC with respect to ground, just 180 degrees out of phase with each other.
+1 on having the meter pulled and re-evaluating your grounding situation. I'd also consider adding some kind of surge suppression at the panel if you live in an area that gets thunderstorms. I had a TVSS breaker in the panel at my last house and when a tree dropped a HV line onto a 240VAC line near the house I only lost a couple items (I think the control board for my dishwasher, power supply for the electrostatic air filter, and one really old surge protector/power strip) whereas a neighbor/coworker a block over lost a whole bunch of electronics including several TVs; PEPCO refused to pay for anything stating it was an "act of God" or some such... I can't say for sure that it saved me but having surge strips at all electronics plus the TVSS breaker seemed to be a prudent step.
Now after reading some of your replies, this fuse panel seems to be a *sub* panel to the new main panel which is located in the addition to the house, correct? If that is the case you should actually have FOUR conductors from the main panel to the fuse box; hot, hot, neutral and ground. The neutral and ground should be isolated from each other at the subpanel. Neutral and ground should be bonded together only at the main panel where the service entrance is, not any panels downstream.