There are quite a few things one should never do to an old house (any house for that matter). One of them is illustrated quite clearly here, which is cutting almost completely through a floor joist to run hot air ducting. This was undoubtedly done by the company who supplied the furnace for the changeover from hot water.
Floor joists are sized and installed, believe it or not, to support the load of the floor, the occupants of the house, and the walls above, and should never be hacked apart in such a fashion. Luckily the floor hasn't sagged much, and I have enough room to 'sister' a plywood brace into position, after figuring out what to do with the wiring. Not to the right, the newly relocated duct which is running to the upstairs bathroom, and shortens the duct length by about 16 feet.