If it's leaking long after the shower has ended, it may be a supply line problem, OR, it could be the trap or drain line has given up (i.e., corroded away). A couple of things to check on the tub: take a long level and see if the tub is level; make sure the drain basket is tight and not loose; make sure that the overflow gasket is intact - it could be dry rotted and fall apart; see if you can move the trim from the shower arm away and if there's any space, see if there's any water visible behind there; do the same for the shower valve, if possible. You may be able to see leaks behind the wall. If the tub is original, and 75 years old, the plumbing is ancient as well. Touch it, and it may fall apart! I did some work at my mother's house, and just looked at the tub trap...it fell apart, and her's was put in in the early 50's.