If the wall is running at right angles to the joists above it, it is load-bearing. Even if only 4 feet long, you shouldn't tear it out without at least investigating whether you will have adequate structure remaining. Even as new as the 1940s, houses were often under-engineered in those days, so a little change can be critical.

Walls running perpindicular do not necessarily indicate a load bearing wall, but could signifigantly have importance supporting the ceiling joists, as matt stated, a 40's house more than likely is underengineered.I've seen 2x4 joists on older homes, so removing a fairly large spanned section will result in ceiling sag. Your joists might also splice on the wall depending on span. Load bearing concerns bracing off the wall as a means of support to the roof framing calc'd for snow load, roofing weight, etc.This is commonly referred to as live load.The wall is generally supported below by a footer if on a slab, or piers if on a crawl space/basement.The wall supports the roof framing above. If you have short spans with no bracing to the roof framing, your joists aren't spliced on the wall, and the ceiling joists are structurally sound to carry across without wall support, then you would be safe to remove them. The best bet is to pay, (usually around $300), for a structural engineer to come out and give you a detailed inspection of your project.