Hardwood floor slat is split/sagging
I think the most likely cause is that a part of the subfloor has split/broken. You can attack this from below (messy!) or from above (hard to cut hardwood out nicely). The solution would be to support it from below, probably with  lumber screwed between joists (though there are many ways to do it).

If on the off chance you have a joist that's bad enough to require jacking, I'd suggest you have a bigger problem, as joists don't "go bad" after 100 years.