I recently bought an older home (1895) and have all hardwood floors. In the second floor I have a floorboard that is split and sags as you walk on it. How can this be fixed? Reinforced?
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.
For some reason that part of the floor is unsupported. Sometimes it is because a joist is warped and has a bow in it, or is badly cut and has a hollow on the top. If you remove the ceiling below you can potentially see what it is. Normally it is fixed by forcing in shims to the gap, but if the joist is warped over a length, it would be better to jack it. To do this, you take out the whole ceiling in that area and wet the wood, then jack it up about a 1/4" a week or so and hold it in place with a screw jack. Keep wetting the wood with a spray bottle. The jacks have to go to the foundation. So, in addition to the jack on the first floor, you need a jack in the basement holding the first floor firmly in place, because you don't want to push the first floor down at all.