I think you would probably not be able to. Any instrument you would use would melt and burn up before you ever even got to the hot center of the earth. Its quite hot down there. Anyone ever blame the earths core for global warming? Consider this the first.

if said hole could exist, more like a tunnel, all the way through the earth from one end to the other; gravity, presuming it were still the same and the earth didnt collapse a litte in on itself due to the hole, gravity would pull you to the center. you would most likely have enough inertia, once again presuming this is a hypothetical and you could reach terminal velocity without melting, you would go through the center and make it about half way through the other side, or roughly three quartes all the way through the earth before gravity slowed your descent/ascent and began to pull you back towards the center. much like a yo-yo or a rubber ball. if you drop a rubber ball it will only bounce about half way to three quarters of its original drop height. hence the same might be true for a human passing through the quasi-bowel created on our blue planet.