Thanks for your reply. What does RH stand for?
I know I have to replace the whole thing, the bottom bracket I linked to on Harris Cyclery is french threaded (so I'm assuming 35mm) but I'm not sure how to determine the other size (103mm, 107mm, 110mm, etc) to figure out which one I need. I'm also wondering whether that BB will compatible with modern crank systems, like the one I linked to.