Yes, there's a good chance they are. There was a Francis Babington who came to Brooklyn from New Jersey with his wife, Phebe. They had a large family, and many of the sons became ferrymen, like Francis. You'll find them in directories and census reports listed as ferry masters, ferrymen, pilots. I guess they ran the boats from Brooklyn to Manhattan, up until bridges were built. Then I think a few of them became conductors.

Was one of Joseph's children a Mabel? There was a Mabel Babington who fell from a window when she was about three, and lived. You might want to check out the Brooklyn Public Library's website. They have free access to the Brooklyn Daily Eagle, from the 1850s to about 1902.

I haven't really looked into Joseph's line, since it was Lorenzo my mom remembered from her youth. I wish I could tell you more about that particular line.