Here's another of the Famous Studios Screen Songs in which they spend three and a half minutes doing blackout gags, three minutes singing a song with some relevance, and then one last gag. The gags are pretty good, with lots of references to trees, moose and lobsters. The song is "The Maine Stein Song."
Usually I'm pretty good about recognizing the tunes the Bouncing Ball bounces to, but this was one I didn't recognize. According to Wikipedia, the words were written by Lincoln Colcord about 1902, and Rudy Vallee covered it, turning it into the only college song to become a number one hit.
I certainly don't dispute that assertion, though I have my dark doubts.