Thanks to Chris Hill for submitting! You can play along in the same key as The Clancy Brothers recording.

The traditional, "Rosin the Bow" (not "Beau") refers to rosin with the bow of a violin, but both "Rosin the Bow" and "Rosin the Beau" cover the same general subject. There are many variations of the song(s), and the tune has been re-used in other songs for political campaign jingles, comedy songs, or other folk songs. Both the tune and early lyrics for "Rosin the Bow" are traditional (with no known author). In 1838, the variation "Old Rosin the Beau" was published as a "Comic Song Dedicated to the Members of the Falcon Club by the Publisher" (Ld. Meignen & Co.), arranged by J. C. Beckell.

Early American versions of "Old Rosin the Beau" relate the story of a man, Rosin, who was popular in his youth with the ladies and had many children by many women, so later in life the ladies referred  to him as “Old Rosin the beau”. As a drinking song, the chorus chimes, "Take a drink for Old Rosin the Beau" and uses dark comedy, with jests about his grave or tombstone.

There’s also another verse which is found in American versions which reflects Rosin's popularity with the ladies and the resulting next generation:

I’ve only this one consolating, as out of this world I go

I know that the next generation, will resemble old Rosin the Beau…

The popular triple-time melody "Old Rosin the Beau," or "Rosin the Beau," has a varied and widespread history, and has served a number of functions. A song version, "Old Rosin the Beau" (Roud 1192), was published in America in 1838 ("A Comic Song Dedicated to the Members of the Falcon Barge by the Publisher"), and, while this may be (one of) the earliest printings, it is thought that versions of the air and words predate this, probably from Great Britain or Ireland. The tune was borrowed for numerous songs, particularly in America, but it was most popular as "Rosin the Bow/Beau."