It does seem that there was more to it originally, though you'd be hard pressed to find anybody who remembers anything other than the chorus; even if you search for the right words (The moon shines bright, not down).

Apparently the lyric was written by Edward Stanning and Thurland Chattaway, set to Kerry Mills' tune 'Red Wing' (for which Chattaway had written the original lyric); the song was published in 1915 and popularised by the actress Lillie Soutter. You'll find reproductions of the chorus part of the score, and the front cover of the music sheet (or an advert for it) at http://chaplin.bfi.org.uk/:

music (page 3)

cover/ad

The chorus is quoted in numerous old threads here, of course; with various minor variations. I doubt if we need any more of those, but if anybody does know the rest of the song that would be interesting. Note, though, that the DT file Charlie Chaplin is not the song Chris is looking for, but a relatively modern collation of children's playground verses mentioning Chaplin, grafted onto the familiar chorus.