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This version of the song is American in origin. The chorus was added by Scotty Wiseman in 1935 to popularize the traditional Irish song upon which it appears to be based (The Rare Old Mountain Dew, 1916).
The Clancy Brothers did the definitive version which starts with them whistling the melody.

Real Old Mountain Dew

by trad
( Chorus
Hi da [G] diddle idle um
diddly [C] doodle idle um
diddly [G] do rye diddly dye [D] day
Hi da [G] diddle idle um
diddly [C] doodle idle um
diddly [G] do rye [D] diddly dye [G] day )

Let grasses grow and waters flow
in a free and easy way
but give me enough of the fine old stuff
thats made near Galway Bay
and Peelers all from Donegal
Sligo and Leitrim too
We’ll give them the slip and we’ll take a sip
of the real old mountain dew

Chorus

At the foot of the hill
there’s a neat little still
where the smoke curls up to the sky
by the smoke and the smell you can plainly tell
that there’s pocheen brewin nearby
for it fills the air with odours rare
and betwixt both me and you
when home you stroll you can take a bowl
or a bucket of the mountain dew

Chorus

Now learn’ed men who use the pen
have wrote your praises high
this sweet pocheen from Ireland green
distilled from wheat and rye
Throw away your pills, it’ll cure all ills
of Pagan or Christian or Jew
Take off your coat and please your throat
with the real old mountain dew.

Chorus x2