I have a memory of reading somewhere that it was a real ship, which transported planters loyal to the British Crown and their slaves from the USA to the Bahamas following defeat in the War of Independence. The wreck was rediscovered off Nassau in the '30's.
Also that the song is traditional, long predating the Beach Boys.
(Can't vouch for this, but I expect the real story is somewhere on Google!)
We looked for the Sloop John A; We looked for it all day;
all around the solent we did roam,
A man on the pier, Said it wasn't here;
We didn't find it, And then we went home.
Where can the John A be? Maybe the A's at sea;
We had a good look round, Then we went home.
Then we went home, We had to go home.
We didn't find it And then we went home.
The first mate was not there, Maybe he was elsewhere;
Maybe he was on board the Sloop John A;
Wherever he was, We didn't meet him because
We didn't find it, And then we went home.
Where can the John A be? Maybe the A's at sea;
We had a good look round, Then we went home,
Then we went home, We had to go home.
We didn't find it, And then we went home.
The day was a non-event, It seemed the A had went;
Then they told us that there's another called B.
B was OK; I had my heart set on A;
We didn't find it, And then we went home.
Where can the John A be? Maybe the A's at sea;
We had a good look round, Then we went home
Then we went home, We had to go home. I wanna go home.
We didn't find it, And then we went home.
A quick google gives...
"John B Sails" is a traditional sea chantey of the Bahamas. It's the story of the grounding of the ship off of Nassau. The wreck was excavated in 1926.
Carl Sandburg published the chantey as a poem called "The John B Sails" in 1927.
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