Scientific American, 48:292,1883.
Captain Augustus G. Hall and the crew of the schooner Annie L. Hall vouch for the following:
On March 30, while on the Grand Bank, in latitude 40 10', longitude 33, they discovered an immense live trunk turtle, which was at first thought to be a vessel bottom up. The schooner passed within twenty-five feet of the monster, and those on board had ample oppurtunity to estimate its dimensions by a comparison with the length of the schooner. The turtle was at least 40 feet long, 30 feet wide, and 30 feet from the apex of the back to the bottom of the under shell. The flippers were 20 feet long. It was not deemed advisable to attempt its capture.
Comment: This story seems pretty believable. Firstly the latitude and longitude are correct (many hoaxed sea serpent sightings have been given erroneous latitudes and longitudes; one such "sighting" had coordinates that would of placed it in the middle of the Sahara desert!).
Second, it seems possible for sea turtles to gain this size, if it was old enough (turtles never stop growing), but no doubt the report is likely somewhat exaggerated. Perhaps, if the sighting was real, the giant sea turtle was either an exceptionally outsized individual of sea turtle, or perhaps even an surviving Archelon, a very large turtle (but still not as large as described!) that swam the seas of the late Mesozoic.
In any case, it mentions that the turtle was a trunk turtle; I have never heard of this turtle, but they are probably talking of leatherback turtles, which can grow very big (but not as big asin the report), and can be found in colder waters, having appeared around England and Patagonia. Still a definite mystery!