After Yom Kippur I did a little Googling. It was easy to track down the story I remembered reading - and to track down its debunking. The story as I remembered reading in one of its earlier versions:
The whaling ship Star of the East, was in the vicinity of the Falkland Islands, searching for whales, which were very scarce. One morning the lookout sighted a whale about three miles away on the starboard quarter. Two boats were manned. In a short time one of the boats was near enough to enable the harpooner to send a spear into the whale, which proved to be an exceedingly large one. With the shaft in his side, the animal sounded and then sped away, dragging the boat after him with terrible speed. He swam