Hi Dan, What was the ship name & date?
The info you need on Longitude would be recorded in the ship`s deck logs. A deck log identifies a ship's location and movements daily. If the ship is underway, its latitude and longitude are to be entered three times each day in blocks provided for the purpose. Deck logs are not narratives, and do not describe or explain a ship's operations.
If he was on a commisioned US Navy ship during WWII, the deck logs are at the Modern Military Branch, National Archives, 8601 Adelphi Road, College Park MD.
"Logs from 1941 through those that are 30 years old or older are in the Modern Military Branch, National Archives, 8601 Adelphi Road, College Park MD 20740-6001 [Telephone (301) 837-3510]. These logs are open for research. Requests for research appointments, and inquiries concerning log information, should go to the National Archives office holding logs from the time period of interest."