Journal of a Cruise Made to the Pacific Ocean… in the United States Frigate Essex, in the Years 1812, 1813, and 1814.

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The second edition is the only complete edition and generally regarded as the best one. The 1986 introduction added much information of importance and interest. – Hill. Samuel Eliot Morison called it the best bit of sea literature of the period. (See also Smith II, 1632. Howes P-484 (aa). Hill 1373.)

A Voyage in the South Seas, in the Years 1812, 1813, and 1814. With Particular Details of the Gallipagos and Washington Islands.

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A one-volume edition of the following year seems to cover the same voyage as the 1822, but it is hard to discover that through the Hathi indexing. It might be worth comparing them for any changes or omissions.