The first USS Trenton was a wooden-hulled screw steamer, classified as a screw frigate, in the United States Navy. She was named for Trenton, New Jersey.
Trenton was laid down by the New York Navy Yard in 1875; launched on 1 January 1876; sponsored by Miss Katherine M. Parker; and commissioned on 14 February 1877, Captain John Lee Davis in command.
The Trenton was the first US naval vessel to use electric lights, which were installed in 1883.
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On 17 July 1878, she headed for Gibraltar, and on the 24th exited the Mediterranean. She cruised north, visited Lisbon, Portugal; Cherbourg, France; and Yarmouth, England; and then returned to the Mediterranean, reaching Villefranche in mid-October. Trenton resumed her cruises between Mediterranean ports, adding Genoa, Naples, and Tangiers to her itinerary in the spring of 1879. In June, she again headed out through the Strait of Gibraltar to visit Portsmouth, England; Terneuzen, Netherlands; Antwerp, Belgium; and Copenhagen, Denmark. She was back at Villefranche late in September. In mid-November, she sailed to Gibraltar and waited there until 7 December for Constellation to arrive with Trenton's replacement crew. The warship remained in the western Mediterranean until early April 1880.