I do not recognize the ship from the picture, but it seams as if maybe the name contains the word "Prince". Could it be the "British Prince", owned British Shipowners Ltd.?
I don't know if you have solved your ship riddle, but here's my guess, based on the following: 1. Barque rigged. 2. Name ending i ...NCE 3. American flagged 4. Pictured in Plymouth England. Searching the web I found two Barques named FLORENCE. the first plied the routes between Plymouth or Southhampton to Quebec or Prince Edward Island mostly during the 1840s and was apparently wrecked. The 2-nd Florence was launched on Prince Edward Island in 1874. A shipping notce reports that "the American Barque Florence" was wrecked off Fortune Island, Bahamas in Dec of 1888. I could find no pictures and don't have time for further research. If you find this checks out or can find other pictures. it would be fascinating to hear of your results.