In answer to a PM, the sail behind the limp US flag is a topsail. In the years following the 1860's that sail was divided into an upper & lower topsail. That rig gave sailors greater flexibility in adjusting the sails to wind conditions. A split sail was easier to raise & lower.
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"Amsterdam " Dutch East indiaman. Note the lantern spanker.
Today, the only square rigged ships with full cut single topsails are reproductions of historic vessels.
I notice that the movie "Master & Commander, Far Side of the World" is on numerous online sites. The ship used in the movie was originally built as a Bicentennial project. The HMS Rose was built as a reproduction of a 6th rate frigate laid down in 1757.
After a career as a sail training vessel, the Rose was purchased & converted into the HMS Surprise of Patrick O'Brian novels fame. The Rose/Surprise is at a museum in San Diego.
The at sea sequences in the movie such as setting stunsails are a very accurate depiction of what period sail evolutions were like.
Captain Bailey & his crew had a unique body of seamanship that was brought to bear on that voyage.