The Countess of Scarborough was hired by the Admiralty in November 1777, as a 20 Gun Sloop for convoy and north sea patrol duties.
With HMS Serapis she fought a superior combined enemy squadron of French and American ships under the command of John Paul Jones until eventual capture by the French 26 gun frigate Pallas off Flamborough Head on 23rd September 1779.
Although both Serapis and the Countess of Scarborough were taken, they had stopped the American and French from capturing any of the valuable merchant ships they were protecting.
The document although difficult to read does appear to have an addendum in black ink referring I believe to her having been "taken by a squadron under the command of Paul Jones".
An excellent detailed account of the action can be found at: yorkshirehistory.com