Barber's capped Liberty design in gold. This design was also made as an eagle J1579-J1580/P1772-P1773.
Only 2 examples are known J1575/P1768. Roger Burdette found the following notation in the Mint Archives. "Feb 19, 1878, Two eagles and two half eagles of Barberís design in gold for directorís office."
The 2 pieces have the following pedigrees:
1) Parmelee, V. Brand (journal id #12720) to Horace Brand, Judd, Wilkison, Rothchild-Stacks 10/03, southern collection, Simpson collection - PCGS66, illustrated above courtesy of PCGS, click on the thumbnail to see an enlargement.
2) Massamore 11/1884 lot 506, Barclay-Steigerwalt 4/1885 lot 988, Foster Ely-Scott Stamp and Coin 11/1888 lot 113, Byron Reed, Durham Museum - ICG64, illustrated below.
Photo from the Byron Reed Collection; owned by the City of Omaha, Nebraska; on loan to The Durham Museum.
Examples were also struck in copper J1576/P1769 with about a dozen known including the example illustrated below, several of which have been gilted.
Photo courtesy of Ira & Larry Goldberg's Coins & Collectibles.
Additional information on these can be found in the article "The 1884 Connection: A History of the 1878 U.S. Gold Patterns" in the November 1981 issue of The Numismatist.