The 13-star "boat" flag version of the w:Ensign of the United States, commonly used in the 1800s on smaller-sized U.S. Navy ensigns (flags flown on ships) so the stars were still visible at a distance.  This practice was formally approved in 1912 in s:Executive Order 1637, with the precise dimensions being specified, but was discontinued just four years later with s:Executive Order 2390.  After that time, all U.S. Navy ensigns (regardless of size) had the full number of stars.
Own work
Carl Lindberg