This is the X-259, or Antares II, the third-stage, solid-fuel rocket motor for the all-solid fuel U.S. Scout launch vehicle. Antares II produced about 23,500 pounds of thrust. Like the other stages of the Scout, Antares was named after a star constellation. (The Scout's first, second, and fourth stages were the Algol, Castor, and Altair, respectively.)
The Scout was conceived in 1958 as a low-cost launch vehicle for light payloads. The first Scout was launched in 1960 and continued as a very successful vehicle. This object was donated to the Smithsonian in 1968 by the Alleghany Ballistic Laboratory.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.