Image is the Smithson Portrait, National Portrait Gallery, object number NPG.96.28: http://npg.si.edu/object/npg_NPG.96.28.
Annual Report of the Smithsonian Institution for the year 1849, p. 46, 51.
Annual Report of the Smithsonian Institution for the year 1877, p. 9.
Summary:
The Board of Regents authorizes Smithsonian Secretary Joseph Henry to purchase a small portrait painted by James Roberts of Mr. James Smithson whose bequest founded the Smithsonian The portrait is now in the possession of Mrs. John Fitall, widow of a servant of the late Mr. Smithson. On June 1, 1850, Henry reports that the painting has been received from England. In the 1877 Annual Report, Henry lists all the existing portraits of Smithson. He describes this one as a small full-length picture that represents Smithson in the costume of a student at Oxford University. This portrait is now on display in the Crypt Room of the Smithsonian Institution Building or "Castle."