U.S. National Archives (Record Group 104, Entry 19, Letters Sent by Treasurer) Pubblico Deposited
National Archives entry description: LETTERS SENT BY THE TREASURER OF THE MINT. 1816-48; June 1850-Dec.1874. 25 vols. 2 ft. Fair and press copies of letters sent by James Rush (and his successors) to the Director of the Mint, the Treasurer of the United States and other Treasury Department officials, insurance companies, banks,and private persons. The letters relate chiefly to fiscal operations of the mint. Arranged chronologically. In two of the volumes (from 1816 to 1845) there are a few letters received from the Director of the Mint; these volumes are known as the "James Rush letters." This material was scanned in Philadelphia under the direction of R.W. Julian, operating through a grant from the Central States Numismatic Society.
National Archives catalog record: https://catalog.archives.gov/id/567572 [there listed as 20, 19 is correct]. See also the National Archives & Records Administration numismatic finding aids at https://nnp.wustl.edu/library/archivedetail/538870.