Dear Mr. Richford,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located Reports of Tests and Experiments on Various Types of Ordnance and Ordnance Stores, 1820 - 1861; Correspondence and Reports Relating to Experiments, 1818 - 1870; Reports and Correspondence of Ordnance Boards, 1827 - 1870; Reports of Experiments, 1826 - 1871; Registers of Correspondence and Reports Relating to Experiments, 1812 - 1870; and Subject Index to Reports of Experiments, 1822 - 1844 in the Records of the Office of the Chief of Ordnance (Record Group 156) that may include air rifles. For more information about these records, please contact the National Archives at Washington, DC - Textual Reference (RDT1) at firstname.lastname@example.org.
We also located Reports of Tests and Experiments with Small Arms, Ammunition, and Other Ordnance, 1858 - 1860 in Record Group 156 that includes records of the Watervliet Arsenal. For more information about these non-digitized records, please contact the National Archives at New York (RE-NY) at email@example.com.
Next, we located Letters Received from the Chief of Ordnance and Other Officials and Officers of the War and Treasury Departments, 1816 - 1905; Letters Sent, 1815 - 1896; Reports of Tests of Ordnance and Proceedings of the Boards Making the Tests, 1864 - 1905; and Reports Relating to Tests of Ordnance, Routine Work, and Other Matters, 1/1863 - 12/1908 from Springfield Armory in Record Group 156 that may include records about testing of air rifles. For more information about these non-digitized records, please contact the National Archives at Boston (RE-BO) at firstname.lastname@example.org.
Finally, we located Patent Case Files, 1/1/1836 - 12/31/1978 in the Records of the Patent and Trademark Office (Record Group 241) that may include patents of air rifles. For more information about these non-digitized records, please contact the National Archives at Kansas City (RM-KC) at email@example.com.
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We hope this is helpful. Best of luck with your research!