Dear Mr. Slack,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located 3 series titled Records of Field Artillery Regiments Numbers 1 through 351, 1912-1930; Records of Field Artillery Regiments, 1919-1943; and Returns and Rosters of Field Artillery Regiments, 1917-1921 in the Records of U.S. Regular Army Mobile Units (Record Group 391) that may contain information about the 340th Field Artillery Regiment. The records are not yet digitized and available in the Catalog. For access to and/or copies of these records, please contact the National Archives at College Park - Textual Reference (RDT2) via email at email@example.com.
We also located the series titled the Draft Registration Cards, 1917-1918 in the Records of the Selective Service System (World War I) (Record Group 163) that are in the custody of the National Archives at Atlanta (RE-AT). For access to and/or copies of these records, please contact RE-AT via email at firstname.lastname@example.org.
We suggest that you request a copy of your grandfather’s Official Military Personnel File (OMPF). OMPFs and individual medical reports for enlisted men of the U.S. Army who were separated from the service after October 1912 and prior to 1958 are in the custody of NARA’s National Personnel Records Center in St. Louis. In many cases where personnel records were destroyed in the 1973 fire, proof of service can be provided from other records such as morning reports, payrolls, and military orders, and a certificate of military service will be issued. Please complete a GSA Standard Form 180 and mail it to NARA’s National Personnel Records Center, (Military Personnel Records), 1 Archives Drive, St. Louis, MO 63138-1002. You can also fax the form to 314-801-9195 OR view the record by visiting the NPRC Archival Research Room in St. Louis, MO. For more information see Official Military Personnel Files (OMPF), Archival Records Requests.
We hope this is helpful. Best of luck with your family research!
Mr. Slack, I also found this short article about the "Immigrant Army" on the USCIS website that briefly addresses non-English speaking soldiers in World War I. It might be of interest to you. joan