The Arthur Langley Searles Collection of H. P. Lovecraft Research Files at Temple University has…
photo-reproductions of Lovecraft letters of 1912 to Nelson Rogers in Mt. Vernon, N.Y.
Who was Nelson Rogers, and why was Lovecraft writing to him in 1912?
Possibly this was “John Nelson Rogers” b. 30th Sep 1893, and who lived at Mount Vernon in 1920. He was a railroad repairman in 1920, which may suggest the connection. The young Lovecraft had been greatly enamoured of railroads and, via his avid reading of magazines such as Railroad man’s Magazine, he may have come into contact by letter with someone his own age who worked on them.
Update: While the above candidate may have been a younger member of the correct Rogers family, I now see that the correct candidate is revealed by Ken Faig in Lovecraft Annual No.9, 2015 (page 176). This being one Nelson William Rogers (1878-1951), who had been a friend of Lovecraft’s mother in her youth. Also, I would add that Lovecraft’s father had lived for a time at Mt. Vernon.
Nelson Rogers seems to have been quite the fascinating character. During the 1930s he lived in Putnam County, NY and was better known as Judge N.W. Rogers, having served as a Justice of the Peace in the hamlet of Tompkins Corners. N.W. Rogers gained a reputation for rabid anti-semitism, promoting the Protocols of Zion and authoring tracts published by the Concord Press of Mount Vernon, Washington. https://digital.library.temple.edu/digital/collection/p15037coll19/id/9570