Found him. The 1930 census was a help because of the presence of Ben Landon "relative". I hypothesized that Ben was a younger brother of Jesse. Found the brothers with their parents in the 1920 census: District 8, Ward 3, Carthage, Hancock Co., Illinois (pp 5-6):
Langdon, Benjamin [Sr], 63, b Illinois; father b Illinois; mother b Ohio; Laborer
- Malinda J., wife, 47, b Illinois of Illinois-born parents; laundress
- Mabel, dau, 14, b Illinois
- Jessie, son, 13, b Illinois
- Bennie, son, 8, b Illinois
- Elza, son, 6, b Illinois
Also living in the same household is Chas. H. Belville, 59 with wife Lida B., 60 and their granddaughter Eddie Atood, 10.
Working backwards, I then find Benjamin and Malinda in Chili, Hancock Co., IL in the 1910 census:
Langdon, Ben. F. 53, first marriage, married 19 years [therefore m. abt 1891], b IL of US-born parents; day laborer, odd jobs
-, Malinda J., wife, 38, 9 births, 7 living; b. Illinois of US-born father and IL-born mother
-, Amy, dau, 18, b IL
-, Clara, dau, 16
-, Lurlan, dau, 11
-, Lora, dau, 8
-, Stice, da, 6
- Mable, da, 5
-, Jessie, son, 3
In 1900, Benjamin and Malinda Langdon are in District 58, Industry, McDonough Co., IL:
Langdon, Banjamin, b Jun 1856, 43, m9 years, b IL of Kentucky-born father, and Ohio-born mother; farmer
-, Malinda, wife, b Mch 1873, 27, 5 births, 5 living; b Illinois of IL-born parents
-, Annie, dau, b May 1892, 8
-, Chara or Clara, dau b May 1894, 6
-, Liland, da, b Sep 1895, 4
-, Lurlan, dau, b Jul 1892, 7
-, George, son, b July 1889, 10 [must have been this one who died before 1910]
Can't easily find Benjamin in 1880 or 1870 although he might be the son of widow Eunice Langdon, 56, in the 1880 census in Versaille, Brown Co., IL.