In 1870 Keokuk County, Iowa Elizabeth "Herndon" is 50, and kids Caleb K. 23, Harriet A. 25, Judith E. 21 "Apelton" 15, and J.C. 11.
In 1885 Polk / Red Willow Counties, Nebraska, Appleton, 30, is with bother J.C. Herenden 28 and his wife Rachel M. 25 and their three daughters, Hattie 4, Mattie 2, and Edith three months.
Appleton proved up a quarter in 6, 7N 48W in 1896, and cash-claimed one next to it in 1891.
In 1900 Rockland precinct, Appleton born Oct 1854 in Ohio, is single, and he's still there in 1910 and 1920 - but in 1920 he says' he's retired.
Appleton - Oct 10, 1854 - September 5, 1935 is buried in Fleming, Colorado - one descendant wrote "Son of Joseph and Elizabeth Kirk Herendeen. Brother of Joseph C Herendeen (my Great-Grandfather) and Caleb Kirk Herendeen. "App", to the best of our family's recollection never married, and lived out his life farming in Logan County, CO"