According to his death certificate, the parents of the Noah Perkins who was married to Augusta Carter were Jacob Perkins and Rhoda Sullivan. He is also listed with Jacob and Rhoda in the 1880 federal census for Mayfield, Graves County, Kentucky.
James Monroe Perkins and his wife, who are listed here as Noah's parents, did not have a son named Noah.
This Noah's pedigree on his Perkins line is:
Noah Perkins 1872-1944, son of Jacob Person Perkins 27 Oct 1827-12 Dec 1910, son of Ebenezer “Eben” Perkins about 1792-about 1850, son of Jacob Perkins 7 Apr 1746-after 1821, son of Wright Perkins after 1700-bef 24 Apr 1750, son of Isaac Perkins (born 18 Oct 1671 Hampton, Rockingham, New Hampshire, died 1746 Kent County, Maryland)
Other researchers have extended Noah’s pedigree beyond the research I’ve done - since this isn’t my family line, I haven’t researched beyond the Isaac Perkins born 1671. See, for example, https://www.ancestry.com/family-tree/tree/4434176/family?cfpid=4222...
This Noah is not related to, or descended from, Joshua Perkins of Accomack County, Virginia, who was nicknamed Old Jock in an 1858 Tennessee trial.