I am not related to the Hamilton family. However, after I read your query on the Sheridan County message board, I researched this family. Here is what I found.

1860 Sullivan County, Missouri

1568 1568 Joseph Hamilton 28 Tenn
Mary Ann 23 Mo
Sarah Jane 5 Mo
Alexander 3 Mo
James B 2 Mo
Elizabeth 1 Mo

1870 Buchana, Sullivan County, Mo

115 109 Hamilton Joseph 41 Ky
Mary E 30 Tenn
Alexander 14 Mo
James 12 Mo
Elizabeth 10 Mo
Richard 5 Iowa
Nancy 3 Mo
Samuel 1 Mo

1880 Jackson, Putnam Co MO

6 6 Hamilton James B H Head 21 Mo Ky Tenn
Hester A Wife 19 Ill Ind Ill
Theodore P Son 1 Tex Mo Ill
7 7 Hamilton Alex D Head 23 Mo Ky Tenn
Mary E Wife 17 Mo Ill Ill
Joseph Son 3 Mo MO Mo
Emma B Dau 5/12 Mo Mo Mo

1900 Licking, Texas County, Mo

153 153 Hamilton JBH Jan 1858 42 M 10 Mo Ky Ky
Isabella May 1871 29 M 10 4 3 Ind Ky Ind
Walter Oct 1882 17 S Mo Mo Ky
Mary Bell Dec 1883 16 S Mo Mo Ky
Joseph Dec 1885 14 S Mo Mo Ky
Agnes Aug 1887 12 S Mo Mo Ky
Harvey Feb 1889 11 S Mo Mo Ky
Oliver May 1891 9 S Mo Mo Ky
Franklin Apr 1898 2 S MO Mo Ky
Carles Jan 1900 5/12 S Mo Mo Ky

1910 Meade County, Jansas

168 168 Hamilton James B H 52 M2 1 Mo Mo Mo
Huldah 43 M2 1 4 3 Ia Ind Ky
Frank A 12 S Mo Mo Mo
Ransom C 10 S Mo Mo Mo
Alva 4 S Kan Mo Mo
St John William Stepson 14 Mo Iowa Mo
Arthur " 11 Mo Iowa Mo

1920 Sheridan County, Nebraska

31 31 Hamilton James B H 61 Mo Ky Tenn
Blanche 48 Eng Eng Eng
Ransom 20 MO Mo Ind
Alvah 13 Kan Mo Ind

1930 Sheridan County, Neb

26 27 Hamilton Oliver 38 M 18 Mo MO Mo
Etha wife 33 M 15 Kans US US
Eulla 17 Kans Mo Kan
Elden 15 Kan Mo Kan
Raymond 13 Neb Mo Kan
Lee 12 Neb Mo Kan
25 26 Hamilton James 19 M 18 Kan Mo Tenn
Mabel 22 M 21 Neb Ia Neb
19 20 Hamilton Ransom 29 M 27 Mo Mo Mo
Thelma 23 M 21 Neb Neb Neb
Harold 2/5 S Neb Mo Neb
James Father 72 M 19 Mo Ky Tenn
19 20 Hamilton Alvah 24 S Kan Mo Mo

According to this, James Buchanan H Hamilton had at least four wives: Hester A (1880 census); Isabella (1900 census); Hulda (1910 census); and Blanche (1920 census)

Here are the children I find:

Theodore P Abt 1879 Mo 1880 census
Walter Oct 1882 1900
Mary Bell Dec 1883 1900
Joseph Dec 1885 1900
Agnes Aug 1887 1900
Harvey Feb 1889 1900
Oliver May 1891 1900
Franklin Apr 1898 1900 1910
Carles (Ransom) Jan 1900 1900 1910 1920
Alva Abt 1906 1910 1920

WWI Registrations"

Theodore Pleasnt Hamilton
21 November 1878
Pueblo County, Colorado (Residence)
Med Med Blue Brown
Next of Kin Opal M Hamilton

Charles Ransom Hamilton
11 January 1900
Sheridan Neb

Harvey W Hamilton
22 Feb 1889 Raymondville Mo
Holly, Prowers County, Colo Med Med Grey Black

James Oliver Hamilton
May 1891 Houston, Mo
Sheridan Neb Tall Med Brown Brown

Walter Anderson Hamilton Med Med Blue Brown
10 Oct 1882
Licking, Texas County, Mo
Rosalann Hamilton

1920 Pueblo County, Colorado
330 Gaylord

20 25 Hamilton Theodore P Head MW 39 Tx Mo Mo
Opal Wife FW 23 Kan Mich Oh
Eugene Son MW 1 Colo Tx Kan

1930 Pueblo County, Colorado

366 369 Hamilton Theo P Head MW 50 Tx Tx Tx
Opal Wife FW 33 Kan Ill Ill
Mary A Dau FW 3/12 Colo Tx Kan

Harold Hamilton, the son of Ransom Hamilton, may still be alive and living in Sheridan County, Nebraska. He would be about 81 years old.