(Ten-to-one that son Peter E. is Peter Ely and son William H.H. is William Henry Harrison.)

.  Mary BARR, b. 1823/4, OH
.  George W. HORTON, b. 1836/7, OH
.  Socrates PERRY, b. 1842/3, TN
.  William GILL, b. 1842/3, NY
.  John KELLUM, b. 1851/2, IN
.  Henry LYMAN, b. 1852/3, IL

1a.  Anon.  1966.  Marriage Index:  Ohio, 1789-1850.  Liahona Research, Orem, UT (Broderbund CD-400):  not found.

1b.  Illinois Statewide Marriage Index, 1763–1900:

Groom	Bride	Date	Vol/Pg	Lic#	County
HAMMEL, John	ANGELOW, Hannah R	12/18/1851	B/081	2521	Morgan
HUMMELL, William H H	HORTON, Elizabeth J	12/24/1857	B/377	0333	Fulton
HAMEL, Peter E	GREEN, Sarah Jane	09/06/1866	C/031	1235	Morgan

Is our subject's son, John, really the one who married Hannah, as it says in the LDS Ancestral File?  Because in the 1860 census, John's wife appears to be named Louisa.  I couldn't find a marriage between a John and Louisa, but if his name was badly misspelled or misread, I could have missed it.

2.  1830

3.  1840

4.  1850 Census Every-Name-Index/Images (online at Ancestry.com; Image #18-19 of 27):  Jackson Twp., Knox Co., OH, Roll M432_700, p. 384A, 2283/2338, enumerated 18 Sep 1850 (extracted by Diana Gale Matthiesen):

William Hammel	44	M		Farmer		Penn
Ruth      "	37	F				do
John      "	19	M		do		Ohio
[next page]
Peter Hammel	17	M		Farmer		Ohio
William  "	14	M				do
Mary Barr	26	F				do

5.  1860 Census Index/Images (online at Ancestry.com, Image #134 of 563):  Jacksonville P.O., Jacksonville Precinct, Morgan Co., IL, Roll M653_213, p. 456, PN 134, 236/906, enumerated 20 Jun 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

William Hamille	50	M		Farmer	8000	1000	Penn
Roseanna   "	45	F					"
Peter      "	27	M		Farmer			Ohio
John       "	21	M		do			"
Louisa     "	22	F					"
William    "	25	M		Farmer			Ohio
Elizabeth  "	21	F					"
George W Horton	23	M		Farm laborer			"

John should be 29, not 21, and I would have guessed that Louisa is his wife.  Is her name enumerator error?  Elizabeth must be the junior William's wife, and George W. HORTON is probably Elizabeth's brother.

6.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #6 of 17):  Linville P.O., Linville Pct., Morgan Co., IL, Roll M593_263, p. 576B, PN 6, 48/48, enumerated 29 Jul 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Hamond William	62	M	W	Farmer	1000	1000	Penn
"   Rosanna	58	F	W	at Home			Ill
"   Emma	12	F	W	"			"
Perry Socratis	27	M	W	Laborer			Tenn

7.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #18 of 21):  Lynnville Pct./Corp., Township 14, Range 11 West, Morgan Co., IL, Roll T9_238, p. 281B, PN 14, SD 6, ED 175, enumerated 14/15 Jun 1880, official enumeration date 1 Jun 1880 (extracted by Diana Gale Matthiesen):

1880:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

1

2

3

4

5

6

8

9

11

13

24

25

26

148

148

Hammil Rosa

W

F

68

W

Keeping house

PA

Ger

PA

"   Emma L

W

F

22

G-Dau

/

IL

OH

IL

Kellem John

W

M

28

Boarder

/

Dry Goods Clk

IN

IN

IN

Gill William

W

M

37

Boarder

/

Blacksmith

NY

Eng

Eng

Lyman Henry

W

M

27

Boarder

/

Blacksmith

IL

IL

NY

8.  LDS.  Family Search: Internet Genealogy Service:  AF - Ancestral File (online at FamilySearch.org).