More Information:

About Elijah Eads:

Elijah Eads is mentioned in the book "A History of Dearborn and Ohio Counties" (Ancestry.com) in a list of citizens of Dearborn County who served in the War of 1812.
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Found in 1820 Census, IN, Dearborn Co., Logan TS, img. 5.
0101120100101
1 male 10-15, 1 male 16-25, 1 male 26-44, 2 males 45 & up, 1 female 10-15, 1 female 45 & up.
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Found in 1850 Census, IN, Daviess Co., Washington TS, img. 50
The 1850 Census gives Elijah's birthplace as Maryland, and his wife's name as Elizabeth (a second or third wife?). Four children, ages 11 to 16, with the surname "Holmes" are living with them, presumably from Elizabeth's previous marriage. One child, Louisa Eads, 11, could have either been Elijah's from a previous marriage (most likely), or from his marriage to Elizabeth.
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Found in 1860 Census, IN, Daviess Co., Washington TS, p. 36.
Elijah Eads 68 MD (Magistrate)
Elizabeth Eads 54 VA
Alexander Holms 23 VA (Cabinet Maker)
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Elijah Eads was profiled in the book "Daviess County History" :

"Elijah Eads was one of the pioneers of Indiana who migrated from New Jersey in the early part of the nineteenth century, locating first in Dearborn County, later coming to Daviess County in the 1820's. He owned a 320 acre farm in the Sugarland area of Washington Township. Late in life, he and his wife Eunice (Hageman) moved into Washington.

Their son, John H. Eads, born 2/21/1821, was also a farmer in the Sugarland area. On 5/8/1845 John married Charity Wykoff and seven children were born to them. Eliza Ann, Lucy and Hannah (twins), Lida, Sarah, and John who had a twin brother who died in infancy."

NOTE: The following article about James Buchanan Eads indicated some confusion about Elijah and Eunice Hagerman:

"People & Events: Eunice Eads

James Eads married Eunice Hagerman Eads on May 2, 1854, a year and a half after his first wife Martha died. Eunice was the widow of Eads' first cousin, Elijah Clark Eads. Eunice and James had long been good friends. In 1849, after Elijah died, leaving Eunice very little money, Eads rescued her from an unpleasant living situation, helping Eunice pay the rent in more comfortable lodging."

I believe that this Eunice Hagerman was married to a different Elijah Eads than the one in my tree, since the one referred to above died in or before 1849.
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Trees found on RootsWeb give Elijah's wife as Lucinda Hutchinson from Virginia.
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About Lucinda Hutchinson:

Name from 1652604.GED.

About Louisa Eads:

Found in 1850 Census, age 11.