Not my family line, just sharing.
From the book "HISTORY AND BIOGRAPHY, COUNTIES OF WHITE AND PULASKI INDIANA. Historical and Biographical. Illustrated. Chicago; F. A. Battey & CO., Publishers. 1883."
page 292, Honey Creek Township, White County, Indiana
"WILLIAM H. RINKER was born in Union Township, this county, May 26, 1836, and is the third of the eight children born to JOSHUA and LOUISA (REECE) RINKER, both natives of Virginia, respectively of German and Scotch descent, born June 10, 1801, and February 14, 1809, and married in Hampshire County, Virginia, August 28, 1828. In 1831 or 1832, this couple moved to Clark County, Ohio, whence, in the fall of 1834, they came to Union Township. For two years, Joshua farmed on shares. In 1836, he entered 130 acres in Big Creek and Honey Creek Townships. He at first erected a rude log-cabin, but subsequently built the first brick house ever put up in this township. He died December 1, 1869, a zealous member of the Methodist Episcopal Church, in which for several years he was a class leader. His wife had gone before, April 20, 1864, and she also was a worthy member of the Methodist Episcopal Church. WILLIAM H. RINKER received his early instruction at the frontier subscription school, and assisted on the home farm until twenty-three years old. He then farmed on shares about six years, and in the fall of 1866 bought the farm of eighty acres on Section 34, this township, on which he yet resides. He was married, August 19, 1860, to ESTHER BUNNELL, a native of Big Creek Township, who has borne him seven children, five still living. In December, 1864, he enlisted in the Fifty-ninth Indiana Volunteer Infantry, and served until the following May, when he was discharged at Indianapolis. In politics, he is a Republican, and both he and wife are members of the Methodist Episcopal Church, in which he has held various official positions."