Individual Details

If daughter Louisa was born in Lincoln Co, TN - this might be William
1820 Census. Lincoln, TN
William Bates: 2m under10, 1m 16-18, 1m 16-26 (likely duplicate), 1m 26-45 (b. 1775 at the earliest).
5f under 10, 1f 10-15, 1f 26-45

1830 Census. Marion, AL
William Bates: 2m 5-10, 2m 10-15, 1m 15-20, 1m 40-50 (he should be older if this is the same William Bates but it more or less agrees with 1820)
1f -5, 1f 5-10, 1f 10-15, 1f 15-20, 1f age 40-50

Birth

Ca 1770

Kentucky

Spouse	Frances "Fannie" Proctor (1790 - )
Child	Louisa Caroline Bates (1816 - 1872)