Ohio achieved statehood in 1803, so there was a Federal Census of Ohio in 1810; unfortunately, the 1810 census was lost, except for Washington County.  Note that Franklin, Chester, and Bloomfield Twps. became part of Morrow Co. when it was formed in 1848.  The most critical period for township formation was between the 1820 and 1830 censuses, and I am not 100% confident in the details of the maps below with regard to those changes.  I will continue to work on documenting them.

Norton (1862) and Hill (1881) disagree as to whether the southeastern corner of the county started out in Union or Morgan Twp.  I follow Norton for a variety of reasons.

The census included a separate listing for the county seat, Mt. Vernon.

Brown cannot have been formed in 1826 from Jefferson if Jefferson was not formed until 1829; yet, Hill (1881) contains this anomaly.  I'll have to find another source to determine the correct dates; however, whatever the dates, it makes no difference as regards county layout at the time of the census (i.e., both townships were formed between 1820 and 1830).