I have to disagree somewhat on your description of what a township is. Here is another definition of township from a more historical & statewide perspective.
http://en.wikipedia.org/wiki/Township_(United_States)

The 'form' for the most census years indicates the 'township' relationship. For example, finding myself in the 1940 census I am enumerated in the State of Ohio, County of Miami. Township of Washington, City of Piqua, Ward 2 .... SD #4/ED 55-30 .... in this case the City of Piqua sits within the boundary of Washington township .. and there are governing bodies for both the city and the township.

3rdthawkins wrote:
"Agree Cynthia,

Townships are small portions of a bigger city, they are only there for voting purposes, like Precincts.

They are just names, nothing more, you have to keep scouring the pages and don't give up or give in when you see a township end. But using google maps and maps from that era can help you understand things better."