The census record I found is for Monck County, Cardwell County or Bothwell County. I can't find these counties on a map!

Monck, Cardwell and Bothwell were three counties created for municipal purposes by "borrowing" townships from other counties for the purpose of enumeration and political representation. You can find out more about these three counties in Research By Area.

The 1871 census lists an area called Cardwell, what is the present day name of this area?

Cardwell was an electoral and enumeration district that existed briefly in the late 1800's. The townships that formed this area are now part of Dufferin County, Simcoe County, and Peel County. See Cardwell District for more information.