Hi, Doug. I'm afraid I can't help you on the Bad Axe Turks at the moment, although my Turk ancestors do keep popping up all over the state of Michigan at various times, so it's possible there's a connection that just isn't clear yet. However, I am a descendant of Robert J. Arnot, whose son Ira is married to Amanda Oliphant. I have seen the entry in the 1870 census you refer to, but as I am living overseas now, my photocopies are packed up in storage. But for some reason I do recall seeing a Jane Turk living with them, and I also wondered if there may be a connection to some of the Turks in my family. If I remember correctly, she was a "domestic servant" and was born in England, which means she wasn't one mf my Turks, who came from Ontario and New York. Maybe I'm confused with another census record, but if you have access to the 1870 census again, have a look at her occupation and place of birth.