I am researching this line also. Could you please tell me how you discovered that William's father was named Frederick? The only information I have found is on a German/Danish family tree of William and it says "son of physicus Dr. Schacht i Fredericksstadt i Sydslesvig." Frederiksstadt is a location. I would be expecting the name to be Wilhelm or Hinrich. Frederick does not come down through either of his sons or his grandsons. Have you found anything since your last post? I have some possibilities from the Danish census and Danish and German vital records.