There has been plenty of speculation on Josiah's parents - some claim a Daniel or Nathaniel with the mother being Elizabeth (maiden name unknown. However we cannot substantiate this and probably never will never know. Mary Williamson's line can be traced back to Timothy Williamson (England) and Mary Howland (Arthur Howland and Margaret (Walker) Read/Reed). This line is more provable and you should have little trouble with it. Good luck.