There are quite a number of difficulties with the current scenario, and with the lists of Burton Meacham and Clarence Mitcham. Sadly, it appears that all of the 17th century Virginia Meachams need to be re-confirmed against hard evidence. This is the same as what Burton and Clarence had, except for Henry 1702, which could not be found. The IGI has Henry born 1709 son of John and his second wife Mary Atwood. 1679 James 1682 There could be some mistaken identities and other confusions here.
Clarence seems to have thought so.
These questions aside, taking the list at face value there are two distinct groups of births here, which could suggest that Jo. We then have Joshua, John, Henry and perhaps Edmund as possible sons of John Machem. And there seems to be NO direct evidence that the father of ANY of them was the immigrant John Machem. Middlesex Co. He must have been born ca 1680 or earlier, and so could be second or third generation, or from another line altogether. Finally, I discovered a John Meekins, imported in 1654 according to Early Virginia Immigrants .