As part of the great ongoing discussion about the arrival of the Burnham Brothers to Massachusetts, there is a list of Ipswich soldiers who received payment for service during the Pequot War and is dated 5 December 1643. The list can be seen here. I will concede I am no expert in the Native American wars of the 17th century and you can read about the dates of the Pequot War in its wikipedia entry. Basically it was from 1636 to 1638. Since this list does not give the date or duration of service, it is impossible to know how much of the war John or Thomas Burnham took part in. I'm also wondering if a garrison of soldiers was needed even after 1638 to safeguard the Ipswich planters. In any case, we can see that both men were in Ipswich in 1643 and were given land in payment for services rendered as early as 1636. However, there are no intermediary documents for either man. So, when they came over specifically is still a question (ca. 1636-1638) and on which ship is simply never going to be known.
However, I want to examine the other men on the list to see if we can glean some patterns. I wish I could get better sources by going out and researching, but this is what I have at hand.
- John Perkins is the John Perkins, Jr. 1609-1684 who arrived with his parents on the Lyon in 1630. See Walter Goodwin Davis, Massachusetts and Maine Families in the Ancestry of Walter Goodwin Davis (1996) III:173 and Great Migration Begins III:1431-33.
- Robert Roberts in Pope's Pioneers of Massachusetts, p. 387 notes this as his first record. Savage (Genealogical Dictionary of New England Settlers), claims he was in Boston in 1640.
- John Burnham, the question at hand.
- Humphrey Gilbert, Pope notes this as his first record.
- Robert Filbrick, Savage notes this as his first record.
- Thomas Perkins, 1622-1686, brother of John above.
- Francis Wainwright, Pope notes this as his first record.
- Thomas Harris b. ca. 1618-1687, Pope notes this as his first record. According to Davis, II:170, he came with his father Thomas Harris alias Williams in 1630 in the ship Lyon. Great Migration Begins II:864-66 agrees on the year but not on the ship.
- John Layton, Pope notes this as his first record. Savage notes him at Ipswich in 1648 and claims he may have been at Newport, R.I. ten years earlier.
- Ralph Dix, Pope notes this as his first record. Savage notes him in Ipswich in 1647.
- Daniel Wood, Pope notes this as his first record and that his inventory is taken in 1648.
- Thomas Burnam, also the question at hand.
- William Miller, Pope notes this as his only record, whereas Savage notes him in Ipswich in 1648 and moving to Northampton.
- Jeremy Newland, probable son of Anthony of Salisbury, this family relocates to Taunton. Pope notes this list as his first record.
- Richard Hutley, arrived in 1635 on the ship Hopewell. Great Migration 1634-35, III:484-85.
- Nathaniel Boswell, can't be readily identified, although an Isaac Buswell lived in Salisbury as early as 1639.
- John Wild 1618-aft 1690, arrived in 1635 on the Elizabeth. See Davis III:619 and the Great Migration 1634-35 hasn't gotten there alphabetically yet.
- Theophilus Shatswell, arrival unknown, this is his first record. His brother John was in New England by 1633 Great Migration Begins III:1656-57. See also NEHGR 150-180-89.
- Henry Green, minister, this is his first record according to Pope, although Savage says his the man who became a freeman in 1641.
- Sergeant Howlett, no doubt Thomas Howlett, arrived in 1633, see Great Migration Begins, II:1024-28.
That's 20 men, 18 not counting the two Burnhams. Of those 18, six can be proven to have arrived in 1635 or earlier; one cannot be identified, and 11 are known to have arrived by this record [if you don't count guesses by Savage]. So basically twice as many of these men probably arrived in 1636-7 as did those who arrived earlier. So, the odds are that the Burnhams did too. Even then, it only seems the eldest two arrived (perhaps) together, and Robert arrived later.