"As there is no reference to a son James, or his family in the father's Will, [as well as no birth record for James found,] it might raise a doubt whether John had such a son; but the record of his marriage, by Rev. Mr. Bailey, must remove all doubt. 'Upon the 25 March, 1687, at my own house, in Watertown, I married James Begalow, the son of John Begalow, and Patience Brown, the daughter of Jona. Brown, with their parents' full consent, being legally published', &c."
[See the actual marriage record (different in very slight ways than Bond presents) on the Family page. According to the Bigelow Genealogy, p. 20, the father's will does mention son James in the 7th item, and well as James' son James or any "surviving children" of James.]