"The name of his first wife, whom he married about 1637, does not appear [emphasis added], but it should be noted, however, that a Mary Clifford, aged 25 years emigrated to New England in the same ship with him in 1635, her name standing next to his on the passenger list, and that Edward Belcher, grandson of Jeremiah, had a son Clifford."
[This is actually pretty wild speculation, based pretty much on the coincidence of their names being adjacent on the passenger list. Note that it is not even known if his wife was named Mary (though their only daughter was named Mary: but equally likely is Abigail, the first daughter after she died, often named after the deceased wife). Further, the grandson Edward [p. 253] m. about 1700 Mary ---, "said by tradition to have been Mary Clifford". Which would explain why they had a son named Clifford. Even if Edward's wife was not Mary Clifford, Edward had his wife's maiden name and his mother's maiden name available, but we are to believe he bypassed both of those to use the maiden name of a grandmother who died before he was born? Bottom line: we have no idea who Jeremiah's first wife was.]