A possible clue to Alice's family background may be found in the 1622 Will of her son, John Parsons, who appointed his cousin John Say 'the Younger' to be one of the overseers of his Will. John Say junr. of Wootton Bassett (c. 1595-1669) was the son of John Say senr. (d. 1631) and Joane (d. 1644). This identification gives rise to at least three interpretations, keeping in mind that the use of the word 'cousin' in these old wills was often more general, also carrying the meaning of 'kinsman' and 'kinswoman', which terms can sometimes refer to nephews and nieces. So, if John Parsons and John Say jr. were (first) cousins as the term is used today, then Alice may have been a member of the Say family. On the other hand, John Say jr. was at most a generation younger than John Parsons, and so John Say could have been John Parson's nephew. By the same token, the age difference could also indicate that they were first cousins once-removed, which again allows for the possibility that Alice was related to the Say family of Wootton Bassett.
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Alice wife of John Bath (burial record)