Kate, he mentions these children:
"....of my Five Children, Richard Smith, Elizabeth Smith, Robert Smith, William Smith, and George Smith,..."
all from his wife Elizabeth.
The only marriage I have found is this one:
On the Hants Marriage Index there is a marriage of a Walter Smith to Grace Goslin on 1 Jan 1755 at Sopley.
However, I can't find a burial before Walter's marriage to Elizabeth Langford.
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