You do not say how you have proved that your wife's ancestor is the William Yerks listed on the Militia muster roll published in the book.

Militia muster rolls are not proof of active-duty service unless otherwise noted on the roll.

Without looking at the original, one could not determine even if the list of persons was a list of those who actually reported for the drill and nose-counting. Transcripts can omit details, such as additional notations entered by whoever drew up the original list.

Lack of an original and lack of evidence of active duty would be impediments for use of such a list in a lineage society application.