According to William Mortensen Vaughan's Genealogical Spreadsheet Numbering System (W.M.V.G.S.N.S.), William (P3VR-XV5) would be G-1, the paternal grandfather of my great-great-great-grandfather, Joseph Vaughn-3016 (L6VH-346), who would be E-1. William's son, James Vaughan (P3VR-L76), would be F-1. William's father, J.M. (P3VR-1XY), would be H-1.
According to Ancestry.com, William Vaughn allegedly served in the 4th Virginia Regiment of the Continental Army, during the American Revolution. He was, allegedly, born between 1710 and 1722. He allegedly died circa 1775. Allegedly, he married a woman named Mary Frances Green, who bore him at least four or five children*:
Catherine Vaughn
James Vaughn
John Benjamin Vaughn
John Powell Vaughn
William Vaughn, Jr.
The primary sources for this information seems to be family lore. Upon searching for such a William, I discovered one source, which is "Virginia, Vital Records, 1853-1934," which indicates that a male child named "W.B. Vaughn" was born, to a father named "J.M. Vaughn," in Graham Forge, Virginia, British Colonial America, on October 4th; it doesn't specify which year.
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* John Benjamin Vaughn and John Powell Vaughn were allegedly born within about two years of each other, but both survived to procreate, so they are probably the same man.