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According to Memorials of the Earl of Stirling and of the house of Alexander, Charles Rogers, Edinburgh, W. Paterson, 1877, pages 38, 253 and 254, John Alexander, the 4th son of William Alexander, Earl of Stirling, was born about 1612, and died 1641 in Scotland. John was matriculated a student in the University of Glasgow in 1630 (Reg. Col. Glasg.) He was roughly 18 years old at that point.

About 1633/1634, John Alexander married Agnes, the only daughter of Robert Graham of Gartmore, Perthshire. Agnes was married to John when her father died in 1634 and was described in estate documents as "lawful dochter of . . . Robert Graham of Gartmoir, and with consent of John Alexander, lawful son to ane noble and potent erle, William, Erle of Stirling, Lord Alexander, her spouse." Agnes Graham Alexander died some time prior to 23 January 1636, when her husband, John Alexander, was "invested in that portion of the lands of Gartmore which had passed to her at her father's death." There is no evidence that John Alexander married for a second time after the death of Agnes Graham Alexander.

Agnes Graham Alexander had a brother Gilbert Graham who also inherited a portion of Gartmore, on the death of their father Robert Graham. Gilbert died in 1641 without children or siblings to inherit. As a result, his niece "Janet Alexander, only daughter of John Alexander and the deceased Agnes Graham" received her uncle's share in the lands of Gartmore (Sheriff Court Book, Stirling). If John and Agnes Graham Alexander had other children, they were dead by 1641, otherwise they would have inherited from their Uncle Gilbert along with Janet Alexander.

"On the 20th April 1635, [John Alexander] was, conjointly with his father, appointed Master of Minerals and Metals in Scotland (Reg. Mag. Sig., vol. iv., p. 60, Paper Register). He was afterwards nominated General of the Mint, an office which yielded his successor £500 per annum, with perquisites (Reg. Mag. Sig, lib. iv., No. 237)." John served as General of the Mint until 1641, shortly before his death in Scotland.

A number unrelated Alexander families in North American, with immigrant ancestors who appeared in Massachusetts, New York, New Jersey, Maryland, Virginia and North Carolina in the 17th century, all claim to be descended from John Alexander, son of William Alexander, Earl of Stirling. In fact, none are.