Found William's exact death date in 1753 on Geni.com:
https://www.geni.com/people/William-Miller-of-Glenlee-and-Barskimming-WS/6000000017849744126
"William Miller of Glenlee and Barskimming - Second son of Matthew Miller of Glenlee, Kirkendbrightshire. Died 16th September 1753. Mar. Janet, eldest daughter of Thomas Hamilton."
Christening date used as birthdate from FamilySearch.org:
William Miller
Scotland Births and Baptisms
Name William Miller
Gender Male
Christening Date 26 Jun 1676
Christening Place , KILMARNOCK, AYR, SCOTLAND
Father's Name Mathew Miller
Mother's Name Agnas Guthrie
Citing this Record
"Scotland Births and Baptisms, 1564-1950," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:XTVG-8FP : 10 February 2018), William Miller, ; citing Kilmarnock, Ayrshire, Scotland, reference 2:16DS2PN, index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 1,041,386.
Marriage info. on FamilySearch.org:
Wm. Miller
mentioned in the record of Wm. Miller and Janet Hamilton
Name Wm. Miller
Spouse's Name Janet Hamilton
Event Date 10 Sep 1713
Event Place Glasgow,Lanark,Scotland
Citing this Record
"Scotland Marriages, 1561-1910," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:XTBC-3PV : 10 February 2018), Wm. Miller and Janet Hamilton, 10 Sep 1713; citing Glasgow,Lanark,Scotland, index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 102,924, 919,484.
William was born in 1676. He was the son of Matthew Miller and Agnes Guthrie. He passed away in 1753.
MILLER, Thomas (1717-89), of Glenlee, Kirkcudbright Stewartry and Barskimming, Ayr. Published in The History of Parliament: the House of Commons 1754-1790, ed. L. Namier, J. Brooke., 1964: This source notes Thomas Miller's father was William Miller and his mother Janet Hamilton, daughter of Thomas Hamilton. Also noted is that William Miller was "town agent to Glasgow 1733-1753" -appears to be up to the time of William Miller's death. (link to this source below):
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