I went up both lines, went from beats to Beat.
Sarah Smith Beat died in Dundee Gros ref. 1898 BEAT SARAH SMITH F 76 ST ANDREW (DUNDEE) DUNDEE CITY/ANGUS 282/04 1114 I downloaded both hers and Joseph Beat 1900 BEAT JOSEPH M 83 ST ANDREW (DUNDEE) DUNDEE CITY/ANGUS 282/04 0628 if anyone wants them, no connection to the Powrie surname, but it is a placename from Dundee area. There are two castles, south powrie and north pourie, which may be near to one of the them, worked on the estate of one.
joseph's siblings:
Alexander Burns Beat <https://familysearch.org/pal:/MM9.1.1/XB8M-8J3>
Scotland, Births and Baptisms, 1564-1950
birth: 31 Jul 1827
christening: 05 Aug 1827 DUNDEE,ANGUS,SCOTLAND
parents: Andrew Beat, Helen Grubb
David Beat <https://familysearch.org/pal:/MM9.1.1/XBZ1-7S9>
Scotland, Births and Baptisms, 1564-1950
birth: 20 Jan 1830
christening: 31 Jan 1830 DUNDEE,ANGUS,SCOTLAND
Elizabeth Beats <https://familysearch.org/pal:/MM9.1.1/XYP5-YQ1>
Scotland, Births and Baptisms, 1564-1950
birth: 10 Dec 1857 DUNDEE,ANGUS,SCOTLAND
parents: Joseph Beats, Sarah Smith
Powrie Beats <https://familysearch.org/pal:/MM9.1.1/XY16-QFZ>
Scotland, Births and Baptisms, 1564-1950
birth: 27 Aug 1862 DUNDEE,ANGUS,SCOTLAND
parents: Joseph Beats, Sarah Smith
parents: Andrew Beat, Helen Grub
Joseph Beat <https://familysearch.org/pal:/MM9.1.1/XB8M-CNY>
Scotland, Births and Baptisms, 1564-1950
birth: 23 Nov 1822
christening: 01 Dec 1822 DUNDEE,ANGUS,SCOTLAND
parents: Andw. Beat, Helen Grubb
If I were in country I could check guild records, rental records etc. but I will search the Angus Monument inscription books I have at home. Mary Powrie schacht, oregon registered one name study researcher for Powrie surname.