If the S.I. stands for Sarah Isabella I think they're mine.
I've just today stumbled on some information that makes me think this Carlton daughter married a Birkett. Not at all sure how this fits.
Thomas & Jane (McLean) Carlton had at least 5 children in Cumberland, England. The oldest was Sarah Isabella born c.1846.
I had lost track of her. Thomas, a daughter (Mary Jane, future Mrs Fred VanArsdale), and a son (David Carlton) emigrated to Louisville, Boulder, Colorado c.1880.
When he died a "Sarah Isabella Birkett" and a "John Irving Carlton" (a known son who stayed in England) gave Power of Attorney to a William Carlton ; and all 3 gave a quit claim deed to "Mary Jane VanArsdale" in Boulder County, Colorado in 1892.
Also the son David's oldest was Ann Carlton who married Robert Knowles in Louisville, Boulder, Colorado in 1883 ; and they lived in Wymore, Nebraska from c.1890 to c.1910.
I'm interested to see if we have a fit. David Knowles