.....hate to break the news

This Agnes's birth, actually born end of Dec. 1874 but registered early 1875, looks to probably have been illegitimate going by the birth details showing on IGI:
AGNES MITCHELL MALCOLM Birth: 11 DEC 1874 Hamilton, Lanark, Scotland
Parents: Mother: JANE MALCOLM
No father's name showing on the birth registration in would appear. I would certainly start with the marriage cert. for verifaction of details.
Regards.
Monica