Frances Holmes
born April 1831–April 1832
  in Co. Durham
died very roughly 1901

1841 census: (as Francis Holms) living in Waldridge with grandmother, uncles, and cousin. Age is 9, born in county.

My first thought was that she and the Anthony shown in the same household were children of Mary Holmes as the 1841 census doesn't show relationships, but according to Amanda Cozens, she was the daughter of Thomas Dixon Holmes.