This name has been transcribed as Mary E Douglass (Manchester 1878) but I'm not absolutely convinced it does say Mary.
She appears on the 1881 census in the household of my G/Grandfather William Walker(Manchester 1862).
She is listed as a grandchild of the head of the household - Elizabeth Walker(Leek 1825). I have only found one sibling for William, who was in the household, Agnes 1865.
I'm trying to find out about this 3 year old, as it may be the child of another sibling of William.
Have tried you looking for her on the 1891 census?
Perhaps her pob may not be Manchester (it's dittoed as Manchester on 1881c)
So far I've not been able to find a marriage for Elizabeth to James Walker, I need to investigate further with that.
Elizabeth Walker born c1825 Leek looks to be living with her brother
James NEWBY at School Farm Warbrick
he died 1933 probate to Emma NEWBY spinster (his daughter) living with him 1891.
There this marriage entry FreeBMD & Lancashire BMD
Marriage 1856 Salford
Elizabeth NEWBY name on same page
James WALKER1856 Salford Register Office or Registrar Attended Salford
NEWBY Elizabeth
WALKER James
possible baptism from Lancashire OPC
Baptism: 9 Mar 1828 St John the Baptist, Tunstall, Lancashire, England
Betty Newby Baptism: 20 Dec 1831 St John the Baptist, Tunstall, Lancashire, England
James Newby Abode: Leck James Newby Occ Farmer mother Mary