Right, after some refreshment
I looked a little deeper into the relationships in 1881
The Philirn Barker 29 I suspect when you look at the page image will be a Phillip, he is enumerated as brother to William the head of household
The Walter Forsyth 34 is enumerated very handily as brother in law suggesting that Euphemia was a FORSYTH also
Looking at new familysearch finds some interesting hits
A possible marriage
William Barker
Scotland, Marriages, 1561-1910
marriage: 04 Jun 1875 Saint Rollox,Glasgow,Lanark,Scotland
spouse: Euphemia Forsyth
groom's name: William Barker
bride's name: Euphemia Forsyth
marriage date: 04 Jun 1875
marriage place: Saint Rollox,Glasgow,Lanark,Scotland
indexing project (batch) number: M11929-1
system origin: Scotland-ODM
source film number: 6035516
And three deaths in Ohio, the images of the death registrations are also on familysearch
William Barker
Ohio, Deaths, 1908-1953
spouse: Euphemia Forsyth
child: James Barker
name: James Barker
event: Death
event date: 26 Nov 1950
gender: Male
death age: 63y4m21d
race: White
birth date: 05 Jul 1887
birthplace: Glasgow, Scotland
estimated birth year: 1887
father: William Barker
mother: Euphemia Forsyth
digital folder number: 4109348
William Barker
Ohio, Deaths, 1908-1953
birth: Scotland
spouse: Euphemia Forsyth
child: Ann Livingston Campbell
name: Ann Livingston Campbell
event: Death
event date: 06 Dec 1922
event place: Cleveland, Cuyahoga, Ohio
street address: 3413 High View Ave.
gender: Female
death age: 46y 8m 16d
marital status: Widowed
race: White
occupation: Domestic
birth date: 20 Mar 1876
birthplace: Scotland
estimated birth year: 1876
burial date: 09 Dec 1922
cemetery: Riverside Cemetery
father: William Barker
father's birthplace: Scotland
mother: Euphemia Forsyth
mother's birthplace: Scotland
spouse: John Campbell
digital folder number: 4000534
William Barker
Ohio, Deaths, 1908-1953
spouse: Euphemia Forsythe
child: Phillip Barker
name: Phillip Barker
event: Death
event date: 17 Apr 1952
gender: Male
death age: 68y6m16d
race: White
birth date: 01 Oct 1883
birthplace: Scotland
estimated birth year: 1884
father: William Barker
mother: Euphemia Forsythe
digital folder number: 4109418
This all suggests they are the right family
The marriage and births should be available on Scotlandspeople and should give you more detail
Nivard Ovington in Cornwall (UK)