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To start with, I think this is the family in the 1911 census- but father is Daniel, not Patrick:
www.census.nationalarchives.ie/pages/1911/Londonderry/Gelvin/Formil/903923Listed as Kane (interchangeable with O'Kane). Says couple married 14 years on transcription which is unlikely since Martha supposed to be only 25, Daniel supposed to be 23 and eldest child age 9.
http://www.census.nationalarchives.ie/reels/nai002822931/I think I have information on the family and the school photos I have from Lisnascreagh will likely show the children so will ahve a look in files to see what I can find.
Possibly some of Daniel's family?
"Letters of Administration of the personal estate of Patrick Kane late of Formil County Londonderry Farmer who died 7 March 1890 at Brockaghbuoy were granted at Londonderry to Ellen Kane of Formil the Widow." See
www.proni.gov.uk (unfortunately link 'image' is for wrong page in Will Book)
and this one? "Administration (with the Will) of the Estate of Patrick O'Kane late of Formil County Londonderry Farmer who died 27 June 1910 granted at Londonderry to Charles O'Kane Farmer." (no Will available online but PRONI will have it along with paperwork regarding the settlement of his estate).