Kelk family disapearance

[Slizzy Kelk]

My great, great grandfather was Joseph Hill Appleton (Chemist) and I am descended from his second marriage to  Ann Appleton (nee Webster).
He married Martha Kelk his third wife (Spinster) in Attercliffe on July 8th 1853 Joseph was 42 and Martha was 27, she was the daughter of George Kelk a Shoemaker.
They had two children, Josephine b 1853 who married Frederick Foster Hibbert of Sheffield clerk to the American consul and Mary Ann Appleton b 1855 in Attercliffe.

I am descended from Martha Kelk by her son John Kelk born out of wedlock in 1845. I have the birth certificate. Along with a friend and family member who is also descended via John to Martha (but by a different grandchild) we are currently researching Joseph Hill Appleton and his life with Martha alongside their 2 daughters Josephine & Mary Ann (our descendants half sisters).