Of the three Jeremiah's living in Co Durham in 1871 I chose this one because they are resident in Cockfield where the first 3 children of Mary in my first post were born. Also the names Robert and Jane are there. BUT the marriage certificate is the sure way to know you are following the correct family. None of this may be relevant.

This Jeremiah was born Northumberland
1971 RG10/4942/34/5
Cockfield Teasdale Durham
Robert Atkinson 48 coal miner Wallsend Northumberland
Jane wife 38 County Armah Ireland
Jeremiah son 18 coal miner Newcastle Northumberlan
Robert 15 coalminer Counden Durham
William 9 Howden Close Durham
John T 5 Cockfield
Jane 2 months Cockfield