John and Ann were wed in 1853 and by 1861, Ann was a widow. They had two know children (at date 4 Sept 2018), Margaret, born 1855, and Mary Ann. Margaret was born in Auckland District, and it is probable Mary Ann would have been as well. There is one 1856 Auckland birth entry on Free BMD for a Mary Ann Ranson. There is however birth entries, 1856, for a Mary Ann Ranson in Chester-le-Street, Stockton and Gatehead Districts as well. Mary Ann was not in the 1861 census. Only one District has a death entry for a Mary Ann Ranson pre 1861: Chester-le-Street. If the family had stayed in County Durham, there are four death entries for a John Ranson between Mary Ann's birth and the 1861 census: 1857 S. Shields District; 1858, Auckland, Houghton le Spring,and Sunderland Districts.
"England and Wales Marriages", Durham, Durham, England, 1853, 2nd Quarter, Volume 10A, Page 256, John Ranson and Ann Cowey: online database Find My Past Website. Accessed 4 Sept 2018.
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