1851 Census ( page ref 2402-614-4)
John Arrowsmith unmarried Iron Moulder 24 b.Gateshead
In his father's household George widow 57 cordwainer b.Ferryhill
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Marriage Dec 1851 Gateshead
John Arrowsmith >< Susannah Sibbet
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1861 30 Railway St, Elswick 3815-102-32
John and Susannah with three children, including John, 2, b.Newcastle
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1871 same address, 5080-83-37
Sarah, wid ( shpuld be Susannah ! 49 with 12 yr old John.
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1881 2 Middle St Elswick ( 5054-87-51)
John single 21 cartman, with his widowed mother, susannah, 58
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John marries Margaret Noble Newcastle June qtr 1883
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Susannah dies aged 61, Sept qtr 1883 Newcastle.
Then into 1891 and 1901 censuses>>>>>
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Seems to fit ok !
John the cartman named his second son William.
His father John had a younger brother called William

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John Arrowsmith/Margaret Noble registered dtr Ellen at Newcastle RO in Mar Qtr 1890... " Ellen McBeth Arrowsmith"... but don't know where they got McBeth from ?
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Michael Dixon