ARROWSMITH, John Head 38 1853 Engineman Tow Law, Durham ARROWSMITH, Elizabeth Wife 36 1855Tow Law, Durham
Have you considered that he may just have been working a night shift on census night. They were only supposed to be listed on the census form if they have slept in the house listed on census night. A night worker technically should not have been listed with his family.
Son James also a mechanic was not home on the 1901 census so maybe he was working with his father on census night