Hi John,
and welcome to rootschat.
Just seeing Joe's post... never mind, here's the son...
Is this what you are searching for?
1861 Census
RG9/937
Folio 41 p. 36
Northampton St Andrew
26 Vernon Street
Thomas Arnsby, head, 36, Shoemaker, b. Northampton Woodford
Charlotte, wife, 32, (Late ?) Ladies Maid, b. Hunts Gt Catworth
Thomas, son, 10, scholar, b. do.
William, son, 9, scholar, b. do.
George, son, 7, scholar, b. do.
Joseph, son, 2, b. Beds Casow (?)
William Water, boarder, unm, 20, shoemaker, b. Nthampton (something)
Edwin Corsbey, boarder, unm, 18, shoemaker, b. Rugby
There is this other Thomas Arnsby who might be the father:
RG9/959
Folio 186 p. 22
Woodford, Northamptonshire
Thomas Arnsby, head, 77, Pauper, b. Woodford
Mary, wife, 84, b. Huntingdonshire Bythorn (?)
Tanja