Had a look at the 1851 census - bingo. William's Father must be an older son of this Elijah
In Hookagate .....
Elijah Hartshorn Head Married Male 54 born c1797 Coal Miner born St Julian,Shropshire
Elizabeth Hartshorn Wife Married Female 52 1799 - born Meole, Shropshire
Mary Hartshorn Daughter Unmarried Female 25 c1826 - born Meole, Shropshire
Hannah Hartshorn Daughter - Female 12 c1839 - born Meole, Shropshire
William Hartshorn Grand Son - Male 12 c1839 Scholar born Birmingham, Warks
I didnt notice if he was a Grandson back on the earlier 1861 census - and now wondering if theres a couple of Elijah's floating around !
Just checked and there are indeed 2 Elijah's - so not sure why this 1851 chap doesnt show up in 1861 in Hookagate .... hmmm