Thanks for that, probably means that the elder William had died before then.
Does you reply mean that the younger William was not found at all, or just not found with his father?
If it helps, in later censuses, the younger William was consistently recorded as being born in Pershore in 1837, as :-
William SMITH in 1851
William Henry SMITH in 1861 & 1881
William Hy SMITH in 1871
William H SMITH in 1891
Regards, Dave