The Oxford University Press' "Dictonary of Quotations" has the following version:
The noble Duke of York, He had ten thousand men, He marched them up to the top of the hill, And he marched them down again. And when they were up, they were up, And when they were down, they were down,, And when they were only half way up, They were neither up nor down.
It adds the information that its was "first printed in A. Rackham: *Mother Goose' (1913)."
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sj