There is no account of this in Herodotus' History that I can find. I just
searched on the word day through the entire work (on disk) and nothing like
a long day report showed up.
There is one aspect of this account that needs to be raised. I mentioned
earlier that one could not currently verify the account, since the relative
positions of the sun and moon were such that when things started up again,
all was the same as if no time had intervened.
But there is another unverifiable part of the story. How did the army know
that the day had lasted for twice the normal time? They did not have
watches and so could not independently verify the length of time. Since
they were busy fighting, it would seem unlikely that they would be able to
time the event by measuring their own pulse of their hearts. So how did
they know that the actual time was twice that of a normal day?
Let me suggest that the long day was an appearance, a psychological
perception to the battle participants. Watching Discover Magazine last
Wednesday, they told about a cop who was faced with a desperate situation in
which he needed to draw his gun and kill the bad guy before he himself got
shot. The cop said he was holding a night stick in his hand. He remembers
dropping the stick, drawing the gun, aiming at the wrong person, adjusting
his aim, then firing and then hearing the sound of the night stick hitting
the ground. An object dropped from 1.5 meters high hits the ground in .55
second. The cop thought that a lot of time had passed.
If Joshua's army was filled with adrenalin, their perception of time might
have been quite skewed. But such an adrenalin rush could easily have been
the miracle in answer to the prayer.
Foundation, Fall and Flood