I'm not a famous explorer, but I think I would go UP the river to look for the source.
The Nile flows from South to North? Hey, that could explain it. Of course so does the Monongohela here in the USA. But a north flowing river is a rarity. And I doubt if much of the world cares the Nile is 66 miles longer than we thought. After all most are more intrested in who is going to win IDOL!bwhahahaha!
BTW...before somebody else posts it:
"Dr. Livingston, I presume?"
Well, Capt., that is why you are not famous and they are, you would do it the conventional way. It is also the reason the river was longer than they expected.