River of the Gods by Candice Millard is a solid book subtitled Genius, Courage, and Betrayal in the Search for the Source of the Nile. The book tells the story of Richard Burton and John Speke as the two British explorers searched in Africa to find what feeds the longest river in the world, and then to prove their dissenting opinions.
Burton was the leader of the 1856 first expedition to find the source. He was a master swordsman, impersonated a Muslim to go to Mecca, and was adept at languages, later to become known for his translations. Speke joined the expedition as a surveyor and the men were in Somaliland when their expedition was attacked and men killed. Speke was taken, but managed to escape while suffering eleven stab wounds. Burton was stabbed through his jaw, and the effort abandoned and the men returned home to England. Speke felt that the expedition was not prepared and it Burton's fault.
Despite this start to their relationship, the two set off on a second trip to Africa in search of the source of the White Nile. Joining the expedition was an African named Sidi Mubarak Bombay, who would prove important to their efforts, particularly Speke's. The expedition traveled from the Indian Ocean through East Africa and six months after they left the coast, Burton was almost completely paralyzed with malaria. Burton recovered somewhat and the two men came across Lake Tanganyika, the longest and second deepest freshwater lake in the world. They were the first Europeans to reach the lake, which Arabs had been to for decades. Burton believed the White Nile flowed out of Lake Tanganyika, but Speke had heard of another lake and wanted to go in search of it. Burton agreed to let Speke go without him and Speke and Bombay traveled on to Lake Nyanza, which covers nearly 27,000 square miles, more than twice the size of Lake Tanganyika. Speke immediately felt he had found the source of the Nile, and without his expedition lead, but Burton was skeptical of Speke's claim.
Speke returned on his own to England and immediately made the case for Lake Nyanza, which he renamed Lake Victoria, as the source of the White Nile and painted a picture of Burton as bedridden and unable to make the journey there. Speke received funding from the Royal Geographic Society to return to Africa and hopefully settle the matter of which lake fed the White Nile, with Speke now leading his own expedition. Speke returned to Zanzibar in 1860 and then he and the expedition got to Lake Nyanza, and a waterfall roughly sixteen feet high and nearly a thousand feet wide, with water from the lake going into the river. He didn't complete navigation of the lake or do anything else to definitely prove it the source, but he felt he had seen enough.
Speke returned to England in 1963 and wasn't very good at proving his assertation about Lake Nyanza over Lake Tanganyika. He didn't have enough evidence to back his claim, and Burton was a much better writer, providing detail that Speke did not. Burton and Speke were to debate the source of the Nile in a Royal Geographic Society talk on Sept 16, 1864, but Speke shot himself prior to it. Nearly a decade after Speke's death, someone else confirmed what Speke had said, Lake Nyanza was the source of the White Nile. It was later found that while Lake Nyanza the principal source, the lake is fed by many smaller rivers and streams, the largest of which is the Kagera River. Speke ultimately was proven correct, but history remembers Burton more, with his books, poems, and translations providing a greater measure of fame than his exploration.