It started with a quest to solve the "greatest geographical mystery" of the age. It ended, more than a century later  and if you follow the rather narrow logic of this book  with ethnic cleansing in Darfur. The "mystery" was the source of the Nile, which had exercised Europeans and Egyptians ever since Ptolemy in the second century CE.

It was this that drew Tim Jeal's protagonists  Richard Burton, John Hanning Speke, Samuel Baker, David Livingstone and Henry Morton Stanley  to central Africa in the 1850s and 60s; together, of course, with the allure of the fame that being the first to crack the riddle would bring. On their way they were shocked by the atrocious slave raiding they found there, provoking a campaign against it that came to bear some of the attributes of a literal crusade  the slave traders were mostly Muslim Arabs  and later colonialism, ostensibly to protect the Africans but with exploiters and "great power" ambitions also muscling in. It was this that gave rise to the drawing of Sudan's present artificial border with Uganda, which has caused such an "incalculable amount of suffering" in all these countries in modern times. That's the final link to Darfur.

The first part of the story has been told often before: hagiographically in contemporary books and memoirs; classically in Alan Moorhead's The White Nile (1960); and more recently in Jeal's own biographies of Livingstone (1973) and Stanley (2007), which he draws on heavily here. These two books offered revisionist assessments of both their subjects, the first pulling the missionary Livingstone down a little, the second making some interesting excuses for the usually excoriated Stanley, one of which was that he deliberately exaggerated his own bloodthirstiness in order to satisfy his American newspaper readership. This book does much the same for Burton and Speke, originally travel companions who came to loathe each other as a result of various imagined slights and betrayals. They also disagreed on the question of the "source".

The battle between them should have come to a head at a meeting of the British Association in September 1864, had not Speke killed himself the day before on a partridge shoot. It was almost certainly accidental, but Burton hinted that Speke had taken his own life, scared of the confrontation. In fact Speke had been right about the source of the Nile, and was the one who should have been awarded the palm for discovering it; but his reputation never recovered from Burton's slanders. Jeal puts this right, puffing Speke and demolishing Burton  not an echt explorer, he thinks. Baker also comes out of this account badly, being mainly responsible, in Jeal's view, for the switch from humanitarian protection to a more formal and brutal kind of imperialism in the 1880s and 90s.

Jeal is right to insist that this stage should not be confused with the earlier, more "innocent", one, when most of Africa's explorers were motivated not by greed or the urge to control, but by simple curiosity, competitiveness, and the desire to pit their bodies and minds against the appalling hardships that African travel at that time involved. Jeal is graphic about these: the climate, terrain, diseases, dangerous animals (especially the tiny ones), and natives understandably suspicious of interlopers after their experiences of the slavers and of others who sought to "eat their countries".

Most European explorers suffered terribly, and many died horrible deaths. At least one had his genitals cut off first. But this only spurred the others on. Jeal wonders whether the Christian doctrine of "redemption through suffering" might have had something to do with it. Others might suspect an over-developed machismo, were it not for the several women who went out there too. Jeal restores these to the picture  Baker's wife Florence, for example; and also the contributions of their hundreds of African and Arab guides, translators and porters, without whom the Europeans would have got nowhere at all. Often they were carried by them. (Isn't that cheating?) Still, as Livingstone stated heroically in April 1873: "It is not all pleasure, this exploration." That was just a few days before his own wretched and lonely death, near the edge of the Bangweulu swamp in present-day Zambia.

Livingstone's personal failure as a missionary is well known. (He made just one African convert, who later relapsed.) He was also wrong about the source of the Nile. Even if he had been successful here, however, would it have mattered? "Suppose you get to the great lake," Chief Commoro of the Latuka asked Baker in 1863, "what will you do with it? What will be the good of it?" Baker's own great chief, Lord Palmerston, thought much the same. "No doubt Speke has, at much personal trouble, risks and expense, solved a geographical problem, which it is strange nobody ever solved before," he responded to those lobbying for a knighthood for him. "On the other hand  the practical usefulness of the discovery is not very apparent." (So Speke was never knighted; later his family added a hippopotamus to their coat of arms.) In the end the source of the Nile turned out to be roughly where Ptolemy had put it. So no great surprise there. But that may have been immaterial. It was the hopeful travelling, rather than the arrival, that stirred the explorers, and fascinated their contemporaries back home when they read about them.

They might have been even more fascinated by Jeal's splendid account here. One of his discoveries is early manuscript and proof versions of Speke's Journal of the Discovery of the Source of the Nile (1863), which reveal the excisions his publisher insisted on (Speke called it "gelding"). These include some shockingly favourable judgments of African societies  shocking because they left no room for the renovative powers of Christianity; a passage on sex advice he gave to the son of a chief (basically, that size doesn't matter); and a touching account of his love for a Bagandan woman, Méri, which was unrequited. Her chief couldn't understand why he didn't force himself on her; Speke's reply was that "cords of love were the only instruments white men knew the use of". If only.

Bernard Porter's The Battle of the Styles is published by Continuum.