ON A JANUARY MORNING in 1941, his country at war and civilization as he had known it crumbling on three continents, Josslyn Hay, Earl of Erroll, was found dead in his Buick on a dirt road outside Nairobi, Kenya. There was a bullet wound in his head.

Murdered at 39, Erroll had been the instigator and, for over a decade, uncrowned king of what came to be known as the Happy Valley Set. Sinfully handsome--or "beautiful" as his contemporaries termed him--Erroll was a man of enormous charm, some ability and no discernible morals. He was a natural leader with flawless manners and impeccable style. Sportsman, gambler, drunkard and cuckolder of genius, he was also hereditary Lord High Constable of Scotland, and even a world at war was bound to take some notice of his violent end in an African ditch.

In due course Sir Delves Broughton, the husband of Erroll's latest and last paramour, and the most likely suspect, was brought to trial and then acquitted. During the trial, in a stuffy colonial courtroom thronged with friends and enemies of both the victim and the accused, a tale was unfolded so bizarre, so filled with hints, innuendo and outright accusation of multiple adulteries, seductions, blackmail and anonymous letters, that it makes most modern crimes of passion seem mundane as bread and butter. Within months of his acquittal Delves Broughton was dead by his own hand, but his wife Diana, a woman with the clear, remote beauty of a Dietrich or Lombard, after an initial period in Kenya settler's Coventry, settled down comfortably with the richest man in East Africa for her third husband. The mystery of Erroll's death remained unsolved.

Ten years later, when I arrived in Kenya, the murder and those involved in it, were still topics of "sundowner" conversation at the Muthaiga Club. At that time it seemed that the crime which had dealt a well-deserved death blow to a way of life as destructive as it was extravagant, must remain forever unsolved, although (mind you!) everyone knew someone who knew someone else who could finger the culprit if they so chose.

However, in 1969 the noted literary critic Cyril Connolly, author of Enemies of Promise and The Unquiet Grave, and a frequent visitor to Kenya, succumbed to a long-standing obsession with the mysterious crime and decided to find out more about it than could be learned from the transcripts of the lengthy court case. Connolly was in an admirable position to grapple with the enigma. He had been the contemporary at Eton of Erroll and several others concerned in the case; he belonged to the right London clubs, and had access to the right social circles. Above all he was, according to James Fox, a man "who took his obsessions seriously, blazing with mental energy and capable of storing and retrieving detail with startling powers of recall."

With Fox acting as Archie Goodwin to his own Nero Wolfe (the comparison, by the way, is appropriate-- from the physical inertia and powers of deduction to the love of food), Connolly set to work and eventually produced a 6,000 word article for the London Sunday Times Magazine, for which publication Fox was then working. The article drew the expected flak from a righteous public, but it also called forth a flood of personal reminiscence and a whole new trail of evidence. Connolly died in 1974, but bequeathed his voluminous collection of notes on the Erroll murder and (apparently) his unassuaged compulsion to his legman. Fox then took up the challenge of discovering who had actually shot Josslyn Erroll on that long-ago January night, and this book is the result--a quest incorporating a whodunit.

Washed in the wake of the First World War to the rolling game-infested plains and forested hills of Kenya, the Happy Valley Set was composed largely of what Fox terms "the victims of the British system of primogeniture." Aristocratic remittance men, playboys and moneyed adventurers, with the occasional American or European spouse or adjunct, they grasped joyfully at the freedoms possible in a new pioneer country with a beautiful climate, superb scenery and unnumbered natives who could be bought or bullied into a semblance of the loyal serfs they imagined they had known in England before 1914. The group was small and elitist and very different from the hard-working civil servants, engineers, farmers and tradesmen who constituted the majority of Kenya's tiny white population.

For a decade and a half they existed by their own iconoclastic code, unrolling their colorful excesses before the startled eyes of the more prosaic settlers like some bizarre forerunner of the most titillating afternoon soap opera. In this little coterie fortunes were made and lost with the same ease and celerity as marriages, and wives were so negotiable one wonders why the devalued state of matrimony was ventured on at all. The women were as predatory as the men and called the roll of their lovers at bougainvillea-strewn dinner tables with the same boastfulness as the men recounted their "bags" on safari. Voyeurism, sado-masochism and fraud passed almost unnoticed in the general welter of adultery and seduction, and every aberration was accompanied by prodigious quantities of liquor, drugs and food. Just to read the menus exhausts one, to say nothing of the safaris that were undertaken at the drop of a double Terai hat--often to cure a hangover. One famous hostess insisted that her guests watch her bathe and dress before dinner; one of the nastier males riddled his house with peep-holes to spy on his friends in their more private moments; they offered each other heroin in silver syringes, stole or set fire to their own possessions for the insurance, dropped hens from aircraft to see if they would fly, and showed far more concern for horses and dogs than for their unfortunate children.

When Delves Broughton introduced the young and beautiful Diana into this society, bets were immediately laid as to how short a time it would take to persuade her out of his bed. It was not very long. Within weeks she was desperately in love with Erroll and, in accordance with a marriage pact made with her elderly husband, insisting on being "made over" to her lover for keeps.

During their investigations of this nest of hedonists Connolly and Fox discovered several suspects, male and female, with all the classic motives for wanting Lord Erroll dead--jealousy, envy, lust and rage. Several of these were available for interview, others they researched with scholarly thoroughness. They questioned friends, neighbors, enemies and servants; pondered, compared and deduced, and eventually Fox was enabled to offer a solution.

This is hardly an edifying book, but Fox has done an admirable job not only of investigative reporting but of arrangement. Told on two time planes, with many knotty threads and strange cross-currents, it reads like the best sort of thriller, sustaining tension from crisis to crisis by way of Christie-ish clues and red herrings (even the policeman is named "Poppy"), to the final denouement. Of course, given the cast of characters he had to work with, it would have been difficult to produce a dull book. Somerset Maugham, it is said, toyed with the idea of writing a novel around the Erroll affair, and one can only suppose the activities of the Happy Valley Set struck him as a little too much for the fiction-reading public of his time.

It is difficult to see that circle today as anything but the plague of parasites their less privileged contemporaries considered them, although, in his dry and detached manner, Fox manages to elicit a moment of sympathy from the reader as at last the champagne is finished and the final roses fade. However, for the socially- conscious and the sententious it will be a relief to know that many of the wicked Earl's companions came to a sticky end through suicide, drugs and drink. But Diana, the eye of the storm, married for a fourth time to Lord Delamere, continues to live comfortably in Kenya and when the mood takes her fishes for marlin in the warm blue waters of the Indian Ocean.