ISABELLE The Life of Isabelle Eberhardt By Annette Kobak Knopf. 258 pp. $22.95 IN OCTOBER 1904 a torrent of water rushed down the dry riverbed running through a French garrison town in southwest Algeria. Houses were submerged, families swept to their deaths. Next day a search was ordered for a European woman who had disappeared. They found her, dressed as an Arab cavalryman, buried under mud and fallen beams. She was 27 and her name, so far as she had a real one, was Isabelle Eberhardt. She was born in Geneva in 1877, the fifth, and unwelcome, child of a Russian lady who had left her husband in St. Petersburg and set off to wander with her children and the family tutor, an Armenian anarchist named Trophimowsky. The child was given her mother's maiden name. The father was "unknown" and never during her life did Isabelle acknowledge that he could be the man who ruled the scatty household in which she grew up. The tutor, so far as she was concerned, was a great-uncle; her real father she fancied as some Russian Muslim or Turk who had ruled in her infancy. Isabelle's mother was cool and indifferent, but the tutor was an exacting mentor. He saw that she was dressed like a boy, with hair cropped. He undertook her education, teaching her half a dozen languages, among them Arabic, which she learned to write with a fine hand. Her reading included Plato, Heraclitus, Rousseau, Voltaire, Tolstoy and the Koran in Arabic. To this diet she added the heady languors of Pierre Loti, the celebrant of Islamic life. "I was already a nomad as a young girl," she wrote later, "when I used to daydream as I gazed at the enticing white road leading off, under a more brilliant sun, it seemed to me, into the delicious unknown." Little wonder her heart was set on North Africa. When she was 20 she finally made the escape from the decaying villa near Geneva to which she had been confined, and crossed the Mediterranean. In Tunisia and Algeria she took up the pattern of life she was to lead for the next seven years, traveling restlessly from town to town and oasis to oasis, with forays to Marseilles, Paris and Geneva, but always returning to the edge of the Sahara with relief and melancholy joy. For along with her passion for the Arab world she had a Russian soul. "For us two," she wrote to her brother, "solitude is absolute, remember that! No one, ever, will understand our suffering, our aspirations and disappointments." But for the rest of her life she endeavored to express them in letters, diaries, essays, sketches and stories. Many of these were published in literary journals in Paris, Russia and Algeria during her lifetime. She had been dressed as a European boy during her childhood in Geneva at Trophimowsky's insistence; now as an adult in North Africa she wore the clothes of the young student of the Koran she wished to be taken for -- a white burnoose over a billowing silk shirt, baggy trousers, yellow slippers and, on her shaved head, a fez. The name she took was Si Mahmoud Saadi. Even she eventually realized that the Arabs were probably not taken in by the charade but gravely accepted it as a matter of tact. She was no figure of fun to them, winning the respect of the sheikhs by her knowledge of the Koran (on occasion, indeed, discussing the corruption of Mohammed's sayings that she believed must have come about during centuries of orthodoxy -- a liberty that has earned Salman Rushdie his death sentence). Her serious purpose, her familiarity with their beliefs and customs, and her active sympathy with the Arab grievances against the French, who had arrogantly and disdainfully been ruling Algeria since 1830, won her the friendship of Arabs of all classes. To the French she was an alarming nuisance. A Russian girl in male Arab dress who took part in anti-French demonstrations could hardly go unremarked. The police and the army kept close tabs on her, though efforts to expel her from the country finally ended in 1901 when she married an army officer from an Algerian regiment, gaining French citizenship. She had married for love, however, and was passionately faithful to her Slime`ne for a time, though before her death they drifted apart. He could not measure up to her exalted ambitions for him. Her unbridled sexual activity before her marriage was highly distasteful to the French and the fact that it was conducted with Arabs deeply threatening. She liked rough trade and approached sex in the spirit of a man -- insatiable and impersonal -- though in her coupling she played the woman's part. It amused her to be taken by men to watch dancing prostitutes performing, though women were of no particular interest to her either sexually or sociologically. For all her deep and sincere feeling for the Arab peoples, she never in her writing or recorded conversation alluded to the total repression of women in their society. Even now, Isabelle Eberhardt's sexual license seems excessive, and she paid a nasty price for it. Syphilis, as well as hashish, tobacco and malaria, dragged her down in her last years. But she had her other, cerebral side -- an intellectual curiosity that was as eager in its way as her sexual appetites. Though much of the speculation in her diaries was self-centered, wondering at her strange destiny -- "this inexplicable drama called my life" -- she had larger thoughts that ring true a century later. "Civilization," she wrote, "that great fraud of our times, has promised man that by complicating his existence it would multiply his pleasures." She was drawn, she wrote, only to people who suffered from "that special and fertile anguish called self-doubt, or the thirst for the ideal," but for all her Russian soul and her preoccupation with it, she was surprisingly down to earth in practical matters. It was plain to her that politics was totally inadequate to bring about the changes needed in Algeria's future, and as for Europe's colonial prospects in Africa, she was doubtful: "It is useless to fight against deep-running and immutable influences, and . . . a durable transplantation of civilization is not possible." In her own brief life, short of giving up her Muslim identity, she was quick to compromise to avoid trouble. "If the strangeness of my life were the result of snobbery, of a pose, yes, then people could say, 'She brought these events on herself,' but no! No one has ever lived more from day to day and by chance than I have . . ." Her cross dressing, whether in Arab or European costume, was not for effect -- she shunned poses -- but to establish an alternative to the identity that she had been deprived of in her childhood by parents who lied to her. Disguise, writes Annette Kobak, "represented an identity she genuinely wanted to assume. Her whole background had predisposed her to want 'the Other' -- not as an amusing ploy, but because she found it deeply seductive." She struck her friends as enigmatic. Kobak ascribes that to a basic emptiness. "Yet this emptiness itself becomes a powerfully interesting factor once it is understood as a central loss, and not as a failure." For all her masks and disguises, Isabelle was no phony. Frenchmen as well as Arabs admired her for her sincerity, simplicity, intelligence and courage -- all this quite detached from sexual attraction, for few men felt that. One left this picture: "Isabelle spoke slowly . . . with the most disagreeable and the most monotonous nasal accent in the world, showing all her teeth but no exuberance . . . Her bearing was always dignified, even grave; I should add that she completely lacked sex-appeal." Among her last written words were these: "The fact is that I no longer regret anything. In moments of calm and reflectiveness it seems to me that I've found the very point of my vagabond and tormented existence. A great serenity has settled on me, as if, after a painful climb, I had finally come through the zone of storms and found the clear sky. And yet, I don't flatter myself that I can easily communicate this state of mind. I don't seek to analyze myself, much less to strike a pose. I have no audience . . . I still bless my solitude, which allows me to believe, and which is remaking me into a simple and exceptional being, resigned to her destiny." After her death an editor who had been her friend collected her diaries, stories and essays and, souping up her vivid but austere prose to suit his own idea of fine writing, published a flowery volume that set in motion the legend of Isabelle Eberhardt. Much has been published since then, but surely no biography of her so fastidious and perceptive as Annette Kobak's. Eve Auchincloss is an editor at Connoisseur Magazine.