By Kate Simon

Harper & Row. 240 pp. $19.95

"COMING back was what life did, it seemed," muses Kate Simon late in this, her third volume of memoirs. "Nothing was ever quite finished, always the misshapen shadow, the distorted whisper of a half-forgotten tune."

Writing in full awareness of her impending death (which came earlier this year, at 77), Simon peers bravely into the shadows of her life: an unhappy marriage and failed love affairs, the untimely deaths of her first husband, of a beloved younger sister and -- most bitter -- of her only child. Intermingled with these painful passages are vivid scenes from her many years of travel writing and expatriate living.

Simon was already well-known as the author of admirable guides to Mexico, Italy and New York when, in 1982, she published Bronx Primitive, an arresting memoir of her turbulent childhood as the daughter of Jewish immigrants from Warsaw who settled in the Bronx after World War I. In 1986, she followed it with A Wider World, in which the adolescent Kate escapes from her repressive father to Hunter College and the Bohemian precincts of Manhattan.

While still in college, she writes in Etchings in an Hourglass, Simon fell in love with a medical student. He became a distinguished endocrinologist but died of a brain tumor in his early thirties, leaving Simon to raise their small daughter, Lexie, alone. Simon married again, uncongenially, in part to be able to give Lexie a stable home. She was to need it, for, like her father, Lexie developed a fatal brain tumor. After Lexie's death and the breakup of her marriage, Simon became a full-time travel writer, a professional itinerant with 40 addresses over the years.

This sequence of events emerges only gradually in Etchings, which begins with Simon's hospitalization for stomach cancer sometime in her seventies. In the second chapter she writes of a powerful love affair in her early thirties. The third is about a much-later trip to India. The fourth, "A Cluster of Enlightenments," sketches a variety of insights garnered from chance meetings over the years.

Though this helter-skelter structure is not very satisfying aesthetically, the emotional reason for it is clear: It is a kind of painful circling around the central event of Simon's adult life, "the memory fleeing, reluctant, darting here and there harried by emotions and attempts to avoid recalled emotions." That event, the prolonged dying of her bright and multitalented teenaged daughter -- partially paralyzed, incontinent and furious with her mother for reasons that are never clear -- is finally recounted by Simon with a clipped dispassion that is almost unbearably chilling.

The willed coldness -- "my coat of ice," she calls it -- that Simon adapted in the face of suffering (her sister's death followed her daughter's by only a couple of years) took its toll. "I . . . began to think of God, or Nature, or Life, as one of the most powerful of the criminally insane." But her detachment is also one of her great strengths as a descriptive writer. In the hospital at book's beginning, following a cancer operation, Simon lifts her gown and calmly inspects "a small railroad track of staples . . . I'm amazed and amused: I had expected stitches concealed by bandages and here I was, raw flesh clamped together as if it were a bundle of papers." The tormented shrieks of a terminal cancer patient in the next bed she translates "into raucous jungle bird calls."

The second half of Etchings in an Hourglass is a collage of her travels -- exotic scenes, oddball adventures, eccentric characters in Paris and Rome and London, of course, but also in Haiti, Tunis, Leningrad, and Cozumel in the days when it was an undeveloped paradise. (Here the book's random organization becomes tiresome. It is almost impossible to date any given episode -- to figure out, for example, how old Simon is during a romantic idyll on that Mexican island.)

Simon is a bit of a sexual adventurer, falling into unlikely beds out of curiosity or indifference -- "my usual promising and dangerous 'Why not?' " -- as often as out of lust. Some of these episodes are funny, others bizarre, one or two disturbing. All are described with remarkable candor.

Simon loves and writes well of Renaissance art, of food and wine, of wild dancing and all kinds of music. She analyzes with authority, for example, the many influences on a Cozumel band: "the propelling beat" of Cuban salsa, "the rueful tunes of Haiti," "the long wail of Mexican ballads" and "the merry jumpiness of Veracruzana songs, like 'La Bamba.' "

She has the gift for friendship with people from many backgrounds: a Scandinavian seaman and his Chinese wife in Oaxaca; a grown-up Italian street waif who believes he is a nobleman by birth; an elderly French woman mayor, who during the war had been the guardian of jewelry and paintings for Jews fleeing the Occupation. And a writer's eye for the varieties of human absurdity: "How did an elderly Italian, cheery and pasta-paunched, come away with a creamy blond Viennese hausfrau and settle with her in Haiti, both gigglingly happy and both formidable masters of dominoes, their victories a generous source of extra drinks?"

There are happy moments in this book, but the shadows are always there. Simon writes near the end: "At seventeen I was so enamored of life, of its vagaries, its soaring flights and precipitous depths, that I promised myself I would experience everything, stipulating no qualities good or bad, and it has pretty much all happened. Little more than I knew at seventeen do I surely know who I am at seventy-five. At five o'clock on a gray winter morning I am alone in the world, its oldest orphan, singing with Leadbelly, 'Good morning blues. Blues, how do you do?' "

Kate Simon's last song is a sad one, but she sings it well.

Nina King is editor of Book World.