Compelling look at elderly woman's plight; Kate Quinton's Days, by Susan Sheehan. Boston: Houghton Mifflin Company. 158 pp. $15.95.

Feb. 24, 1982, was a cold day in New York City. Kate Quinton, a pale, thin elderly woman, lay in bed at Lutheran Medical Center in Brooklyn. The winter-gray afternoon light filtered into her room. ... She lay still. She occasionally glanced across the room at her closet (it was marked ''A'') and at her roommate's closet (''B''). She looked at A and then B, B and then A, as she had been doing for days....m

From the very first, Susan Sheehan captures our attention with prose so transparent we find ourselves staring, as if through a window, at people who seem to be going about their lives unaware that we are watching them.

Sheehan, a staff writer for The New Yorker, is the author of ''Ten Vietnamese ,'' ''A Welfare Mother,'' ''A Prison and a Prisoner,'' and a Pulitzer Prize-winner, ''Is There No Place on Earth for Me?'' - a harrowing, intensely fascinating documentary account of a young woman suffering from mental illness and the institutions designed to serve her problems.

In ''Kate Quinton's Days,'' Sheehan turns her attention to the problems confronting a self-reliant woman forced by age and illness to rely upon others. Upon her release from the hospital, Mrs. Quinton (who, like most of the other people in this book, is real but whose name is a pseudonym) is chosen to be part of a New York City pilot project aimed at providing home care to people who might otherwise have gone into nursing homes. How does such a project work? And how well does it work for Mrs. Quinton? Sheehan's book answers these questions by investigating them in depth and detail, setting forth a complicated situation with masterly economy.

As in her previous books, Sheehan has chosen a subject so worthwhile as to give new meaning to the phrase ''redeeming social value.'' But social value alone does not guarantee an interesting or readable book. Sheehan's subject matter would seem to be as daunting as it is admirable. Will many people want to read about an old woman's encounters with doctors, social workers, home attendants, and insurance forms - a veritable odyssey through an alphabet soup of bureaucratic agencies? Yet Sheehan succeeds in making ''Kate Quinton's Days'' more absorbing than many works of fiction.

How does she manage this? Certainly not by sensationalizing or sentimentalizing her material. ''Kate Quinton's Days'' is not a calculatedly heart-wrenching story of a sweet, helpless old woman at the mercy of a faceless, inhuman bureaucracy. Kate can be as irritating as she is admirable, and is often stubborn and downright unreasonable. She emerges from Sheehan's calm, crisply understated prose as a very real individual with a history and personality all her own.

Eschewing the subjectivism of the ''New Journalism'' as well as the sensationalism of old-fashioned ''yellow'' journalism, the author never editorializes, choosing instead to record a wealth of objective details without apparent regard for whether or not they will appeal to potential readers.

The result of this seeming disregard for grabbing the reader's attention is that the story holds our attention because we are convinced that Sheehan is telling the truth and because the truth, clearly told, is always interesting. In the journalistic tradition of Orwell, Sheehan has achieved power through directness and clarity.

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