SHE WAS A stunning beauty, exceptional even by Hollywood standards; and she was an actress of extraordinary dramatic promise. As a movie newcomer, she rated as "good copy" in the fiercely independent tradition of Katharine Hepburn and Margaret Sullavan, who preceded her by only a few years. Paramount, the studio that signed and began to build her, adopted the line that she would be the most magical star since Garbo.

In similar stories, the phrase ". . . and now she is forgotten" would appear about here. But Frances Farmer is not forgotten. Official Hollywood may have sought to erase her memory, but the legend that flickered for a while is once again full-flamed. If William Arnold has his way, Frances Farmer not only will be remembered but substantially rehabilitated in movie history.

William Arnold is a sedate, friendly, neatly bearded young man whose new book, "Shadowland," might well be titled "The Search for Frances Farmer." Arnold, a reporter for the Seattle Post-Intelligencer, spent three years piecing together the puzzle of the turbulent, doomed actress who once had been Seattle's special pride, but then was "crucified" by the city over the years, according to Arnold.

It began in 1973, when Bill Arnold, then 27, joined the Post-Intelligencer as an editorial writer. He was already addicted to old movies, and a nearby revival house was offering one he hadn't seen: a 1936 Samuel Goldwyn production called "Come and Get It," from one of Edna Ferber's generations- spanning novels. The male leads were Joel McCrea and Edward Arnold, and also in the cast was Walter Brennan, whose performance won a supporting Oscar.

But the revelation to Arnold as he watched "Come and Get It" was the gorgeous leading lady, by the name of Frances Farmer. He hadn't even heard of her. He found her" . . . so incredibly beautiful, so hauntingly mysterious" that he decided to find out all about her. That took some time and effort, and for a while Arnold suspected a Hollywood conspiracy to turn Frances Farmer into a nonperson. But eventually he learned that she was a Seattle girl (entirely a coincidence), that her tempestuous movie career spanned just half a dozen years and ended abruptly when she was jailed in 1942 on charges of drunken driving and resisting arrest.

That was only the beginning of Frances Farmer's harrowing descent. For the rest of her life she was in and out of mental institutions, most appallingly in Washington's Western State Hospital for the Insame --tion camp.

Yet in 1957, the 43-year-old Frances Farmer was an unexpected "comeback" story, as far as it went. Still (or once again) alluring, she sang "Aura Lee" on the Ed Sullivan show, and months later was the subject of one of Ralph Edwards' more dramatic "This is Your Life" surprises. In 1958 she even made another movie (of a sort), playing with the late Bobby Driscoll -- another of Hollywood's Tragic Case Histories -- in a teen-age exploitation item called "The Party Crashers." It did not exactly rekindle memories of the luminous blonde who had once been leading lady to Bing Crosby, Cary Grant, Joel McCrea, Ray Milland, Fred MacMurray and John Garfield.

In any event, the comeback did not fully ignite, nor did Frances regain an emotional equilibrium. She did some stage work and settled in Indianapolis, and was hostess of the afternoon movie on local TV there; but in 1964, when NBC's "Today" show planned an hour-long profile on her recovery from a lifetime of mental illness, she became surly and unglued, alienating network personnel and managing to get the project scrubbed.

In Indianapolis she began living with a widow named Jean Ratcliffe, with whom a lesbian association was accepted by their neighbors; and after Frances Farmer's death in 1970, Jean Ratcliffe took over and completed the Farmer "autobiography," published two years later as "Will There Ever Be a Morning?"

Bill Arnold rejects most of the Ratcliffe book, which he says opens more questions than it answers. In "Shadowland," he retraces the odyssey of Frances Farmer thus:

As a talented drama student at the University of Washington, she became enamored of the local radical movement and made a trip to the Soviet Union, for which expenses were paid by Voice of Actgion, a local radical newspaper. Frances' mother, Lillian Farmer, attempted to prevent her daughter from making the trip, which she felt certain would make a Communist of Frances.

Returned from the USSR and uneasily reconciled with her parents, Frances in that same year was signed by Paramount; and playing opposite Bing Crosby in only her second picture -- "Rhythm on the Range" in 1936 -- she attracted such favorable notice that Goldwyn borrowed her for "Come and Get It," the picture that made her a sensation.

Graduated to star billing and regarded as perhaps the most promising young film player in 1937, she also acquired a reputation for hostility and uncooperativeness. She left Hollywood against her studio employers' wishes to play Lorna Moon in the original Broadway production of Clifford Odets' "Golden Boy," for which she joined the fabled Group Theatre and (her mother would later claim) absorbed another communist brainwashing.

She returned to Hollywood in 1938, but Paramount was no longer interested in her, relegating her to minor features. Her brief marriage to actor Leif Erickson broke up. She continued to acquire enemies, but took such film work as she could get and seemed on the threshold of better things when cast in "Son of Fury" with Tyrone Power and Gene Tierney. But her first arrest occurred soon afterward, with the rest of the story becoming ever tawdrier -- including two more short, hectic marriages in the 1950s, more or less "between engagements" in institutions.

In "Shadowland" Bill Arnold is enormously sympathetic to Frances Farmer. Although he does not believe she was treated fairly by Hollywood, the villain in his story is not so much filmland as it is Frances, own late mother, who, he feels, always hated her. ("And I think she hated her mother, too.") Lillian Farmer contended that the communist influence was what ruined her daughter. The other view is that Frances was a victim of such anticommunist hysteria as her mother embodied.

Bill Arnold does not want Frances Farmer to be remembered as a stringy-haired, snarling tigress who was forever getting her pictures in the papers for kicking and cursing the officers trying to get her into the paddy wagon. Instead, he would have us consider the luminous young lady whose performance in "Come and Get It" is still revealing of major accomplishment, or the gorgeous creature who, romancing Cary Grant in "The Toast of New York," still suggested a budding major star.

He is counting on his book, as well as the magic of film and its very permanence, to enshrine Frances Farmer as one of the great might-have-beens.