A WOMAN'S place in public is to sit beside her husband, be silent, and be sure her hat is on straight." So said Bess Truman early in Harry Truman's political career. In this biography of her mother, Margaret Truman convincingly shows that the private Mrs. Truman (teasingly referred to by her husband as "The Boss") was anything but content to sit silently by in private. She assiduously read newspapers and The Congressional Record, let her preferences for appointees and policies be known, was not above nepotism (she once had Harry employ her alcoholic brother) and, for a while, was on Truman's office payroll. Domestically, she kept a tight rein on finances, to the point of subjecting her husband to lengthy separations from his family rather than pay high Washington rents.

Elizabeth Virginia Wallace was born in Independence, Missouri, in 1885. Her handsome father was a political-appointment wangler with no head for business and no tolerance for alcohol. In marrying Madge Gates, daughter of a prosperous miller, he was kept from insolvency by regular infusions of cash from Queen of the Pantry Flour.

Bess was the first of five children born to the couple. After one died in infancy, Madge went into physical and emotional decline, leaving her adolescent daughter to take charge of the boys. At 16 Bess graduated from high school an expert horsewoman and tennis player, a "demon ice skater" and "champion slugger" at baseball. Lack of money prevented a college education.

The great trauma of Bess Wallace's life took place shortly after her 18th birthday, when her father, chronically depressed by debt and drink, shot himself. A gruesome description of the suicide appeared in the Independence Examiner. "The ball passed . . . out at the right temple and fell into the bath tub." Madge Wallace "went to pieces," moved into her parents' 14-room mansion at 219 North Delaware Street, and became a social recluse. Bess took on her role as matriarch of the Wallace clan (caring not only for her mother but also her weak brother and his family) until her mother's death 49 yaars later.

Meanwhile, a bespectacled, unathletic farmer named Harry Truman had been enamored of Bess since she was 5. "She sat behind me in the sixth, seventh, and high school grades," he later recalled, "and I thought she was the most beautiful and the sweetest person on earth." Living in style in her grandfather's house, Bess had richer suitors, but none of them relished taking on a dependent mother-in-law. Harry was the exception.

One night in 1910 he appeared on Bess' doorstep, ostensibly to return a cake plate from a cousin's house across the street. He was bronzed and muscular from working the family farm, a four-hour buggy ride away. Bess was intrigued by his frank talk and multiple interests in literature, history and music. They began a correspondence which lasted throughout their lives. It forms the core of this biography. Margaret Truman found 1,600 letters from her father in the attic on North Delaware Street. Unfortunately only about 100 others survived the fire to which her mother consigned hers in old age.

Harry Truman's early letters are earthy, humorous, full of ardor and ambition. "Would you wear a solitaire on your left hand should I get it? . . . I've always had a sneakin' notion that some day maybe I'd amount to something . . . I doubt it now though . . . It is a family failing of ours to be poor financiers . . . Still that doesn't keep me from having always thought that you were all that a girl could be possibly or impossibly . . . I've been crazy about you ever since we went to Sunday school together."

BESS WAS interested but reluctant to repeat her mother's experience in marrying a poor man. She kept him waiting 3 1/2 years before accepting his proposal of marriage, little knowing the enormous extent of his dreams. "How does it feel," he half-jokingly asked, "being engaged to a clodhopper who has ambitions to be . . . Chief Executive of the U.S."

Six years later, when Harry returned from World War I, they were married. In 1922, he was elected eastern judge of Jackson County. Margaret was born in 1924 after two miscarriages. There were no other children. From then on, perhaps inevitably, this becomes the story of Harry Truman confronting his destiny, dragging his somewhat reluctant wife along with him.

Truman's loneliness in Washington after becoming senator in 1934 is a constant refrain in his letters to Bess, who stayed with the Wallaces in Independence most of the time. He compares her to the goddess Proserpina, who spent six months of each year with her husband in Hades, separated from her grieving mother. As for Margaret, she admits to being "a total daddy's girl" from age 5, preferring her outward-looking father to her inward-looking mother.

Whether in Independence or in Washington, Bess practiced thrift in managing the family budget. She made clothes, painted the house, and encouraged Harry to drive from the capital to Missouri rather than take the train. Her one extravagance was in having a cook.

As time passed, her interest in politics became intense. She cried bitterly at the possibility of Harry's losing the nomination for a second Senate term, and came to enjoy Washington life. But the distance she had placed between them, both emotional and geographical, while he climbed the political ladder, had caused a strain in their marriage. By the time he reached the pinnacle, he was used to operating without her. Some momentous decisions, such as dropping the bomb on Hiroshima, were kept from Bess. "She had become a spectator rather than a partner in Harry Truman's presidency," writes their daughter, "and that made her very, very angry."

Truman articulated his own disappointment. "You can never appreciate what it means to come home as I did the other evening after doing at least one hundred things I didn't want to do and have the only person in the world whose approval and good opinion I value look at me like I'm something the cat dragged in . . ."

When he died, this letter was found in his desk at the Truman Library, the only one of hundreds to Bess that he kept there. Paradoxically, she was capable of inspiring devotion while apparently withholding affection herself.

The relationship improved after Madge Wallace severed the maternal string by dying. Having the presidential salary raised from $50,000 to $100,000 a year also helped. Yet Bess found it difficult to appreciate her good fortune, and experienced her role as first lady as having "enjoyable spots -- but they are in the minority." She kept the press at bay and discontinued Eleanor Roosevelt's practice of talking to women reporters. When Truman announced he would not run in 1952, she looked to an observer "the way you do when you draw four aces."

The pictures in the book tell a story in themselves. Bess is shown changing with some rapidity from an attractive teen ager to a plain, overweight, and unfashionably-dressed matron.

There are irritating stylistic traits. Such colloquial cliche's as "That was no mean trick to gum up that job," and "It was creepy the way bad weather pursued FDR," and a reference to Lauren Bacall's "gorgeous gams" mar the text. But these are minor quibbles.

In his new biography of Harry Truman, the British politician Roy Jenkins says that Margaret Truman's book about her father, though partial, is accurate, and near to being the best book about him. The same will probably be true of this biography of Bess.