The Life and Adventures of a Clever Woman.

By Pamela Neville-Sington.

Illustrated. 416 pp. New York:

Viking. $29.95.

''Clever'' is hardly sufficient to describe Fanny Trollope. Essayist, novelist, travel writer and, not incidentally, mother of Anthony, she was clever to be sure. But ''indomitable,'' ''tireless'' and ''determined'' seem closer to the reality of her breathtakingly energetic life. Beginning her writing career under duress at the age of 53, she rose each day before dawn to produce, over the next two decades, more than 40 books. If some critics thought her surname an apt epithet for her stature as a writer, if Robert Browning warned his wife against seeing ''that vulgar pushing woman who is not fit to speak to you,'' still Fanny Trollope became, in her own time, nothing less than a literary phenomenon.

A contemporary of Jane Austen, Frances Milton grew up learning the skills that should have enabled her to glide effortlessly into a good marriage, but she managed to reach the age of 29 without an offer. In ''Fanny Trollope: The Life and Adventures of a Clever Woman,'' Pamela Neville-Sington, an American literary scholar who now lives in London, suggests a few reasons: Growing up motherless, Fanny never developed what one observer called ''taste and female intelligence in regard to dress.'' A more significant drawback to marriage was her lively mind, invigorated by her father's abundant library. Women's ''terror of being called learned,'' she later wrote, ''is in general more powerful than that of being classed as ignorant.''

She was a formidable match, but at last, early in 1808, she met a man who was not daunted by her. He was Thomas Anthony Trollope, a shy, serious barrister who had just moved into the Milton family's London neighborhood. By summer, the two were exchanging books and letters. In May 1809, they married. Immediately, the Trollopes began a family; within nine years, they had six children. With Fanny in charge of the nursery, Thomas assumed control of the budget, for which he had little talent. As financial worries took their toll, Thomas became increasingly morose and withdrawn. He was no companion for his wife.

But in the early 1820's, she found one: the Scottish social reformer Frances Wright, recently returned from Tennessee, where she had established Nashoba, a community dedicated to educating freed slaves. Trollope was beguiled by her intrepid friend and leapt at the chance to accompany Wright back to America. In early November 1827, Trollope, with her 16-year-old son, Henry, her two daughters and Auguste Hervieu, a struggling young artist who had tutored her sons (and whose relationship with Trollope generated considerable gossip), left England.

After two months of arduous travel, they finally reached Nashoba, outside Memphis. But one glimpse of its dismal, roofless log cabins, Fanny said, ''sufficed to convince me that every idea I had formed of the place was as far as possible from the truth. Desolation was the only feeling -- the only word that presented itself.'' There was no question of staying, and within two weeks Trollope had devised a new plan. Her party would head up the Ohio River to Cincinnati, reputedly the fastest-growing city in America.

She brimmed with ideas for making money. First, she advertised her son as a Latin tutor, but no students appeared. Undaunted, she proposed to a local museum an entertainment she called ''The Invisible Girl,'' in which Henry portrayed a mock Delphic oracle. The public loved it, and Trollope was given another commission, this time for a wax museum attraction called ''Infernal Regions,'' featuring terrifying scenes from Dante. These successes were not enough to support the Trollope menage, however, and Fanny threw herself into a grander scheme: the Bazaar, a combination mall, theater, amusement park and museum. With the family's future riding on this venture, Fanny spared no cost in making it spectacular. But she had miscalculated. The Bazaar, the Americans decided, was too decadent. They refused to come.

Facing destitution, Trollope needed to act and act quickly. Her next plan seemed just as risky: she would write a book based on her American journey. A woman's view of the frontier, she believed, just might find a receptive audience. Supported by Hervieu's earnings as an artist, she stayed in America until she had gathered enough material; back in England, she found a publisher willing to take a chance on an unknown writer. In March 1832, nine days after her 53d birthday, ''The Domestic Manners of the Americans'' appeared. ''I awoke one morning and found myself famous,'' she wrote to her eldest son, echoing Lord Byron.

The book sold through four editions in its first year. Her candid, often acerbic critique of America fed British skepticism about the supposed wonders of democracy, while at the same time offering a vivid, lively commentary on social conditions in the still-new world. American readers were less generous: Margaret Fuller, for one, felt that Trollope had ''violated the virgin beauty'' of her native land.

But Americans were not Trollope's audience, and the enormous popularity of her book in England inspired her travels to France, Austria and Italy. Her success as a travel writer led her to publish, to equal acclaim, 35 novels. Neville-Sington reads this fiction as a reflection of Trollope's experiences, frequently citing the novels to help us understand Trollope's responses and relationships. Since Trollope, throughout her work, was above all a social critic, this strategy seems appropriate and illuminating. Although at some moments the biography takes on the pace and tone of Trollope's own romances (abundant cheerfulness! many exclamation points!), still Neville-Sington, attentive to historical context and telling detail, has captured the spirit of the times -- and of her subject.

If Trollope merits a biography for her own accomplishments, certainly some readers will come to this book for insights about her famous son, whose literary reputation far exceeds hers. Feeling abandoned when she left for America without him, Anthony never established the rapport with her that his brothers had managed, and his portrait of her in his memoirs often bristles with anger. Yet Neville-Sington believes that Fanny inspired one of Anthony's particularly fearless and charming fictional heroines, Glencora Palliser. ''I do not know that she was at all points a lady,'' he wrote, ''but had Fate so willed it she would have been a thorough gentleman.''