The biography of a dyed-in-the-wool American essayist; E. B. White: A Biography, by Scott Elledge. New York: Norton. 400 pp. $22.50.

The New Yorker has always enjoyed - and courted - a reputation for worldly sophistication; as the magazine's founding editor, Harold Ross, was fond of saying, The New Yorker was not for ''the old lady in Dubuque.''

Oddly, the one writer who did more than any other to create the refined, cosmopolitan style of the magazine was a man who bore not the least resemblance to the Regency dandy, decked out in a curl-brim top hat and peering superciliously through a monocle at a butterfly, that graced the cover of The New Yorker's first issue. He was, in fact, a thoroughly down-to-earth, thoroughly American journalist named E. B. White.

On and off for almost half a century, in hundreds of editorial columns and dozens of essays, this dyed-in-the-wool son of Uncle Sam set the tone for The New Yorker, offering its presumably privileged readers an amused and musing point of view.

In many ways, White himself would not qualify as a member of the audience he wrote for. ''I know nothing of music or of painting or of sculpture or of the dance,'' he once said. ''I would rather watch the circus or a ball game than ballet.'' And as for literature, White was anything but well read in the English and American classics, and looked chiefly to such contemporary journalists as Franklin P. Adams and Don Marquis as his mentors.

One White favorite who would not fall into that category was Henry David Thoreau, and White's affinity for him says a great deal about the strongly American flavor of his writing - its wistful, almost childlike longing for another, less frenzied age, its faith in the regenerative powers of the natural world, and its skepticism about where America was heading in the increasingly technological 20th century. ''In the brooding atmosphere of war and the gathering radioactive storm,'' he wrote in the 1950s, ''the innocence and serenity of (Thoreau's) summer afternoons are enough to burst the remembering heart, and one gazes back on that pleasing interlude - its confidence, its purity, its deliberateness - with awe and wonder, as one would look upon the face of a child asleep.''

That sentence also reveals what made Harold Ross strive to keep the restless White on The New Yorker. White's poetry is mostly forgettable light verse, and his fiction consists chiefly of three novels for children; but he had an extraordinary gift for the essay, and in pieces like ''Death of a Pig'' and ''Afternoon of an American Boy,'' he demonstrated a mastery of nonfiction prose not easily equaled in 20th-century American letters.

Thanks to a decision that White made in 1957 to edit and revise a curious little book on English composition put together by one of his professors at Cornell, the philosophy of writing that lay behind White's graceful prose became available to a wide audience. ''The Elements of Style,'' by William Strunk Jr. and E.B. White has become standard fare for freshman English courses throughout the United States.

White's advice to all these would-be writers is characteristic. ''The beginner should begin by turning resolutely away from all devices that are popularly believed to indicate style - all mannerisms, tricks, adornments,'' he said in an essay on style that he appended to Strunk's rules of grammar and usage. ''The approach to style is by way of plainness, simplicity, orderliness, sincerity.''

As Scott Elledge's biography makes clear, White's life was as wholly cut from American cloth as was his writing. He grew up in a rambling frame house that had ''middle-class America'' written all over it, and after graduating from Cornell in 1921 he spent a year touring the United States in a Model T. He lived most of his adult life either in New York or on the 40-acre farm in Maine that he and his wife, Katharine Sergeant, The New Yorker's fiction editor, bought in 1933.

It might be argued that White's life is not interesting enough to justify a full-scale biography. (White himself reportedly told Elledge that he thought his book was too long.) And it might be argued that White is, after all, a relatively minor literary figure. But it is more than likely that White will be remembered a long time, and not just by literary historians or college freshmen, but by any reader interested in what it means to be an American in the 20th century and, perhaps above all, by any reader who cares about what William Strunk once called ''the sanctity of the English sentence.''