The act was not a great success, but it was the first of many spanning their childhood. It took years of practice, new acts, new teachers and plenty of failure for them to acquire anything close to top billing. “My sister and I had to saw our way through,” Astaire once wrote. They played many one-night stands in “every rat trap and chicken coop in the Middle West,” he said, often receiving equal billing with trained seals, dogs and illusionists.

During these years Fred considered himself a liability to Adele, who was impulsive, funny, lively and bursting with charisma. “The girl seems to have talent,” one theater manager opined, “but the boy can do nothing.” Riley quotes a passage from the manuscript for Astaire’s autobiography, “Steps in Time,” in which he describes himself as “a small boy who went through the motions conscientiously, afraid he would forget his lines.” Years later Vincente Minnelli, who directed Astaire in “The Band Wagon,” said: “He lacks confidence to the most enormous degree. . . . He always thinks that he’s no good.” But lest Astaire’s propensity to endlessly rehearse be pathologized in Freud’s armchair, it is well to remember that Fred preferred to dance on that armchair, while most of us just sit.

At age 14 Fred took on the musical responsibilities for their act, frequenting Tin Pan Alley, where he met a 15-year-old George Gershwin in one of the cubicles at the music publisher Jerome H. Remick & Company. Gershwin was working for $15 a week, plugging other people’s songs, and the boys dreamed of George’s writing a musical for Fred one day. “Lady, Be Good!” (1924) and “Funny Face” (1927) were two of those dreams.

During their last, and best, year in vaudeville, in 1917, the Astaires received telegrams from both an agent for the Shuberts — resulting in a two-year Broadway contract — and the impresario Charles Dillingham, who presented them in “Apple Blossoms” at his Globe Theater (now the Lunt-Fontanne) in 1919. “We killed ’em in the first act,” Fred said, “and ‘panicked ’em’ in the third.” The score was by Fritz Kreisler, who played for their rehearsals. Of the Astaires’ performance in “For Goodness Sake,” in 1922 (which featured their star turn in the show’s “nut” number, “The Whichness of the Whatness”), a critic raved, “Somewhere, sometimes perhaps there may have been a more charming juvenile team than Fred and Adele, but certainly not in the memory of anyone in the audience that filled the Lyric Theater.”

That same year, the “hard-drinking, banjo-playing satirist” Ashton Stevens, “dean of American drama critics” and escort to Sarah Bernhardt, became one of a long list of distinguished intellectuals to fall in love with Adele, some of whom took their adoration across the footlights. Stevens made his declaration in a subtle headline in The Chicago Herald-Examiner: “Falling in Love With Adele Astaire. In Which It Is Told How the Well-Known Heart of Ashton Stevens Is Stricken by the Deftest of the Dancing Girls.” He went on to rhapsodize that “the pliant body of Miss Astaire . . . assumes a slanting partial paralysis which slays boredom where it sits.” Oh, my. Such proclamations do make one wonder what delights have been lost to the annals of theater criticism in the intervening decades since the erection of that annoying fourth wall, a lame beard for bias prevention.

George Jean Nathan, with H. L. Mencken editor of The Smart Set and The Ameri­can Mercury, went one further, choosing to compare George Bernard Shaw’s play “Back to Methuselah” to Adele’s dancing: “If the purpose of theater is to entertain, then I say that the Astaire girl entertains twice as greatly as Shaw’s play.” Nathan proceeded to squire Adele around town, had an eight-month romance with her, followed her to Europe and dedicated his book “The House of Satan” to her. The romance ended when Adele found out that the “French ambassador” her lover was meeting went by the name Lillian Gish. While Nathan conceded that brother Fred was “a fellow of no mean foot,” he asserted that “a dance without skirts is to me not a dance.” Way to go, George.