Transvestism, hermaphroditism, reincarnation, or just plain literary whimsy? You won't know which of these is the key to White's wide-rangingly playful, sometimes deeply beautiful (and sometimes airy-fairy) novel until the last few pages, when it's a little more than half-revealed. We begin in 1914, on the Riviera, where Eudoxia, an Australian ""woman,"" is the mistress of a wealthy, aged Greek; she's plagued this one summer, though, by the presence of one Joan Golson, a Sydney matron on holiday who was a long-time lover of Eudoxia's mother, Eadie Twyborn. Then. . . skip ahead a few years: it's after the war, and now, Orlando-style, Eudoxia is named Eddie--yes, a male. After seeing combat in France, Eddie returns Down Under and gets a job, through a friend of the family, working as a ""jackeroo""--a ranchhand--on a large sheep ranch in the outback. There, it's up for grabs whom he more lusts after: the virile foreman Don Prowse or the ranch-owner's wife, Marcia Lushington. (No light touches these names.) In fact, he has them both, which cancels them out equally--and then he's off. So much for Eddie. The curtain reopens years later on Eadith Trist, ""the bawd of Beckwith Street,"" owner of an exclusive London bordello but chaste as a nun herself (by now the reader can well suspect why). And when, just as London begins to be German-bombed, Eadith encounters her mother Eadie, and readies herself to be revealed, she's killed in the street by a falling building. Silly? Yes. But out of this baroque, shadowed, I-don't-give-a-damn invention, White draws some astonishingly lovely tones; the novella-like structure and the things-are-not-what-they-seem lightness allow him to linger on his style, which often responds marvelously. Stare at it too hard and this fabrication will collapse into a pile of sequins. But if you accept the terms of the waltz with Eudoxia/Eddie/Eadith, it's fun and--for White's shining prose--sometimes even more than that.