Subtitled: Confessions of an Abnormally Happy Childhood, this is a fragment of autobiography from the only child of Florenz Ziegfeld and actress Billie Burke. The author's stated purpose is to preserve for her grandchildren glimpses of her extraordinary early years. Unless the magic name goes to work for the book, the audience may not be a great deal wider than that. There are scanty passages for the theater history buff -- a sharp child's eye view of a mean-mouthed Marilyn Miller and a bit about Billie Burke's plays. The rest is devoted to a series of incidents, told out of chronological sequence, that center on the fabulous homes Ziegfeld supplied for his family. He lavished money like an Eastern potentate -- dinners catered at Dinty Moore's and flown to Palm Beach; a pet elephant on the Long Island estate (with lion cubs and buffalo); a chipped dinner service replaced by the assassinated Russian Ozar's own service (Bille Burke sent it back); and a Canadian wilderness camp turned into a lap of luxury. To her credit, the author speaks with more affection for her parents than the spectacular trappings of her youth. The legendary showman and spender died in the '30's and the dazzle stopped. Her mother's book (With a Feather on My Nose) is much the better one as a portrait of Ziegfeld, his home and his times.