Maybe Edwina Mountbatten (1901-1969)--millionaire, libertine, Florence-Nightingale wife of Lord Louis--shouldn't be left to Noel Coward and the popular press. Mountbatten, we're told, even hoped that the love letters between Edwina and India's prime minister Nehru--her ""first and only great love""--would someday be published. But Hough, a satisfactory biographer of Mountbatten-the-careerist, fails flat with this reprise of Edwina ""from pleasure seeker to crusader."" There's no passion, only spotty psychological penetration, and little detail; the very conception is arid, conventional. Still, Hough's own combination of admiration and distaste for the lordly Mountbattens gives the narrative a bit of an edge--and, even in outline, Edwina's life has a certain fascination. The heiress-granddaughter of Jewish banker Ernest Cassel (and, on her father's side, a Shaftesbury/Melbourne scion), young Edwina wed young semi-royal, unmoneyed ""Dickie"" Mountbatten for the same reason he chose her: mutual benefit. The mutual is important: as quickly as the marriage disintegrated--her restlessness and infidelity, his all-absorbing ambition--Hough does make the point that each took pride in the successes of the other; in being, together, unstoppable. (Hence their various mÃ‰nages Ã trois--he had a permanent comforter--and, in particular, his acquiescence, as India's last Viceroy, in the Nehru liaison.) Half-explored is Edwina's attraction to dark-skinned people--and peoples--which Hough initially attributes to her part-Jewish ancestry. But her 1930 romance with Paul Robeson (and, shortly, another black performer) seems hardly different from the socialite-adventuring of Nancy Cunard and others. The interpretive hinge may be Nehru-biographer Marie Seton's observation that Edwina, who hurtfully denied the Robeson connection in a libel suit, ""paid her debt. . . by her loyalty to India and Nehru."" If, as Hough claims, Mountbatten/Nehru relations were crucial to Indian independence (""there is no friendship in history to parallel. . .""), then the book fails as history for lack of substantiating detail. As biography, it is limited to showing us--if only obliquely telling us--that, from the onset of WW II, Edwina found an outlet for her abilities, energies, and taste for extremes in ""grueling"" disaster-relief tours (she was head of Britain's St. John Ambulance Brigade) instead of ""grueling"" travels back of beyond. Framed in acclamation (Edwina's death-in-harness, posthumous honors), this is not a sympathetic story; yet the reader can occasionally see into the troubled depths.