Cross' new novel is billed as ""A Kate Fansler Mystery,"" the tenth in her series about the N.Y.C. English prof and amateur sleuth. In fact, however, this time Cross (a.k.a. Columbia prof Carolyn Heilbrun) has used the Fansler character merely as a hook on which to hang a modestly intriguing literary/family study: a feminist inquiry into the psycho-dynamics and domestic secrets of a long-dead Great Writer, his long-suffering wife, and their Anglo-American descendants. The action--such as it is--begins when Kate is asked by a big-time publisher to write the biography of Gabrielle Foxx, wife of British literary giant Emmanuel Foxx, who's ""right up there with Joyce and Lawrence and Woolf. . ."" The primary biocritical question: To what extent was Gabrielle an influence on Foxx's masterpiece of female stream-of-consciousness, Ariadne? Kate begins her research by reading an unpublished, 50-page memoir by Anne Gringold, a chum of the Foxxes' granddaughter Nellie; Anne recalls their 1940's adolescence together (in the home of Nellie's wealthy, New Jersey-Jewish relatives) and her 1950's visit to frail widow Gabrielle--who entrusted Anne with her cache of secret letters. (They've been in a London vault ever since.) Then Kate does separate interviews with Anne, Nellie, and Nellie's cousin Dorinda--and eventually, after unearthing a few family skeletons, wins their trust. So finally Kate gets access to those letters--which turn out to be a sensational literary find. Mystery-lovers will be disappointed, of course. But those who read Cross almost solely for the literary atmosphere will find this faintly bookish, faintly gothic tale a pleasant--if thematically obvious--diversion. (The Gringold memoir is the graceful, tart highlight.) And, with blessedly little of Kate's cutesy chatter with hubby Reed, it's certainly preferable to the recent, tepid Fansler whodunits.