NONFICTION : SACCO & VANZETTI: THE CASE RESOLVED by Francis Russell (Harper & Row: $16.95).

This book represents Francis Russell’s third tilt at the murder case that became the political cause of the 1920s. His lengthy “Tragedy in Dedham” (1962) concluded that Sacco was guilty, but Vanzetti innocent; his foreword to the “Fiftieth Anniversary (of the crime) Edition” (1971) argued that Vanzetti was technically an accessory and that “the passionately held belief that Sacco and Vanzetti were innocent philosophical anarchists done to death by a reactionary and fearful capitalist society is, after all, a myth.”

Since his conclusions have not altered, and since the new evidence that he introduces--a letter from the son of Giovanni Gambera, an anarchist comrade of Sacco and Vanzetti, confirming those conclusions--could have been more efficiently presented in a magazine article, it is clear that Russell has grander goals in mind. He has aimed at a definitive retracting of the case, its participants, the evidence, the controversies, and his involvement with all of them.

He has managed that task gracefully, providing both a fine synopsis and a detailed view of the anarchist milieu which helped shape the ideas by which Sacco and Vanzetti lived and the code of conduct for which they died.

He has not, however, managed to overcome the problems integral to books on controversial trials. Russell is from the “I began my research thinking ‘A,’ but the weight of the evidence convinced me of ‘B’ ” school. On the one hand, the reader is grateful for the obeisance shown to the integrity of the record; on the other hand, the author tends to use this admission of fealty and homage to truth as a sign of grace for all conclusions to follow. That purified state causes a second problem--a distaste for ambiguity. No piece of evidence is allowed to be inconclusive.

Russell candidly reveals the hesitations, doubts, and failures of objectivity that accompanied him on his quest for the Grail. Nevertheless, he cannot overcome the obstacle to this case’s notoriety: It could only become a passionate symbol of one’s political persuasion because no direct evidence of guilt existed. The Gambera letter, for example, is hearsay.

While Russell has made a credible effort to investigate the available circumstantial evidence and a plausible attempt to demonstrate that such evidence crosses the threshold of reasonable doubt, he has, finally, only resolved the case to his own satisfaction. He has not solved it.