New light on FBI treatment of Dr. King; The FBI and Martin Luther King Jr., by David J. Garrow. New York: W. W. Norton & Co. 320 pp. $15.95.

On two scores this book, intended mainly for scholars, is remarkable.

First for its voluminous evidence against the practices of the FBI in the 1960s during its investigation of Martin Luther King Jr., so painstakingly documented by author Garrow. As with a Chinese water-drop torture, embarrassment after embarrassment drips down upon that organization. By its cumulative effect, the chronicle shows how scandalously the FBI invaded the private life of Dr. King over several years and tried to thwart his professional advancement.

The book is remarkable, too, for providing powerful new evidence that the FBI's original motive for the probe was sound - a reasonable suspicion that the American Communist Party, and thus the Soviet Union, was exercising substantial influence over Dr. King and the civil-rights movement. The man suspected of being the prime Communist influence, Dr. Garrow discloses, was long-time King adviser Stanley Levison.

However, Dr. Garrow concludes the suspicion was unfounded: Levison's ties with the Communist Party were severed in 1955, and ''he had no active ties to the CP once he became associated with Dr. King in 1956.''

The pity is that many readers will find it difficult to swim through wave after wave of examples before landing at the conclusions. Would that it were more generally accessible.

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