A lively, believable tale about surviving high school; Does This School have Capital Punishment? by Nat. Hentoff. New York: Delacorte Press. $8.95.

As a new student at exclusive Burr Academy, Sam Davidson is eager to do well. Things go along pretty smoothly at first. He begins his interviews of Major Kelley, a legendary black jazz trumpet player for his oral history course, and he makes some friends. Then he and his best buddy, Rob, are falsely accused of possessing marijuana cigarettes, an infraction that leads to automatic expulsion.

The real culprit, Jeremiah Saddlefield, refuses to confess because he fears that his father, a hardboiled newspaper tycoon and the boy's only parent, will disown him. Mr. Monk, the headmaster of Burr, recognizes that Sam and Rob are not likely to be drug users. But the evidence is against them. Monk decides to delay his decision, hoping that more facts will come to light.

Distraught, Sam tells his problem not just to his parents, but also to major kelley, who offers to help, though he refuses to tell how. Through his own sources, Kelley learns that Saddlefield is a lonely and neglected child and decides to befriend him. Before long, Saddlefield is visiting the clubs where Kelley plays.

After one performance, the boy is so overcome by the contrast between the powerful beauty of the music and his feeling of rottenness over what he has done to Sam and Rob that he confides in Kelley. The musician points out that Saddlefield can either keep his secret and allow it to poison everything he does , or he can confess and take the chance that his father won't cut him off.

When Saddlefield at last confesses to his father the boy is surprised to learn the businessman knew all along but didn't think the boy had sufficient backbone to confess. This change in his son alters the father's attitude toward him and gives them a new start.

When Saddlefield tells all to the headmaster, he receives a similar response. Mr. Monk says, "This ought to be your last day here. . . . But . . . I find it very difficult to banish from this place someone who so clearly shows that redemption is indeed possible."

A short plot summary can't begin to share the many true-to-life incidents experienced by these perfectly believable characters. Sam is wonderfully disorganized, but sincere; Rob is a classic hothead, and Saddlefield is a creep's creep until he sees the light. The lesser characters are equally well drawn.

Only one scene -- where a businessman has a nervous breakdown on his way to work and is reduced to making animal-like sounds -- doesn't ring true; the man has no connection with the school or the plot, a minor flaw in an otherwise delightful book.

The author's descriptions of jazz are especially beautiful and vivid. The power of music is an important element in the outcome, too. As Major Kelley says to Sam after Saddlefield has confessed at school. "This music is a mighty powerful force, and it zapped that boy at the right time. Nothing more need be said."

Of this book that exalts integrity and shows in a realistic and enjoyable way that justice can prevail, nothing more need be said either, except that it's well worth reading.

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