The Chief Judge of a federal Court of Appeals, one tier below the Supreme Court in the judicial hierarchy, has publicly criticized the Burger court for not adequately protecting individual rights.

The critcism comes in The Ways of a Judge: Reflections From the Federal Appelate Bench; (Houghton Mifflin, 273 pages, $10.95), by Frank M. Coffin, who is Chief Judge of the U.S. Court of Appeals for the First Circuit. The First Circuit, one of eleven U.S. Courts of Appeals, is responsible for cases from four New England states and Puerto Rico.

Devoted primarily to showing how an appellate court works, Coffin's book traces the evolution of three cases, two fictional and one real. The real case, Fano v. Meachum, arose when a series of prison fires led to transferring prisoners to higher security institutions. The First Circuit held that more stingent confinement meant a loss of liberty for the prisoners and that they accordingly were entitled to procedural due process. The Supreme Court reversed.

In analyzing the reversal, Coffin emphasizes the dissent of Justice John Paul Stevens. Stevens objected to the majority's implying that only state statutes and the Constitution would protect. Coffin seconds the objection, and laments that the Stevens opinion, "for the moment at least," is not the rule.

Coffin clearly is disturbed by the Burger court's models for determining when, and to what extent, constitutional protections apply. He stresses the illogic of the court's doctrines dealing with free speech, equal protection, and due process. He characterizes those doctrines as a "a jurisprudence of clusters and discontinuity."

Coffin believes the courts have a special duty to protect the rights of individuals. He sees that large institutions dominate our lives and that their dominance increases daily.

That courts may be trusted to do their job is the central message of Coffin's book. Discontent with the doctrines of the Supreme Court becomes, by comparison, a minor matter. Coffin's conviction is strong: Wrong decisions shall be righted; appellate adjudication is vital. His confidence emerges in quiet avowals of faith; in his pride in colleagues and staff; and in his detailed, lucid, and loving portrait of his court at work.

That portrait is a valuable one. Judges in the Federal District Courts, the trial courts of the federal system, regularly achieve notoriety or fame, and the Supreme Court stars in The Brethren. But the federal Courts of Appeals have, until now, been the neglected middle child of the federal judiciary.

Roughly the first quarter of Coffin's book is an introductory overview of appellate systems through history and in the United States. Though this section -- best left to true students of the appellate process -- might better have followed the cases that sustain the book, it does include occasional facinating tidbits. Statistics that Coffin cites make clear, for example, that full opinions by the Supreme Court are rarely devoted to affirming lower court decisions; the vast majority accompany modifications or reversals.

Coffin describes appellate judging as "a series of shifting biases." The centerpiece of the book, a step-by-step recounting of deciding three cases on appeal, graphically illustrates his description. The three cases become an artful -- and pedagogically invaluable -- means of probing an appellate judge's preparation for an oral argument, hearing argument, consulting with his law clerks and colleagues and drafting opinions.

The three cases that Coffin uses to show the process of appeals crackle with intellectual excitement. They also give Coffin the chance, in describing oral argument, for a few choice caricatures. An assistant U.S. Attorney irritates the court by his smugness and shoddy briefing. A young assistant attorney general for the Commonwealth of Massachusetts is sympathetic and competent.

The final section of the book more explicitly presents Coffin's views on what might be, and how to determine, the proper role of the judiciary. By that point, Coffin's faith in the judicial process has become contagious. Perhaps the best measure of his book is the conviction one carries away from it: Judge Coffin ranks among his own best arguments for confidence in the judiciary.