Historians study clues to find facts; After the Fact: The Art of Historical Detection, by James West Davidson and Mark Hamilton Lytle. New York: Alfred A. Knopf. 388 pp. $19.50.

Law students don't learn how to be lawyers by studying texts on the principles of contracts and the like. They immerse themselves in hundreds of individual cases, out of which, prodded by a professor's incessant questioning, they deduce the principles that govern our legal code. The point of this estimable book is that a similar deductive method can be used to help laymen understand how historians go about their work of examining evidence, posing questions, and suggesting explanations of historical phenomena. Inevitably, ''After the Fact'' teaches the pleasures of intellectual quest, complete with the frustrations of blind alleys and unanswerable questions.

Robin Winks's ''The Historian as Detective'' (1969) was an anthology of essays written by diverse authors in many fields of history. ''After the Fact'' traverses United States history from colonial Virginia to Nixon's final days in the White House, each chapter taking up a separate problem for historical interpretation. The authors' brisk style is engaging, making the book clear enough for a beginner and never overloaded with scholarly apparatus. A brief essay at the end of each chapter offers suggestions for further reading.

In the first chapter, the abnormally high death rate in Virginia prompts an examination of the colony's transformation into a one-crop economy (tobacco) geared to the export trade rather than to the sustenance of life. This is followed by a textual analysis of the Declaration of Independence and a look at Andrew Jackson's changing image at the hands of succeeding generations of historians.

Other chapters demonstrate how paintings and photographs can be used to reveal an era (or lie about it). And how psychohistory can illuminate or obscure controversial figures like John Brown. Also, how the interaction between interviewer and subject in oral history (in this case, ex-slaves) can result in widely disparate views of an institution (slavery). Huey Long serves as a case study in offbeat political leadership. The authors draw on the drama of executed radicals Sacco and Vanzetti to show how historians may not be able to give definitive answers to legal questions of innocence or guilt, yet their explorations of the background of a cause celebre widen our understanding of an entire era.

Two chapters stand out, the one on the Salem witch trials of 1692, This episode has always exercised a powerful hold over the American imagination, even if, as the authors point out, they were an aberration in colonial Massachusetts society. They review the trials as variously interpreted through the lenses of 18th-century rationalism, 20th-century psychology, and contemporary social history.

The chapter on the US decision to drop the atomic bomb in 1945 is by far the best in the book, probably because it has been a pet research subject of Lytle's. Here he and Davidson utilize organizational behavior theory (in which policymaking reflects the fragmented, less-than-rational outcome of colliding government agencies) to analyze the bomb's progress from vague scientific theory to grim Hiroshima reality.

History, then, is not just what the history books tell us. It is the result of painstaking labor, the personal biases of the author, and the intellectual fashions of the age. It's a lesson, no doubt, that students of History 101 will absorb, using ''After the Fact'' to supplement their text.

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