Presidential politics: a look at history; Every Four Years: The American Presidency. Smithsonian Exposition Books. New York: W. W. Norton & Co. $21.95.

This is, to be frank, a period of great disappointment and strong nostalgia over the American presidency. Disappointment with the four last presidents (Carter's ineffectiveness in solving grave national problems, Ford's failure to give inspired direction, Nixon and the slough of Watergate, Johnson and the Vietnam mess). Nostalgia for what are conceived to be the resolute and firm-gripped chief executives of the past.

How great is the national longing, not necessarily for such titans of the past as Washington, Jefferson, Lincoln, or Franklin D. Roosevelt, but merely for so stalwart and tough a little fighter as Harry Truman! Seldom, if indeed ever, in the nation's nearly two centuries of democratic government has the United States been as concerned over either its ability to choose an adequate president or the latter's capacity to rally national effort to face crises and challenges.

Today is, then, a happy moment for the appearance of this thoughtful and concise work on the presidency. Making no pretense to be either a detailed or profoundly philosophical study of that office, it does provide a highly readable -- and delightfully illustrated -- survey of the ups and downs of that office, the extraordinary range of character and ability which different presidents have brought to their tasks, how the presidency has evolved in some 191 years, and of the monumental difficulties now facing any chief executive in this period of complex economics, worldwide upheavals, changing concepts of loyalties and patriotism, and rising, but frustrated, expectations.

The authors of this book have chosen to divide the American presidential experience into seven segments. First is the presidency of George Washington and his crucial role in defining what a president should and should not do. This is followed by the account of the "patrician" presidents from Virginia and Massachusetts, who were followed in turn by the more populist leaders, of whom Andrew Jackson was the greatest. The fourth period is that of "the presidential apotheosis" or that epitome of patriotism, steadfastness, decency and greatness, Abraham Lincoln. He is succeeded by what this book terms the age of the "politicos," who presided over the vast expansion of American power. With the 20th century there comes a fairly steady succession of presidents from Theodore Roosevelt to Harry Truman who can be termed "progressives." Following come the men, from Eisenhower to Carter, whose images are shaped as much by public relations as by facts.

If such characterizations contain almost as many holes as they do solid cloth , they are nonetheless convenient hooks upon which to hang presidential history. Helpful, also, are the succinct pictures we are given of just how their contemporaries and their periods judged the men chosen for highest office. The power and influence of the presidents have risen and fallen in quite extraordinary sweeps and swoops. And if this zigzagging graph of presidential effectiveness forces us to take a more realistic view of the office than was taken in the past, it also provides a comforting assurance of future greatness in the White House.

This book's profuse illustrations range from sedate and classical portraits of the presidents to the searing cartoons of bitter political animosity. This broad gamut of illustrative comment helps cement the task which this book has undertaken: to present the presidency and the presidents in human, understandable terms.

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