Of all the figures in American history, none is in direr need of rehabilitation than Andrew William Mellon. Mellon the financier created an empire of coal and steel that fueled modern industry. Mellon the art collector gave the country its National Gallery. Mellon the Treasury Secretary outclassed all predecessors but Alexander Hamilton, spending a full decade in the job and presiding over stupendous economic progress. Mellon was the Alan Greenspan of his time, a man of whom it was said that “three presidents served under him.”

But when the Great Depression came, Franklin Roosevelt and Mellon’s own successors at Treasury scapegoated him unrelentingly for four years. Mellon’s opponents never did win convictions. But they did something worse.They obscured in American memory both Mellon’s achievements and his optimistic philosophy. They made a man who was ahead of his time old-fashioned. Postwar historians followed their lead and wrote Mellon down in the books as a flat character. Or, to put the story in television terms: Mellon acquired a reputation something like that of Soames Forsyte in John Galsworthy’s “Forsyte Saga” — a frigid man of property. His own son, Paul, would indeed later compare Andrew to Soames.

Now along comes David Cannadine to supply the rehabilitation. Mr. Cannadine is a distinguished historian — he wrote the prize-winning “Decline and Fall of the British Aristocracy.”Before his death, Paul personally tapped Mr. Cannadine to write the book, and Mr. Cannadine enjoyed luxurious access to Mellon’s records at the Mellon Foundation. “Mellon: An American Life” (Alfred A. Knopf, 779 pages, $35) took a decade to complete and spans an exhaustive and exhausting 779 pages.The outcome: a book that delivers on the dignity and the achievements of Mellon, but falls short when it comes to his philosophy.

Thomas Mellon, Mellon’s father, was an important force of his own, a judge who first established the Mellon bank in a then-frontier town, Pittsburgh. Thomas summed up the story of his people in an autobiography: “The Scotch and Scotch-Irish — the latter but a Scotch colony — monopolize business and wealth … They owe this to their qualities of thrift, economy, intelligence and industry.” Mellon and his brother Dick, the sons of this Scotch-Irishman, took over the bank and expanded from there, supplying capital to industries from coke and oil (Gulf Oil) to aluminum (Aluminum Company of America). A friend, Henry Clay Frick, taught Andy, as he was known, to collect paintings while on a trip in Europe, and later helped him found Union Steel. Mellon’s Pittsburgh was a roaring place, covered with soot, “hell with the lid taken off,” as it was described. “You don’t live here?” his much younger bride Nora said, horrified upon her arrival from Scotland. Still, to Americans, Mellon’s empire seemed invincible.

Yet though Mellon built an empire, he was not imperial. For, as Mr. Cannadine points out, he did not operate as a traditional robber baron did, by seizing land, or natural resources, and then monopolizing them. Mellon and his brother functioned under what came to be known as the “Mellon System.” They liked to build businesses vertically: When it came to oil, for example, the Mellons involved themselves at every stage of production, from pumping oil out of the ground to selling it to the customer.The Mellon System had another distinguishing rule. The investor must find an innovator he liked, fund him by buying a share of his company — and then stay out of the scientist’s hair. Thus, in a period when capital was far less available or liquid than it is today, Mellon became one of the first VCs — venture capitalists.

Mr. Cannadine also covers another Mellon innovation. In those days companies that wanted to improve products had to come up with the improvement themselves or wait for some scientists somewhere to do so. Universities often snubbed their noses at the companies, rewarding their scholars to pursue only pure science. To speed up the process, Mellon created an early version of the modern think tank, the Mellon Institute. Companies paid for scientists to spend a fixed period — say, a year or two — at the Institute, with the defined task of finding a way to improve a product or a process. One study completed at the Institute in its early years looked at the social cost of smoke pollution — the authors who wrote this green project concluded that the cost was $10 million a year. Another Mellon Institute project involved converting petroleum into gasoline. Thus, Mellon said, companies might learn “to utilize the services of qualified scientists to solve its problems.” The concept of applied science seems mundane now, but that is only because Mellon helped to make it so. Indeed, so preoccupied with such things was Mellon that he neglected Nora and their two children, Ailsa and Paul. “He sought friendship loyalty, support and companionship; she craved warmth, fondness, demonstrative love and perhaps passion,” the author writes. One of Mr. Cannadine’s insights was that Nora’s age — she was two decades younger than Andy — doomed the marriage. He notes that Nora’s improbable union with Mellon resembled that of a more recent celebrity couple: Diana’s with Prince Charles.

But Mellon scarcely noticed this, perhaps because his real passion went to another object: paintings. Early on, Thomas had taken a risk in lending a 21-year-old with no capital $10,000 to build 50 coke ovens. That young man, Henry Clay Frick, was also an art collector, with sketches strewn around his office in between documents of the coking process. “Lands good, ovens well built; manager on job all days, keeps books evenings, may be a little too enthusiastic about pictures but not enough to hurt,” one of Mellon’s bankers wrote of Frick’s site in recommending a second loan. Frick became the Mellons’ great partner in business, but also taught Mellon about art. In this relationship it was Mellon’s turn to be junior; Frick called Andrew Mellon “Andy,” Mellon called Frick “Mr. Frick.”

Eventually, great brokers, from Roland Knoedler to Joseph Duveen, helped Andrew build the greatest private art collection in the world, containing Vermeer’s “Girl With the Red Hat,” Raphael’s “Alba,” and Van Eyck’s “Annunciation.” Then, on one of the last days of 1936, he gave the country a gallery on the mall to house them in; at his insistence, it was called not Mellon Gallery but National Gallery. The idea, familiar in all religions, is that anonymous charity is higher than other charity, and that it is more likely to inspire other givers to join him. This was the corollary to the business rule of keeping a low profile. Even before the Gallery opened in 1941, the Kress and Rosenwald families were also giving collections.

It was at Treasury, however, that the Mellon System saw its greatest use.The income tax had been created less than a decade before Mellon took office, but the Wilson administration and Congress had already pushed the surtax on the income tax up to 77%. Many were appalled, the new Treasury Secretary included. Levies that high slowed business. Borrowing an image from railroading, Mellon argued that governments could only charge in taxes “what the traffic will bear.”This was the fiscal version of his old “stay out” philosophy. With the cooperation of succeeding presidents, Mellon pushed rates down five times, bringing the top income tax rate to 20%.

A supply-sider before the supplysiders, Mellon believed that those lower rates would yield more revenue. He proved correct; his budgets ran surpluses. Mellon did raise rates as he departed the Treasury in 1932, but that was only a reluctant measure, taken in the name of sustaining the gold standard. Mellon’s famous response to the Crash was that investors must liquidate their holdings so that the market could find a bottom.Today this sounds sinister, especially because events that took place in Soviet Russia, including the murder of millions, would later give new meaning to the phrase “liquidate.” But Mellon was not wrong: A market that is fluid and transparent is one that is likely to handle bad news better.The only important area where a classical economic liberal would challenge Mellon is his distressing failure to oppose tariffs. But then opposition to tariffs would have seemed inhuman, at least in those days, in an aluminum man.

Mr. Cannadine, a dutiful biographer, covers the slide into Depression in detail, including the legitimate fury of the unemployed.As one angry Pennsylvanian wrote to Washington, “He is a most hated man in Pittsburgh, and when his picture appeared on a moving picture theater screen recently in one of our local theaters, the boys in the gallery yelled ROBBER ROBBER.” The Roosevelt administration took aim at Mellon and sought to prove that he had illegally avoided paying taxes. Treasury Secretary Henry Morgenthau egged his staff on, telling the prosecutor Robert Jackson that democracy was at stake. Mr. Cannadine establishes that Roosevelt himself was aware of the project, and showed deep interest in Mellon’s tax returns. Robert Jackson — the same Jackson who later served as a Supreme Court justice and prosecuted Nuremberg — wrote of Roosevelt that “as a matter of fair history, he did know about it.” On the left, a young congressman from Texas, Wright Patman, smeared the gallery gift by charging that it was a bribe by Mellon to get the government to call off its lawyers. Patman even argued that the gallery ought not to be built, saying,”A lasting memorial in his honor should not be constructed in the nation’s capital, even at his own expense.”

Mr. Cannadine’s work rebutting the bribery charge alone makes the rest of this book worthwhile. For his intensive review enables him to conclude with an authority lacking in all previous historians that when it comes to bribery, “there is not a shred of evidence for that contention.” As Mr. Cannadine points out, plenty of evidence, including Hoover’s memoirs, shows that Mellon was already planning the gallery in his 1920s. Mr. Cannadine highlights the important link between Mellon’s philanthropic side and his business side. The greater fortune could become the greater gift to society — that was his message with the gallery.

There are problems with “Mellon” — three especially troubled me. The first is that this biography sometimes gets in the way of itself. An example: Mr. Cannadine delivers all the minutiae of Mellon’s dedication of the Mellon Institute’s new home in 1937 — that the man’s health was failing, that he left his glasses on the rostrum, forgot his hat, and delivered a speech that “was more than usually inaudible, rambling, and incoherent.” These details set up the event the author must describe next: Mellon’s death that summer. But they obscure the central point of the Mellon Institute dedication — that the Institute and businesses related to it had thrived throughout the 1930s, yielding hundreds of new patents. And that many sectors of the economy had likewise continued to expand in that period. Even in the darkest decade, the candle of innovation was sustaining the country. Thus does Mr. Cannadine subordinate a truth: The dedication was about the immortality of ideas, not the defeat of senescence.

The second problem is that Mr. Cannadine tends to emphasize the cautious, Scotch-Irish culture of the Mellon family. There is plenty of detail in this book that would be of intense interest to Presbyterians, but insufficient material on Mellon’s great love of risk. His propensity to bet boldly was the key to his success, and it was a trait without ethnicity.

The third problem is the sense that Mr. Cannadine conveys that Mellon’s ideas were indeed passé. The author titles the last part of his book “Old Man, New Deal.” Mr. Cannadine likewise refers to economic liberals such as Mellon as a “beleaguered breed.”This is not giving Mellon his due — or acknowledging the respect he was accorded right through the 1930s. On the ex-Secretary’s 80th birthday, reporters gathered ’round at his tax trial looking for a quote. The Depression, Mellon told them, would prove a mere “bad quarter of an hour” in the glorious history of American finance. Many decades, but above all the 1980s and 1990s, have demonstrated that this prophecy was correct. Why did not Mr. Cannadine title his last section: “New Deal, Newer Man”?

But these are smaller challenges. “Mellon” is a complete biography, containing also — how could I forget to mention it? — details of Nora Mellon’s adultery, Ailsa’s self-absorption, and Paul Mellon’s education in philanthropy. It introduces a man we need to know, and all there is to say is: Welcome, Andy.

Miss Shlaes is a columnist for Bloomberg.