(FORTUNE Magazine) – On a Sunday evening in 1879, Thomas Edison and his assistants powered up an electric bulb and took turns watching it. Over the past 18 months their quest for a workable filament had generated nothing but 1,200 failures and $40,000 in expenses. But this time the carbonized sewing thread inside was still glowing more than 13 hours later.

The invention that came to symbolize inventive genius itself spawned a company that would, in turn, become America's flagship corporation. During its 125-year existence, the General Electric Co. has glowed as steadily as Edison's lamp--even while continually overturning its own legacy. The only company remaining from the Dow Jones index of 1896, GE has had fewer leaders since then--eight--than the Vatican has had Popes. Each man stepped into the shoes of a predecessor who, in most cases, was considered the leading industrialist of his day. Each abandoned the approach of his predecessor. And each chose a successor who would change the company's course yet again--a remarkable record of continuity achieved through periodic revolution. "What GE seems to have a genius for," says Jim Collins, a business researcher and author of Good to Great, "is picking the right person for the right time for more than 100 years."

The eighth man in this distinguished lineage was standing, one blustery afternoon in February, on the 70th-story roof of the GE Building at New York City's Rockefeller Center. FORTUNE had coaxed him there during an afternoon interview and photo shoot. The massive slab underneath Jeff Immelt was, proportionally speaking, roughly as big as the 300,000-person, $134 billion organization he stands atop. "God, this is something," he said, standing above the giant "GE" letters that overlook Manhattan. He had never been there before.

He had never been a CEO before, either, until that day in 2001 when he stepped into Jack Welch's shoes. But he had a pretty good idea of what to expect. That's because the first few years of any new GE leader follow a familiar pattern. First come the public comparisons with the great man who came before--the "legend," the "miracle man of American business," as Reginald Jones (CEO from 1972 to 1981) and Owen Young (1922 to 1940) were respectively hailed by the press. Then comes the period of crisis: war, recession, a troubled stock. Eventually come the glowing headlines: MAN OF THE YEAR: OWEN D. YOUNG (Time, 1929); GE DOES IT (FORTUNE, 1942); WELCH POWERING FIRM INTO GLOBAL COMPETITOR (Washington Post, 1984).

The first three years of the Immelt era have been no exception. After incessant comparisons with Welch followed by the period of crisis--in his case, the end of GE's ten-year streak of double-digit earnings growth in 2002--Immelt is now taking his place among these Rushmorean figures and, in the process, quietly putting on a clinic on how to lead a major corporation.

He doesn't command the spotlight the way Jack Welch did, and he probably never will. Immelt, 48, is less a commander than a commanding presence--one of those natural leaders around whom a group tends to spontaneously organize. And his blueprint for GE is firmly in the tradition of breaking tradition. Jack Welch had plunged headlong into financial services. Immelt is getting out of them. Welch had courted Wall Street by setting--and hitting--pinpoint earnings targets. Immelt has given the Street's short-term demands a back seat to long-term strategy. Welch rapidly rotated managers through different divisions to develop generalists. Immelt wants to keep them in place longer to develop specialists. And where Welch tended to grow GE though acquisition, Immelt wants to grow the company the way it used to: through innovation.

What might look like a repudiation of Welch's legacy, though, is Welch's legacy. It was Welch who picked Jeff Immelt. And it was Welch who allegedly gave him the same instructions that his own predecessor, Reginald Jones, had given him 20 years earlier: Blow it up.

Immelt has gone about the task in customary GE fashion: thoughtfully, meticulously, and then--kaboom!--suddenly. In a single week this past fall he spent $14 billion for Vivendi Universal and $10 billion for British medical-imager Amersham--GE's two biggest deals ever--because he thinks those businesses will grow faster than the overall economy. A month later he announced plans to kick loose various slow-growing insurance businesses through a new company, Genworth, to be sold to the public this year. In his spare time, he has picked up two cable channels (Telemundo and Bravo), three water treatment companies, three security technology firms, and Enron's wind-power business.

The buying spree might look like an extension of the Welch era, when roughly 40% of GE's earnings growth came through acquisitions. But there's a difference here. Many of Immelt's deals slowed GE's earnings growth--not the kind that Welch favored--meaning that Immelt isn't buying growth so much as buying the ability to grow. And that, in turn, suggests that the company has a truly long-term thinker on its hands.

Immelt is far too grounded to call himself a theorist (I'm just a "simple businessman," the former applied-math major has said, who's "not that deep.") But more than any other company, GE has always required a theory of how it should grow. It was founded upon the theory of a "benign circle," in which the company created demand for its electrical products by starting rail lines, generating stations, power plants, and the like. Its growing image as a faceless monopolist prompted Owen Young to introduce appliances that would give GE a friendly presence in the home. "To be known," his theory went, "is quite as important a part of management as knowing." And in 1981 much of Jack Welch's first speech to analysts was given over to the theories of Prussian General Carl von Clausewitz. "This company isn't a central strategy," he said, "but a central idea": If a company wasn't No. 1 or No. 2 in a business, it shouldn't be there at all.

If Jeff Immelt's central idea had to be reduced to a sound bite, it would be this: "We have to make our own growth." There's a lot packed into that simple statement, so here's a rough translation:

The economy appears to be entering a period of slower growth. Yes, things may pick up some, but those fat years in the '90s? They're long gone, soldier. So look around: This is your new reality. You can curse the Fates. Or you can find new ways--realistic ways--to grow. You can't buy growth anymore, for the simple reason that, well, there's not a lot of growth out there to buy. So you've got to make it yourself. Where, you may ask, could one possibly grow something out of nothing? Why, in the House of Magic!

Though the name is fanciful, the House of Magic is, in fact, a real place. It is a GE research lab just outside of Schenectady, N.Y. And it used to be famous.

Founded in 1900, the House of Magic was the brainchild of one Charles Proteus Steinmetz, a gnarled mathematical genius who ignited the popular imagination with his man-made lightning storms. Given free rein to pursue his scientific interests and to host visitors with names like Einstein and Kelvin, Steinmetz became a magnet for other creative wizards. There, William Coolidge would invent the X-ray tube and tungsten light. Irving Langmuir would earn a Nobel Prize in chemistry. Ernst Alexanderson would invent the high-frequency alternator that enabled the first radio broadcasts--leading GE to form the Radio Corp. of America and the National Broadcasting Corp. There was no one place on the balance sheet where the House of Magic's contributions could be seen. Then-chairman Owen Young said in 1930: "It is the balance sheet itself."

Where did the House of Magic go? In a literal sense, nowhere. But subsequent company leaders let it wither. In 1955--the first year of the FORTUNE 500--this magazine described an "overhaul of General Electric" that "departed radically from GE management tradition." It was scientific management, not basic science, that interested Ralph Cordiner, the company's president then. His "decentralization theory" spawned a bureaucracy that was more fascinated with its internal workings than with the mysteries of discovery. Cordiner set out to prove his notion that the professional, "wonderfully mobile" manager could oversee anything. So when GE purchased a French computer maker to challenge IBM in the late 1960s, it picked a man to run the place who (1) knew nothing about computers and (2) couldn't speak French. The debacle wound up costing the company $200 million. GE's most conspicuous success, meanwhile, was a division that resisted the rotation of its people: aircraft engines, where Joseph Immelt worked for 38 years.

Now his son Jeff, the Harvard Business School graduate, is out to banish Cordiner's ghost for good. "I absolutely loathe the notion of professional management," he told an MIT audience in September. Which is not an endorsement of unprofessional management but a statement that, for instance, the best jet engines are built by jet-engine people, not by appliance people. Rotate managers too fast, moreover, and they won't experience the fallout from their mistakes--nor will they invest in innovations that don't have an immediate payoff. "If I were to give you a chapter of my business book, it would be called, 'Two Million Dollars From Greatness,'" Immelt said at MIT. "I can't tell you how many GE leaders give me the excuse that 'I could fund new innovations, but I can't afford it. I can't fit it into my budget.' These are from leaders that have a billion-dollar base-cost budget. Investors expect companies to take risk."

What kinds of risk? Things that bypass distributors, like GE's new loan offers to consumers, are good. Things that promise a "services stream," like turbines that require spare parts, are better. Things you can't make in China, like extremely complicated molecular imaging stuff, are best of all. "Ten years out," Immelt declared in 2003, "90% of our company's earnings will have no competition from China. Eighty percent of our businesses will be selling to China."

Yet some risks are too big--or too "out there"--for a single division to undertake. That's where the House of Magic comes in. Immelt has revamped it, giving it a fresh coat of paint and a vastly expanded budget. The Global Research Center (as it is now known) is plunging into nanotechnology, photovoltaics, hydrogen power, advanced propulsion, and other areas that could affect multiple GE businesses. The center that once turned scientists into industrialists, Immelt hopes, can do the reverse too. He has been rotating his managers through the place, where they hang out in a new Adirondack-style lodge and soak up the latest technologies. He has also built similar outposts in Shanghai, Munich, and Bangalore, India.

Revitalizing the research center isn't the only way Immelt is letting engineers know how important they are. Three years ago, he says, just seven of GE's 175 top officers were engineering types. Now roughly 20 of them are. Immelt is also bulking up on marketing people in the belief that the best ones can sell GE products right through an economic slump. Case in point: In the midst of an airline recession that Boeing has blamed for its poor performance, GE's aircraft-engine unit has stayed aloft through aggressive sales techniques.

Immelt has given much thought to economic cycles. GE traditionally classified its businesses as either "long cycle," like engines, or "short cycle," like plastics and appliances. That bothered him because it suggested that GE is at the mercy of the economy when, to his thinking, the economy should be at the mercy of GE. So in January, Immelt reclassified GE's businesses, dividing them into 11 groups within two new categories. "Growth businesses" like transportation, health care, and energy are where he'll lay the big bets. "Cash generators" like lighting, appliances, and insurance will provide the chips to double down his growth bets. Some of these bets may not pay off for ten or even 20 years, Immelt notes. But investors are likely to see results sooner than that. Had Immelt simply kept the businesses he inherited, Bernstein Research estimates, GE would be set to grow its bottom line 9% in 2005. As it is, the reshuffled deck is projected to grow 14%.

Jeff Immelt goes nuts if you dare call his company a "conglomerate." A conglomerate generates returns by trading in and out of businesses; it's basically a giant mutual fund. By contrast, GE generates returns by undertaking projects that only it has the wherewithal to undertake: the biggest, the most difficult, the longest term. Scale is one of GE's traditional strengths. This company was born huge--a "supercompany" with 10,000 employees, a few thousand patents, and J.P. Morgan on its board. Cordiner defined size as a liability. Not Immelt. "It's really a story about faith," Immelt told the audience at MIT. "A big company with conviction, with speed, can change the world in a way that others can't."

Faith? Conviction? Do people still use those words? In the increasingly mercenary culture of CEOs, they sound downright antique. But the more you watch Jeff Immelt (and his unselfconscious avowals of "love for the company"), the more you realize that this new breed of executive is, in fact, a throwback. He's a throwback to GE's first leader, the low-profile Charles Coffin, who would write out customer proposals in longhand. He's a throwback to GE's second leader, Owen Young, who espoused the notion that managers were trustees of something they didn't own. He's a throwback to GE's third leader, Charlie Wilson, who in the '40s addressed rumors of Westinghouse's plan to catch up with GE. "They should live so long," he told his executives at Association Island, a company getaway on the St. Lawrence River. "Now, let's all rise and sing 'Onward, Christian Soldiers.' "

Like those men, Immelt enjoys one final, incalculable advantage: It's understood that unless something goes horribly wrong, he's got the job for 20 years. If GE's stock drops by a third, as it did during his first year on the job, he doesn't have to panic. He's still at the beginning of this thing. So instead of announcing some half-baked turnaround scheme, he can actually do the things leaders are supposed to do. Develop an intelligent plan. Shore up the finances. Inspire the troops. Invest in the customers. Refrain from making dumb promises. Explore technologies whose payoffs will come far down the road. "I run a company that's 125 years old," says Immelt. "There's going to be someone after me, just as there was someone before me."

In some ways, it is the ultimate benign circle. Continuity breeds confidence. Confidence breeds conviction. And conviction breeds something that, had we not grown so cynical, would look suspiciously like ... well, courage.

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