Jangled nerves, of course, are the least of the challenges Weymouth faces. The Grahams today are almost the last of the great American newspaper families. They have managed to nurture and retain possession of a thriving journalistic institution while other media dynasties—the Chandlers of the Los Angeles Times, the Bancrofts of the Wall Street Journal, and the Binghams of the Louisville Times and Courier-Journal, to name a few—have loosened their grip, taken the cash from big corporate buyers, and faded into a gilded oblivion. Even the Sulzbergers of the New York Times are fighting to stay in power amid rising shareholder discontent over the company’s sinking stock price.

“It’s so amazing to see this family continue in control,” says Post Co. vice president at large Ben Bradlee, who served as the Post’s executive editor for 23 years and, with Katharine Graham, transformed the paper from a merely respectable publication into a world-class one. He adds that Weymouth’s ascension guarantees that there will be a member of the family there for another 30 years. “When I heard she was coming in, it made me feel optimistic and good,” Bradlee says. “And then when I saw her and the way she handles herself around here, with total ease and yet no sense of entitlement, I was really impressed.”

It was Weymouth’s grandfather, Philip Graham—Katharine Graham’s husband and Meyer’s son-in-law—who first put the Washington Post Co. on the map as an emerging media power. After World War II, he bought a majority stake in the local 50,000-watt CBS radio station, then the CBS television affiliate, and then a TV station in Jacksonville, Florida. Philip bought the rival Washington Times-Herald and merged it with the Post, launched a wire service with the Los Angeles Times, and acquired Newsweek magazine. But all the while, he battled a severe form of manic depression, and in August 1963 he committed suicide, shooting himself at the family farm in Virginia. Katharine Graham found his body.

The rest of the story is legendary in journalistic circles: Rejecting handsome offers from various media conglomerates to buy the company, Katharine took over as president. Shy and awkward, she felt inadequate to the task and, as she later admitted, terrified, but she was determined to keep the Post in the family. She’d spent her adult life as a wife and mother, driving a car pool for her four children, and knew little of business and nothing about management. But she steeped herself in expert advice and, with the help of a small group of executives who’d been hired by her husband, she presided over the newspaper and its related enterprises with increasing self-assurance and authority.

An outwardly correct and reticent lady (who displayed a wicked sense of humor and cursed eloquently in private), she formed a seamless partnership with Bradlee, whom she hired in 1965 as managing editor after he famously told her he’d give his “left one” to edit the Post. Together, they faced down Richard Nixon’s White House in publishing the Pentagon Papers in 1971, when government intervention could have jeopardized the Post Co.’s plans to go public. They pursued the Watergate investigation at a time when vindictive Nixon operatives were actively considering pulling the company’s broadcasting licenses.

Mrs. Graham, as she is still called by nearly everyone at the Post, died in July 2001 at age 84, after falling and sustaining head injuries while attending the Allen & Co. media-mogul retreat in Sun Valley, Idaho. But her descendants still seem to enjoy an almost mystical bond with their employees. When Weymouth made a heartfelt acceptance speech in the company auditorium on the day her promotion was announced, some Post traditionalists, such as former managing editor Bob Kaiser, were teary-eyed.

Wearing her grandmother’s pearls for luck, Weymouth told the crowd about a recent conversation she’d had with a coworker in the advertising department, where she’d spent the previous three years as vice president and director. The colleague “poked her head in my office,” Weymouth explained, “and said that there was a story that she thought I would want to hear. She asked me if I had ever noticed that often the elevators stop on the lobby floor when you have not pressed the button for the lobby. And the doors open, and no one gets on or off. I said yes, I had noticed that. She said, ‘Well, my girls think that is your grandmother getting on the elevator.’ I got chills when she told me that. And this morning, it happened to me. I was riding up from the garage level, a nervous wreck. And the elevator stopped on the lobby floor, the doors opened, and no one got on.”

The numbers do suck: The Post’s circulation and advertising are down and dropping, the cost of newsprint is through the roof, and advertising revenue from the Web isn’t growing nearly fast enough to stanch the bleeding. In 2007, the Post’s print-ad revenue plunged 13 percent from the previous year—from $573.2 million to $496.2 million (a decline hardly offset by an $11.5 million hike in the website’s revenue, an 11 percent increase over the previous year). Average daily circulation has dropped to 673,180 from a peak of 832,232 in 1993. The staff was cut earlier this year through a round of voluntary buyouts, the third since 2003, a move that cost the company a record $80 million in severance payouts. Over the past five years, the newsroom’s head count has shriveled from about 900 to less than 700, and the threat of layoffs still looms. It’s a sad, scary time. At a recent farewell party for the latest group of buyout recipients, several of them Pulitzer Prize winners, Don Graham was choked up.