Washington may be reeling in a daze from the royal events, but Charles and Diana are clearly up to the challenge.

Consider:

Diana went swimming at St. Albans at 8 on Sunday morning. (Sleep, who needs sleep?)

Charles was deemed an avid museum tourist: "I've never seen a visitor hang on so," National Gallery of Art Director J. Carter Brown said of Charles on the Sunday morning walk-through of the exhibition.

Not all went so smoothly for some hosting events for the couple. Someone in Nancy Reagan's office in the White House, perhaps overwhelmed by the events, typed up a rap session seating chart yesterday for the princess and Mrs. Reagan's visit to a drug rehabilitation center and referred to Diana as "PRINCESS OF WHALES."

Oops.

The royal couple's third and final day in Washington was their fullest and most frenzied, and again they were met by large crowds everywhere they went. They promoted British trade at J.C. Penney, received late-morning guests at the British Embassy, commemorated the war dead at Arlington Cemetery and then went to their third black-tie dinner of the three-day visit, this one for about 100 at the National Gallery of Art.

At dinner the royal couple mixed with the likes of actress Brooke Shields and gymnast Mary Lou Retton as well as private arts patrons and congressional arts supporters like Rep. Sidney Yates (D-Ill.). After dinner, introduced by a regal fanfare of trumpets, Charles and Diana walked across the East Building mezzanine, while waiting guests, their eyes turned on the couple, applauded the entrance. Bathed in camera lights, Diana's silvery beaded dress was a blaze of sparkles. The orchestra played "Pomp and Circumstance" and the couple descended the grand staircase into a much larger waiting reception of 500.

J. Carter Brown had only moments earlier said over a microphone, "May I ask you to spread out in horseshoe groups of 10 or 15 people," but crowds engulfed Charles and Diana as they walked around separately. Charles threaded his way through the smiling faces with a palace detective close behind.

Reception guests like Mayor Marion Barry had already dined with the royal couple at the British Embassy Sunday night.

Barry said he talked at length with Charles. "I said, 'Have you seen downtown Washington?' He said, 'No, they won't let me come downtown. You know, I've never really seen downtown Washington.' So we talked about finding him a way to come downtown."

They also talked about unemployment, drugs, housing. "He's very concerned about it," Barry said. "He said they had some problems with inner-city blacks and unemployment -- same problems we have here. He got right into it. We talked for about 10 minutes." The mayor said that his wife Effi chatted with Diana.

"You know, we were the only black guests there," said Barry. "You feel proud about that -- and sad there were not more."

Sen. Alan Simpson, also at the National Gallery, had sat at Charles' table at the embassy dinner. "Well, we talked about inviting them to Wyoming," said Simpson. Charles has expressed interest in going there. "I told him how his mother and father both loved it." Simpson also said that Charles talked with Secretary of State Shultz. "George was telling him about his visit with Gorbachev."

And Justice Warren Burger, who sat with Diana at the embassy, described her last night at the gallery as "just like the nicest girl next door, and pretty as can be."

Earlier, Charles and Diana briefly went their separate ways -- he to the Library of Congress to discuss the Constitution, she to Straight Inc. with Nancy Reagan to meet with some people working to recover from drug problems.

But before all of yesterday's madness, Diana started off Sunday with a swim at the Lawrence Pool at St. Albans School for Boys. "I'm calling it the royal dip," said St. Albans development director Fran Johnson. Friday, the British Embassy requested access to the pool should the princess want it and swore the St. Albans officials to secrecy.

On Sunday morning, Diana arrived in a white jogging suit accompanied by a two-car entourage of more formally suited men, presumably security people. The pool was closed to the public, and a St. Albans swim coach, Robert Green, was there to open the door to the athletic building on Garfield Street, but the princess, at her request, swam alone, accompanied only by her security people. She swam for about 15 minutes in the pool, which is a few feet short of Olympic size, then left.

The headmaster, the Rev. Mark Mullin, was on the grounds but did not see her. "The embassy said, 'If you don't mind, she doesn't want to meet people -- if you could just have someone to open the door,' " Johnson said.

Later that day, J. Carter Brown had a "wonderful chat" with Diana during their helicopter ride from the National Gallery of Art to the Mellon farm in Upperville, Va. And Charles and Brown's wife, Pamela, "discussed obscure fences and English race tracks," chuckled Brown. The prince also talked about his own artistic leanings: "He's taken up watercolors," says Brown. "He paints landscapes -- he does those in the summer at Balmoral." Early Morning at Penney's

Yesterday the royal tour escalated into one massive runabout of Washington. And somehow the warmer weather seemed to loosen up the couple.

On their tour of the Springfield Mall J.C. Penney, undertaken to help hype the store's "Best of Britain" promotion, Diana appeared, according to some sharp-eyed spectators, to shun stockings and go barelegged as she browsed. But when British Ambassador Oliver Wright was quizzed about the veracity of that report, he said, "I've only gazed into her eyes."

Officials of the company presented the duo with a white quilt hanging on a frame as a gift and Charles inquired, "What size is it? King or queen?"

Queen size, William R. Howell, chairman of Penney, told the prince.

"Is king the large size?" asked Charles.

Two feet away, Diana blushed and looked at the floor.

They had been greeted outside by 6,000 ecstatic royal watchers camped out in expectation, some having arrived as early as 4 a.m. Inside, a bevy of more sedate but just as ecstatic J.C. Penney officials called the coming of Charles and Diana "a tremendous historical event."

When the motorcade pulled up, people started running, trying to follow its progress, and if a crowd of thousands can be said to squeal with glee, this one did. When they emerged from the car, the crowd lost it. Within one minute, they were inside the store and 400 people rushed into the mall, pressing themselves against the locked glass doors to the second floor of Penney's.

Safely inside, the couple were chatty and relaxed, with Charles speaking to staffers and guests on everything from sweaters to John Travolta to profit sharing. And Diana lived up to her husband's earlier wry remarks as the woman behind his sartorial splendor when she struck up a discussion in the menswear department:

James Bradford, president of DAKS United States, whose parent company has operated in London since 1894 and sells to the royal family, was showing her a suit when Diana asked, "Don't you have double-breasted suits in this country?"

Bradford, who was wearing a single-breasted suit, as were most of the Penney executives, said, "Single-breasted is more customary in this country."

Then Diana, looking at her husband, who was wearing a suit in navy blue with a vivid red stripe through it, asked, "Don't you think the double-breasted suits are more flattering?"

Immediately afterward, Bradford said, "Based on those comments we will probably have a double-breasted suit collection next fall which we will probably call The Royal Collection."

And he added, "I will be in a double-breasted suit tomorrow."

He later amended his words to say they were "spur of the moment."

Diana approached the much-publicized exhibit of a Rolls-Royce balanced on china cups with considerable curiosity. Wearing a cream wool suit by Bruce Oldfield with a slim skirt and a jacket with jabot fitted to the waist, Diana dipped slightly and giggled as she looked at the cups. Then she moved to the rear of the car, very cleverly out of full range of the cameras, and bent to the carpet to take a closer look.

But the near highlight, which the press didn't witness at all, was Diana's venturing into the maternity department. As reconstructed by David Miller, the president of J.C. Penney, the princess was heading toward the junior department.

"She wasn't even aware she was anywhere in the maternity department, neither was he. There were no signs, nothing," Miller said.

But both of them did stop to look at a blue two-piece maternity outfit, according to sales associate Jane States. "There was a little chuckling" between the couple, "but Charles did inquire about the price," even after finding out the suit was maternity wear, she said. The suit cost $110.

Diana reportedly bought an $8 silk scarf, which prompted a run on that item as soon as the doors opened to the public. "We were hoping, but we didn't really expect her to buy anything," said Betsy Leonhard, senior merchandising manager for the store.

After their tour, Charles and Diana reappeared outside, and worked the crowd to squeals of delight.

"Everyone pays attention to Diana," said Lisa Perdue of Springfield, in a dark suit more suitable for an office than a mob. Perdue managed a conversation with Charles. "I think poor Charles gets a bum rap, and I told him that, and he said, 'Well, flattery will get you everywhere. Thank you.' For crying out loud, he's the one who's the real royalty. He's got the blood." Morning at the Embassy

After their visit to J.C. Penney, the royal couple met about 170 notables, local and otherwise, at a British Embassy reception and said they generally are pleased with the way the American press writes about them. Diana said she'd found the American press was more factual than gossipy, compared with the British press. She told one guest she was also interested in the amount of access the American press has to its politicians, and she asked how often President Reagan held press conferences.

They arrived about 10 minutes later than scheduled, and Diana, on entering, told the already assembled guests, "Don't stop talking." She crossed the room to begin at the other end from the prince.

The royal couple were well prepared for their guests:

To David Lloyd Kreeger, introduced by Ambassador Wright as a violinist, Charles said he played the cello. He said he was displeased about the fuss at Palm Beach over their ball for the United World College and promised to make a statement about it, according to Kreeger, who is flying down to the event with Armand Hammer, its sponsor.

And to Werner Gundersheimer, director of the Folger Shakespeare Library, Charles recalled that he had played Macbeth when he was 17. The Baron von Stackelberg recalled to Charles he'd once eaten a salmon the prince caught.

Other guests included Richard Berendzen, president of American University; Sen. James McClure (R-Idaho); Arena Stage's founders Tom and Zelda Fichandler; Al Hunt, Washington bureau chief of the Wall Street Journal; Judy Woodruff, Washington correspondent for the "MacNeil/Lehrer NewsHour"; Peter Sellars, director of the American National Theater, as usual in his Japanese-style jacket; Roger L. Stevens, chairman of the Kennedy Center; Sen. John Warner (R-Va.) with ABC's Barbara Walters; Bryant Gumbel, "Today" show coanchor; and Interior Secretary Donald P. Hodel.

Tom Fichandler told Diana that Lady Wright had performed at Washington theaters and that any time the princess of Wales would like to do the same, Arena would be glad to have her. The princess replied that she didn't think she was a good actress. Going Their Separate Ways

The royal couple spent the early afternoon apart. The prince of Wales yesterday entered the Library of Congress with evident relish, where he viewed the Main Reading Room and examined priceless documents of the U.S. Constitution.

"He has a sense of history," said Librarian of Congress Daniel Boorstin, who escorted the prince, after he had left. "He requested the meeting himself, and wanted it to focus on the Constitution. We considered one primary point -- the written Constitution, which differs from the British unwritten one.

"He was interested to hear, from the chief justice, the members of Congress and so on, how the branches of government refer to the intent of the writers of the Constitution. I thought if his predecessor King George III had had a similar interest in American thought, that history might have turned out differently. I was myself impressed by his maturity -- he certainly is not a figurehead. He is a thoughtful man," said Boorstin.

Meanwhile, yesterday afternoon at Straight Inc., a drug rehabilitation center in Springfield, Diana and Nancy Reagan listened to dramatic stories of drug experiences related by parents and their children at an abbreviated version of Straight's Friday night meetings. At one point, Diana looked startled when one youth stood up and shouted, "Phase 3," the first indication his parents had that he would be returning to school and peer pressure again.

Diana arrived with Mrs. Reagan by presidential limousine. It was Mrs. Reagan's turn to wear red. She chose an Adolfo coat, cinched with a gold chain belt, and a matching skirt. The princess wore a white suit with red shoes, blouse and handbag.

In the session, Diana either asked questions or made comments 12 times (compared with Mrs. Reagan's eight). She had obviously done her homework about the family-oriented program, which takes young drug users through five phases.

"I know there are five phases," Diana told Mike Kirsch, 18, who graduated from Straight last May. "Which one are you in?"

When Mike's father, also Mike Kirsch, told Diana that all six of his children are drug users, she said, "Now am I hearing right? You have six children?"

"Six druggie children," the elder Kirsch replied.

"All on drugs?" Diana asked.

Getting an affirmative answer, the princess persisted. "And did they follow each other?" she asked Kirsch. Turning to his son, she asked, "How did you get the money to get the drugs you were after?"

Of Kathy Turner, 17, a high school senior who was in the Straight program 14 1/2 months and now is a paraprofessional working for the center, Diana asked: "Will you feel a stronger person after you leave?" And, finally: "How about the people who love you, the people at home, do they praise you and tell you that they love you? Because I think you need praise for going through that."

Afterward, Turner told Nancy Reagan she had been very nervous. While the first lady reassured Turner, the princess leaned over to the young Mike Kirsch and said, "If it's any consolation, it's more easy to ask questions." Veterans Day Remembrance

At Arlington Cemetery, the royal couple, together again, made a striking presence, he in his ceremonial Royal Navy uniform, and she, having changed outfits, in a snug-fitting purple Bruce Oldfield dress. The crowds loved it.

Their 14-car entourage arrived at 4:05 p.m. to a 21-gun salute and full honor military wreath ceremony. Charles laid a wreath on the Tomb of the Unknowns, which was followed by the playing of taps.

Afterward they proceeded to the cemetery's memorial display room containing medals and other insignia, including Britain's Victoria Cross, that had been presented by the nations of the world.

The mood was considerably more somber than what had greeted the duo on their other stops. However, that didn't stop well-wishers from yelling, "Diana, we love you!"

Security seemed particularly tight, as it has been since they arrived; they have been surrounded by tight, pervasive American-style security. In England and on other tours, they often have much more freedom in walking about, working crowds.

Yesterday, after the crowds had gathered on the steps, a security-type man started yelling for them to clear the steps for the police dogs to sniff for bombs. This did not go over too well with those who had been waiting five or six hours. "Get out of the area," he persisted. "I ain't guaranteeing anything!"

Finally, he let them back in, which looked a little like the running of the bulls at Pamplona.

Said Steve Wood, photographer for the London Daily Express. "I've never seen anyone so in a hurry to get into a graveyard." Dinner at the Gallery

The crowds on Constitution Avenue whistled and applauded as Charles and Diana's motorcade whisked by before entering the driveway of the West Building of the National Gallery of Art. At the entrance the royals stepped out of the Rolls to be greeted by John Stevenson, president of the National Gallery of Art and Franklin Murphy, the museum's chairman.

Diana wore a one-shouldered, long-sleeved, silver sparkly beaded dress that hugged her slender figure. She has worn the dress, made by Japanese designer Hachi, on several formal occasions, including one during her 1983 tour of Australia.

As the couple walked up the stairs of the gallery reporters yelled out to Diana: "How do you like Washington?" The couple hesitated and turned toward reporters. Diana smiled broadly and mouthed, "Very much." Charles quickly added, "Speaking as her spokesman, she thinks it's wonderful." Both grinning, they walked into the building.

While the royals and others dined on quail and apricot mousse in pomegranate shells, the evening B list of about 500 began to arrive in the atrium of the East Wing. The National Gallery's Brown was there to greet them, having sacrificed his meal to perform his hostly duty.

The guests wandered into the candlelit atrium, acquired drinks and hors d'oeuvres and waited for Charles and Diana. Many of them walked through the exhibit in the interim.

Although the names of some guests had leaked out -- Shields and Retton, for example -- the guest list was not released until most of the guests had passed by, and the press scrambled to identify all those people in taffeta and tuxedos.

Shields, looking slender in a white dress encrusted with tiny pearls and sporting a ruffly bustle, said, "I know that my prayers have been answered. I'm a very big fan. I feel like tonight is definitely a dream come true."

Mary Lou Retton, accompanied by her brother Ronnie Retton, was bubbling.

"Oh my gosh!" she said. "Such an honor! Really!"

"She's such a classy woman," the gymnast said. "And I really look up to her a lot."

During remarks at the reception, Charles said of the show, "My wife and I thought . . . it really was one of the most remarkable exhibitions we'd ever seen."

Charles thanked the British Consulate, the National Trust and the lenders for their parts in making the show possible. "My wife," he said, "is rather sorry to find there isn't anything from her family home in the exhibition." Diana's family home is the Althorp estate in Northamptonshire.

"I've read that this exhibition has been dreamt up to lure Americans to Britain . . . to stately old crumbling homes," he said. "I'm amazed constantly that anything remains in Britain after all those United States raiding parties." The guests laughed.

Charles complimented the National Gallery on its installation and said of the "magnificent" East Building, "The architecture isn't at all bad." The guests laughed. One of them was architect I.M. Pei, who designed the East Building.

Charles noted how remarkably friendly all their encounters had been. "We will leave tomorrow with every kind memory and sound ringing in our ears." Guests at last night's National Gallery dinner for the prince and princess of Wales:

Riggs National Bank President Joe L. Allbritton and Mrs. Allbritton

Treasury Secretary James A. Baker III and Susan Baker

Dr. and Mrs. William O. Baker

Mr. and Mrs. Robert M. Bass

Anne Beckwith-Smith, lady-in-waiting to the princess of Wales

Mr. and Mrs. Donald M. Blinken

National Gallery Director J. Carter Brown and Pamela Brown

Sylvia Brown

Evangeline Bruce

Chief Justice Warren Burger and Elvera Burger

Carroll J. Cavanagh

Catherine M. Conover

Mrs. Georges de Menil

Mr. and Mrs. S.J. DiMeglio

Mrs. and Mrs. Philip M. Drake

Joanne DuPont

Lt. Cdr. Peter Eberle

Joseph G. and Penelope English

Mr. and Mrs. William S. Farish III

Mr. and Mrs. John C. Fontaine

Mr. and Mrs. Henry Ford II

Prof. and Mrs. Sydney J. Freedburg

Mr. and Mrs. Donald J. Hall

Industrialist Armand Hammer and Olga Hammer

Pamela Harriman

Daniel Herrick

Tina and Lee Hills

Mr. and Mrs. Carlisle H. Humelsine

Mr. and Mrs. R.L. Ireland III

Gervase Jackson-Stops, curator of the "Treasure Houses of Britain" exhibit

Mr. and Mrs. Philip C. Jessup Jr.

Jacob and Ruth Kainen

Mr. and Mrs. Joseph Krakora

Mr. and Mrs. Yo Yo Ma

Amelia Manice

Sen. James A. McClure (R-Idaho) and Mrs. McClure

Mr. and Mrs. W. Barnabas McHenry

Mr. and Mrs. Richard P. Mellon

Mrs. Seward Prosser Mellon

Mr. and Mrs. Timothy Mellon

Prof. and Mrs. Henry A. Millon

National Gallery of Art Chairman Franklin D. Murphy and Mrs. Murphy

Ford Motor Co. Chairman Donald E. Petersen and Mrs. Petersen

Hon. and Mrs. Ralph S. Regula

Olympic gymnast Mary Lou Retton and Ronnie Retton

Sir John Riddell, private secretary to the prince of Wales

David Roycroft, assistant private secretary to the prince of Wales

National Gallery of Art trustee Arthur M. Sackler and Mrs. Sackler

Charles Savitt

Michael Shea, the queen's press secretary

Actress Brooke Shields and Terri Shields

Barbara Sletten

Mr. and Mrs. James S. Smith

Mr. and Mrs. Robert H. Smith

Hon. and Mrs. John R. Stevenson

Mr. and Mrs. Angus Stirling

Courtney S. Wang

Deputy Secretary of State John C. Whitehead

John Wilmerding

Mr. and Mrs. Wallace S. Wilson

Ian Woodner

British Ambassador Oliver Wright and Lady Marjory Wright

Rep. Sidney R. Yates (D-Ill.) and Mrs. Yate