The president of the United States and the future king of England met yesterday in the grand and glorious splendor of the Oval Office. They talked about falling off horses.

Both do. "Anyone who's going to ride and do things like steeplechasing, polo and that sort," Ronald Reagan said to Prince Charles, "there are going to be times when you and the horse part company."

"If you try hard," Prince Charles picked up from there, "you're bound to fall off occasionally." Lately he has. There were two times in March, and once last Sunday at a polo match near Sydney, Australia.

No horses yesterday, though. His royal highness the prince of Wales was in Washington on a soupy, London-like day to add an air of romance and partake of some local color and food: a clipped tour of the Air and Space Museum, a chat with the president, lunch at the British Embassy, Evensong at the Washington Cathedral, then the black-tie Oxford-Cambridge dinner at the International Club.

The cocktail reception was so crowded that an expedition of university alums, summoning their courage, took a kitchen elevator to the downstairs dining area.

"This has never happened before," said Guy Martin, an Ox-Bridge alumnus and the president of the International Bank of Washington. "Normally it's a bunch of old fellows who walk in very slowly, then fall asleep at the table."

"One of our star events," summed up Burke Wilkinson, chairman of the dinner committee.

Lady Diana Spencer, the prince's fiance who has captivated the British Isles, was back home. He is said to be missing her badly. "I'm pining here," he said on a recent stop in New Zealand, "while she's languishing 11,000 miles away in London."

("And that was three weeks ago," said one British journalist on the American trip. "You can imagine what condition he's in now.")

Prince Charles and Lady Diana have been apart for his six-week tour of New Zealand, Australia and Venezuela, now on its last leg in Washington. Members of his entourage say he seems to be tiring some, proven by a polo accident scar on his left cheek that becomes more noticeable when he's weary.

But in yesterday's chilling rain he was very much HRH, the polite and handsome -- if reserved -- monarch who was last seen among official Washington as a guest of Richard Nixon, the president who appeared to be pairing the prince with his daughter, Tricia. But she got somebody else.

"HOW'S DIANA?" some of those snoopy American reporters shouted at him yesterday.

"Very well," he responded, a little shyly and softly.

But he smiled.

"Amazing," HRH kept on saying at the Air and Space Museum. "Amazing." He's a wing commander in the Royal Air Force, so he knew what he was seeing.

An Apollo command module. The German V-2 that bombed London during WWII. Ballistic missiles. And the spring crowd of tourists who yelled and cheered as he walked into the same backup Skylab that Chinese Vice Chairman Deng Xiaoping toured three years ago.

He has wavy brown hair, big ears and a ruddy, healthy face. Yesterday he wore a plainly cut gray suit and what looked like sensible, polished brown shoes. Throughout his Washington tour, grown women regularly referred to him as "cute," although he is 32 years old and heir to a fortune estimated as high as $150 million. He is not imperial in presence, so people respond to him. Some women find him exciting. He was the best catch in the world until his engagement announcement on Feb. 24.

"Your Royal Highness, would you like to go up in the shuttle?" a reporter at the Air and Space Museum shouted yesterday.

"What -- in the hold?" responded HRH.

"Are you enjoying the museum?" another cried.

"I haven't seen enough of it yet," HRH replied.

"Are you interested in space travel?" came a last try from ABC.

"Yeeeeeeaasss," he said.

Then he mnoved on, lips closed, hands clapsed firmly behind his back in what is referred to as "the royal walk."

The prince was a big hit at the Oxford-Cambridge dinner. He was more at ease, perhaps because he was at a private dinner among fellow alumni.

"One of the most amazing things about being engaged," one guest remembered the prince as saying in his toast to the university, "is the interest the press takes in the family heritage of your spouse-to-be. They take great pleasure in pointing out the fact that your spouse is much more royal than you are yourself, no matter what side of the bed you come from -- or what part of the blanket you take."

The invitation for the annual dinner was printed in its usual manner. It was on a thin sheet of white paper, run off a copying machine. The date of the event was listed first, then the place and parking directions. On the next line was a reminder that the bar was cash.Then the dress requirements: "black tie, college blazer, evening kilt or equivalent."

Following this was a notice that Sen. Bill Bradley (D-N.J.) would preside. And following this, quietly relegated, as all guests are, to the middle of the page: "The guest of Honor this year will by HRH the Prince of Wales (Trinity, Cambridge), who will respond to the toast to the university."

"We do it exactly the same from year to year," decreed Wilkinson, the dinner chairman.

Not quite. This year the place was crowded and buzzing with Lady Diana talk. "It's conceptually quite amazing," said her 31-year-old stepbrother, Viscount Lewisham. He's an insurance broker in New York. "The last time a prince of Wales married an English girl was 300 years ago."

And who did he think was more thrilled about the upcoming marriage -- Lady Diana or the prince?

"That's a good question," he laughed. "I'm not going to be drawn into that."

The prince's world tour was planned months ago, long before he was engaged to Lady Diana. Some say he wouldn't have scheduled it if he'd known what course the romance would take.

The purpose of the tour is to promote British exports and goodwill overseas, and in America, pay a courtesy call on an important ally at the White House. Because the prince is a member of the monarchy, there is more pomp than substance to his visits. He does not take a position on political events, particularly one as controversial as the hunger strike of Provisional Irish Republican Army prisoner Bobby Sands.

After one more day in Washington and Virginia, he will head home to Balmoral Castle, to enjoy a few days of salmon fishing. Lady Diana, whom he calls regularly and writes to almost daily, will join him. That's where their romance first bloomed.

"Jesus said to him," the prince read from the Gospel ofJohn, "I am the way, the light and the truth.'" His voice was clear, in the company of the archbishop of Canterbury, the primates of the Anglican communion, and a thousand eyes glued upon him. The choir sounded under the stone columns tall as redwoods. Despite the rain, the stained glass was alive in royal blue.

Evensong, Washington Cathedral. Beautiful. The prince returned from his reading, kneeling beside Vice President George Bush. Little girls in knee socks stood on tiptoe. Their mothers, too.

It was a fine day for the Anglican Church. The archbishop was in from Canterbury and the prince, the future "defender of the faith," was in the first pew. On July 29, the archbishop will unite the prince and his lady in wedded bliss or, as the archbishop's press secretary put it in a delicious accent: "He's going to tie the knot."

The archbishop appeared to have not quite so many fans as the prince himself, at least at yesterday's afternoon service.

"He's a handsome man," marveled Dorothy Witmer of Brandywine, Md. "And I particularly liked his voice."

And would she particularly like her daughter to marry him?

"Oh, indeed," she replied.

"People are much more enthusiastic here," observed Jonathan Coopersmith, a Washingtonian studying at Cambridge University in England. "It's almost a bit romantic, because it's something we don't have."

Emergency. The prince of Wales was coming to the White House, and they needed flowers in the West Lobby to greet him. White House social secretary Muffie Brandon, flanked by aides, went scurrying through the executive offices of the West Wing, picking up a bouquet here, an arrangement there.

Whew. She made it in the nick of time. And then after the prince was safely on his way, she dutifully picked up the flowers and returned them to their respective offices, a bouquet here, an arrangement there.

HRH does not respond to shouts from the press like American politicians do. It is not thought proper to ask questions about the strife in Northern Ireland. It is also not thought proper to ask if he misses Lady Diana Spencer.

One may, however, ask how he's enjoying Washington.

"It's been very nice," he said. "Except for the rain."

And that was it.