"This must be," exclaimed bearded Laurence Davis, attired in a tuxedo with blue ruffled shirt and a black bowler tilted jauntily atop his head, "the most elegant subway crowd in the history of subways."

His wife, Claire, her evening gown hidden by a tightly buttoned, tweedy to coat, nodded agreement.

The Davises, residents of Capitol Hill, sat Thursday evening aboard a moving Metro subway car among others in formal attire. Some were going home; others were enroute back to a hotel from an inaugural party in the former gallery of Union Station now called the National Visitor Center.

There was Marcia Wolf, a congressional employee, a long dress of royal blue setting off her blond hair, on the arm of her date, Jim Kimble. They had taken a taxicab to the Dupont Circle subway station, and rode down the long escalator to take a train the rest of the way.

And there was Melinda McCloud, whose current address is Washington but whose accent is untainted Texas, accompanied by a home-state beau, Doug Jones.

On this one remarkable evening - and up to 2 a.m. yesterday - Washington's 10-month-old subway, usually the workaday hauler of commuters and shoppers, had become a magic carpet for revelers. It was not only the surest way to thread one's way through downtown Washington; it also was the fastest and most comfortable.

Moreover, according to Metro transit police; it was entirely free of crime or disturbance. There was not one arrest in the subway all day.

Statistically, inauguration day was a premier event for Metro.

In the 20 hours of continuous operation from 6 a.m. Thursday to 2 a.m. yesterday - the first extended day for a line that usually is tucked in for the night 8 o'clock - it carried 68,023 passengers. Of those, 23,944 rode free as the guests of President Carter's inaugural committee in the 2 1/2 hours before the big downtown parade.

Metro's previous one-day ridership record was 51.260 set last March 27, a Saturday, when the line was opened for free rides as a prelude to the start of regular service the following week. On that first day, the subway broke down for long periods under the crush.

That did not happen on inauguration day. There was one breakdown that caused a 22-minute gap between trains in mid-morning, when a 5-minute frequency was scheduled. Metro quickly cleared up the backlog of waiting passengers by dispatching three closely spaced trains.

In daytime and at night, Union Station was the busiest subway stop.

As passengers like Mrs. J. Wilcox Brown, the wife of the Democratic national committee man from New Hampshire, walked across the mezzanine, kiosk attendant Arvel Langley flicked on the public address system's microphone. "Ladies," he intoned, "please pick up your gowns while stepping on the escalators." One woman, he explained, had caught and ripped her skirt.

As 2 a.m. approached, the riders were obviously more bibulous.

One man wearing a stylish Italian-cut suit flashed a $10 bill and asked the station attendant for change. Told it was not available, the man responded: "Oh man, come on, I was partying and not even thinking about getting home . . ."

Right behind him, another would-be passenger overhead the conversation. "Oh, no - no change!" he exclaimed.

The station attendant shook his head, smiled and motioned the pair past the gate. "You two go on," he said.