The Washington that he loved and inspired, from presidents to bus drivers, tenderly sent Hubert H. Humphrey on the last leg of his long, happy journey yesterday.

While thousands huddled in the cold outside, mourning family, friends and colleagues gathered around a flag-draped casket in the Rotunda of the Capitol to say farewell to the senator and former Vice President at a memorial service.

President Carter described Humphrey as "the most beloved of all Americans." Vice President Mondale, a confidant and protege, spoke movingly of the real Humphrey that he and the world revered.

"We must remind ourselves of Hubert's last great wish: that this be a time to celebrate life and the future, not to mourn the past and his death," Mondale said.

"He taught us all how to hope, and how to love, how to win and how to lose. He taught us how to live and, finally, he taught us how to die."

The meaning that Mondale found in Humphrey, who died Friday night at home in Waverly, Minn., after a long struggle with cancer, was echoed in the footsteps and comments of the thousands who came all through the night to pay their last respects.

Of the estimated 60,000 mourners who passed through the Rotunda between 1 p.m. Saturday and 9 a.m. yesterday, Roy M. Smith, a black Metro bus driver from Takoma Park, said it as well as anyone.

"Today is a day to celebrate the birth of Christ, the birth of Dr. Martin Luther King Jr. and the death of the great warrior. I'm sorry to see Ilubert Humphrey pass on," Smith said.

After the 50-minute service, the body of the senior senator from Minnesota, once a Vice President and almost President, was taken in a motorcade to Andrews Air Force Base for his last flight from Washington.

Air Force II, carrying the Humphrey family, the Mondales and others, was greeted at the naval air station in Minneapolis by a solemn crowd of several hundred state officials and political activists. The general public, excluded from the Navy base, gathered in a line of automobiles extending several miles along the fences, trying to catch a glimpse of the entourage.

At the Capitol in St. Paul, where Humphrey lay in state last night, a line had formed hours before the casket arrived. The funeral and burial will be this afternoon, with President Carter expected to attend.

The U.S. Capitol service for "The Happy Warrior," as Humphrey was known through his 30 years as a Democratic Pary pillar, united friend and erstwhile foe in rare veneration.

Former Presidents Ford and Nixon, former Vice President Rockefeller, Mrs. Lyndon B. Johnson, Henry A. Kissinger, present and former members of Congress. Cabinet executives, military brass, diplomats, politicians were there.

Mrs. Humphrey, wearing a cheery pastel outer coat that would have pleased her husband, sat between Carter and Mondale. The President held it was time to leave, he lead her out her hand part of the time and, when by the hand.

Midday sun filtering into the Rotunda created an aura of extraordinary brilliance around Humphrey's casket, placed over the spot that marks the center of Washington.

Violinist Isaac Stern and singer Robert Merrill performed, and Mrs. Humphrey nodded appreciatively. Carter stepped over and whispered to Merrill, who asked the assemblage to join him in another verse of "America the Beautiful." closing the service.

Mrs. Humphrey turned to the row behidn her and chatted briefly, but animatedly, with the Fords and Nixon, who kissed her on the cheek, and with Tricia Nixon Cox.

Then eight military pallbearers saluted in slow motion, the honor guard retired, and Humphrey's casket was hefted gently and taken down the high steps of the East Front of the Capitol to a waiting hearse.

Twenty-four Capitol policemen, some of whom knew the senator personally, lined the steps and saluted as he left the building that was his life for so long.The Marine Corps band played "Hail Columbia" and "Faith of Our Fathers."

Muriel Humphrey followed the casket, and the Carters accompanied her to a waiting limousine. Following them were the Mondales and Lady Bird Johnson.

Cameras whirred when Nixon, drawn back to Washington for the first time since he resigned in disgrace in 1974, entered the Rotunda before the service, and when Senate Chaplain Edward L. R. Elson spoke in his invocation of pardon and forgiveness.

Both Carter and Mondale, the main speakers at the service carried live on national radio and television, described Humphrey as representing the best of the American system, a champion of the underdogs and the disadvantaged, and forgiving of his bitterest enemies.

"At critical times in our history." Carter said, "the United States has been blessed by great people who just by being themselves give us a vision of what we are at our best and of what we might become. Hubert Humphrey was such a man."

Carter continued, "His greatest personal attribute was he really knew how to love. There was nothing abstract or remote about it. He did not love humanity only in the mass. . . in his words, in the clasp of his hand, in the genuine eager interest in his eyes as he looked at you."

"Yesterday, as messages poured into me as President and to the members of the Humphrey family from throughout the world. I realized vividly that Hubert Humphrey was the most beloved of all Americans and that his family encompassed not just the people of the United States but all people everywhere," Carter said.

Mondale, his voice breaking at times and the emotion welling in his words, held the crowded Rotunda in thrall as he spoke of "one of the saddest moments of my life" -- bidding farewell to his friend and mentor of 31 years.

"Hubert will be remembered by all of us who served with him as one of the greatest legislators in our history," Mondale said. "He will be remembered as one of the most loved men in his time. Even though he failed to realize his greatest goal, he achieved something much more valuable than the nation's highest office. He became his country's conscience."

Mondale remarked on the qualities that made Humphrey "simply incredible," as he put it: good humor, optimism and hope, interest, concern for people and belief and "a spirit so full of love that there was no room for hate and bitterness."

"Hubert was criticized for proclaiming the politics of joy, but he knew that joy was essential to us, and is not drivolous. He loved to point out that ours is the only nation to officially declare the pursuit of happiness as a national goal," Mondale said.

He noted the unabashed sentimentality that allowed Humphrey to cry in public without embarrassment. Indeed, in his last major speech in Minnesota, the senator wiped tears from his eyes and said. "A man without tears is a man without a heart," the Vice President said.

The Humphrey tears were "not for himself, but for others," Mondale said --stood by the steady stream of ourners who filed past the bier to say their own personal farewells.

Hundreds were left disappointed, bunched outside the cordons around the vacant East Plaza of the Capitol, after officials close the Rotunda to the public earlier than had been announced. But the important point was, even in their disappointment, that they were there, bearing witness.

While Senate and House members issued statements on their copying machines, penetrating observations were voiced by the little people Humphrey understood so well.

Frank Carpenter of Washington, an employee of the Commerce Department, put it this way: "Humphrey did a lot for black people, more than we've begun to realize. He opened up understanding of white folks to the plight of black people."

Don Loff of Annandale, a civil engineer at the Department of Agriculture: "We just wanted to be here."

Jesse Ross, who came from New York with his wife: "He is irreplaceable."

John McGregor, visiting from Cleveland: "You try to point out the people who are wrong, who do things we don't like. It seems we should do something for those who are good."

At Andrews AFB in Prince George's County, an estimated 300 mourners waited for more than an hour in a blustery wind and below-freezing temperatures for the Happy Warrior's motorcade.

"I loved him. I campaigned for him in Hillcrest Heights. I came here this morning instead of going to Mass," said Molly Monaghan.

"I loved him. I've always loved him. He's been so good for blacks. He was the first person I ever voted for . . . in 1960 when I was 21 and lived in Orangeburg, S.C.,' said Devoyonne Young of Forestville.

The crowd watched in silence, from behind a fence, as the hearse arrived, cannons saluted and a band played.

Then presidential jet 26000, at precisely 1 p.m., lifted off the Andrews runway, taking Hubert Horatio Humphrey home for the last time.