hat hot, muggy August afternoon in 1963 when the words of the Rev. Martin Luther King Jr. - "I have a dream" - echoed over thousands of people gathered at the Lincoln Memorial seems like centuries ago to most people. But not to Coretta Scott King, widow of the slain civil rights leader.

Yesterday morning, as the sun valiantly attempted to warm the 20-degree air, Mrs King and her four children sat at the bottom of the Memorial's stairs, listening to the sermon of Rev. King Sr. at the People's Prayer Service and reliving that historic summer day. "It all flashed by. It was all I thought about," said Mrs King later at a breakfast she sponsored. "I thought of Martin's words that day. Then when Leontyne Price sang I thought of Mahalia (Jackson). Then I thought of Marian (Anderson) and then Martin, again. Just so many emotions washed over me."

At the Memorial, Mrs. King undistracted by the shouts of "Praise the Lord" from a group of Washington gospel singers in the back, appeared very somber. As her father-in-law known as Daddy King, admitted that it was with "a bit of reluctance and temerity" that he stood "on these hallowed grounds where 14 years ago my son delivered a sermon," Mrs King looked straight ahead, smiling very slightly.

"He preached a message with relevance for today and the times in which we live," said Mrs King of yesterday's remarks. "The people who are at least in our society need health care, education and housing. I hope through Jimmy Carter's administration only Martin Luther King Jr's dream, but the dreams of all our people."

- Jacqueline Trescott On That Walk

Guests and guards at the National Archives paradise-watching party reacted to President Carter's walkdown Pennsylvannia Avenue according to their own concerns and experiences.

An Executive Protective Service officer stationed at the Archives said he thought Carter's walk was "fantastic."

"We heard last night that they were arguing about his walking but we weren't sure he really would until he stepped out of the Capitol and the word was passed down the line through the radio.

"I was really tensed up before he got to my post. When he came by here my first thought was to look all around at the people to be sure what was going on. Only when he passed my point and I thought, "Good, he was safe when he passed me,' could I relax and look at him. This was very different from President Nixon's Inauguration. Then we had 300 threats on his life before 9 a.m. Today there were only two, and they were both from people known to be mental cases."

Smithsonian Secretary S. Dillion Ripley, whose mother-in-law has a plantation in Carter country, near Thomasville and Valdosta in South Georgia, said he thought Carter's walk was "epic."

"It was just the way to behave. It had enormous folk appeal. It showed he was a real person. Nixon was a pastiche. Ford had a rugged charm. But Carter has a real instinct for the thing to do."

Librarian of Congress Daniel Boorstin was more restrained in his enthusiasm for the walk. "A nice idea," he said. Writer Katie Louchheim said she thought it was "thrilling, in keeping with Carter's style."

Rep. John Brademas (D-Ind.) said he though Carter's walk was like Adlai Stevenson's style. Brademas recalled a meeting he had in 1955 as a close Stevenson aide. "We talked about the importance of credibility. Carter will be successful because he has great, personal dignity. He is sure of his values and who he is. He has confidence in his own manhood. He doesn't have to keep proving what a tough guy he is."

- Sarah Booth Conroy Peanuts and Song

There were parties in almost every office building along the parade route. Only the closed and boarded and empty Willard Hotel and Occidental Restaurant had no eyes for this festivities.

And Thomas Fadoul, building manager at the National Theatre, said the parade meant extra work for him and his staff and would permit no one to enter.

Elsewhere, there were no buffets and cocktail parties galore in offices and hotels with rooms overlooking the parade. In Room 320 of the Washington Hotel, John Curier, with a gold peanut on his lapel, was expecting some 200 guests throughout the day. He represents the National Peanut Council.

Across the street at Rhodes' Tavern (built in the 1900's and one of the oldest commercial structures in downtown Washington) was a party hosted by Richard Squires, an artist who loves old buildings. "Jefferson," he said, "was the first President to have an Inauguration parade in 1800 and this is the only building still standing along the parade route."

The building, a former boarding house was once run by Barbara Suter who was angry on August 24, 1814, when British Commanders, General Ross and Admiral Cockburn, sat at her tavern and watched the Treasury and White House burn.

Most of the people at Rhodes' Tavern ran to the windows and watched President Carter walk by, and then felt the parade was over.

Eventually, a group sat on the floor, gathered around a bearded guitarist, and began to sing.

- Joseph P. Mastrangelo New Axquaintances

The caterer was late, theguests were early and President Jimmy Carter called a 3 o'clock staff meeting. That put a slight damper on a party billed as a "Get Acquainted" with the new Carter staff, hosted by four black professional women who worked for the Carter transition.

"We just tried to pull off something little different, give a lot of black Carter supporters the opportunity to meet to the new White House staff," said [WORD ILLEGIBLE] Hardon Long, a lawyer who worked at the Talent inventory Project (TIP) searching out black professional talent for the new administration. The other three hostesses at the party in Long's office were Dr. June Christmas; Valerie Pinson, who will bw working on the White House congressional liason staff, and Jefflyn Johnson, who will work at the Office of Management and Budget.

Asked if the women had found a candidate to fill Treasury Secretary Michael Blumentahal's half-humorous request for a black female economist who speaks Arabic and has a Jewish mother, Mrs. Long said, "If we put it in the computer we could probably come up with one."

Clifford Alexander was greeted with applause and handshakes from the guests. Pinson replaced the name tag he had received at the door with one that read "Secretary of the Army Clifford Alexander." The Washington attorney, announced as the Carter choice for the service post Wednesday, said the offer came "from out of the blue" but that it will "give me a chance to be in a management position."

Rep. David Bowen (D-Miss.), wearing a red-lettered "Mississippi Loves Carter" button, said he perceived the new President as "not like a lot of politicans I've met. You know 'I've won, now let's celebrate.' He's not obsessed with having won. He's looking beyond that.

Commerce Secretary Juanita Kreps seemed mildly taken aback not only by the crowd density at the party but the numbers that turned out to watch the Inaugural ceremonies in the cold. "I'll have to get used to Washington and these mass turnouts of people," said the former Duke University vice president who has lived in North Carolina since the '40s.

The party received saturation coverage from the "Children's Express, the Newspaper written by children." Long's son Mark is a reporter and he brought along 13 of his small friends wearing yellow "Children's Express News Team" T-shirts.

Karen Dewitt and William [WORD ILLEGIBLE]