Ruth Williams had it all planned. She would celebrate New Year's Eve with her mother and some friends and check into Arlington Hospital Thursday for the cesarean delivery of her third child.

So when the 28-year-old North Arlington resident started feeling labor pains Monday afternoon, she assumed they were a false alarm. But when the contractions felt even stronger by the time she stopped by a friend's New Year's Eve party later that night, Williams decided that her schedule needed some fine-tuning.

Tuesday morning, at 20 seconds after midnight, "by luck and a little timing," as one of her doctors described it, Williams gave birth to the Washington area's first baby of 1985, a 7-pound, 2-ounce, 20 1/2-inch-long boy named Joe Nicholas Williams.

Williams, a single mother, said she realized she was likely to have the first baby of the new year "about 15 minutes to 12 when they were prepping me and the doctor said, 'We're going to try for one minute after midnight.' "

By the time the clock struck midnight, she said, the thrill of having the first baby had lost much of its allure. "The pain was terrible," Williams said yesterday. "I just wanted it to end."

But the birth provided the highlight of the evening for the New Year's Eve crew at Arlington Hospital, where two maternity-ward nurses stayed an hour after the end of their shift to watch.

"When we clamped the cord, as soon as we saw the baby was fine, we looked at the clock" and congratulated each other, said Dr. Karen Liebert, who assisted in the delivery. "When I was on call on New Year's Eve I was kidding everybody that I was going to deliver the first baby," Liebert said. "I didn't think it was going to happen."

It almost didn't.

"She probably would have had the last baby of 1984 if there hadn't been a Code Blue on 4 East about 11:30" holding up the anesthesiologist, said Dr. David Pettey, who supervised the delivery. Since there is greater leeway in timing cesarean births, "to have the first, we probably would have delayed a bit," Pettey conceded. "As it turned out, we didn't have to."

Since times of birth are rounded off to the nearest minute, Joe Nicholas Williams' official entry into the world came precisely on the stroke of midnight. By 12:03 a.m., when 6-pound, 12-ounce Victor Raymond O'Korn arrived at the Washington Hospital Center, word of Joe's birth had reached the staff there, who had to content themselves with having the runner-up in the annual first-baby battle.

Yesterday, wrapped snugly in a blue, pink and white blanket, Joe slept serenely as a procession of reporters and camera crews invaded his mother's hospital room. His only reaction to the hubbub was a frown that periodically crossed his face in the glare of the television lights.

Williams submitted to a stream of interviews with the aplomb of a cabinet secretary, patiently answering the same questions from different hospital-gowned reporters and shifting the infant so television crews could get a better camera angle.

"Open your eyes, and let the world see you," she coaxed the baby for a television cameraman. "Oh God, I feel like Farrah Fawcett."

Williams, who has two other sons, said the New Year's birth made her latest child "special. He's getting to be on TV. He's getting in the papers. Twenty years from now he'll get to read old newspaper clippings of himself."

Down the hall, 7-pound Sarah Christine Aldunate, who arrived less than nine hours after Joe, was just another 1985 baby, the object of little media attention. But her mother, Vivan Aldunate, was happy nonetheless. "I was two weeks overdue," she said. "I'm just happy she came."