All the gray New York day the radio stations played his music and the crowd grew outside the building. At 7 in the morning there were abut 100 mourners, by 2 this afternoon, many hundreds more.

They stood about quietly, or clustered in groups singing old Beatles standards. They brought flowers -- red carnations, yellow roses -- and tucked them into the wrought-iron gate. There they lay against the dark metal, a good memorial, bright and vivid as a song.

John Lennon, the heart and mind of the Beatles, was dead, shot outside his Manhattan apartment building Monday night by a man who reportedly had requested -- and been given -- his autograph only hours earlier.

The man was identified today by police as Mark David Chapman, an unemployed security guard from Hawaii. He had, according to witnesses, called out to Lennon as he entered his home, the opulent old Dakota on Central Park West.

"Mr. Lennon," the man called out politely.

Lennon turned. The man pulled out a .38-caliber pistol, went into a military crouch and fired.

Lennon was taken immediately to a nearby hospital, where he was pronounced dead. The assailant stood calmy by, according to witnesses, until he was picked up by police.

"Do you know what you just did!" yelled the Dakota doorman, his face covered with Lennon's blood.

"I just shot John Lennon," the gunman reportedly replied calmly. A passerby said the assailant was smirking.

Dr. Elliot Gross, New York City's medical examiner, said today that Lennon was shot twice in the back and twice in the shoulder and died of massive hemorrhaging and shock. "Death occurred within a very short time," Gross said, adding that Lennon was "essentially pulseless on arrival" at the hospital.

The official autopsy report said two bullets entered Lennon's left back, passing through the left chest and striking the left lung before exiting from the body. Two more bullets struck Lennon in the left shoulder. One hit the left arm bone and exited the body. The other passed into the left chest, striking the left lung and lodging in the neck.

This afternoon, under heavy police guard in a packed courtroom in Manhattan Criminal Court, Chapman, 25, was charged with second-degree murder. He was ordered to undergo 30 days of psychiatric tests at Bellevue Hospital, where he will be placed under a suicide watch.

Listening to the preceedings, Chapman was as calm as he had reportedly been at the time of the shooting -- where he shocked bystanders by dropping a gun and taking out a book.

Hefty, impasive, dressed in jeans, a white T-shirt, beige sweater and black aviator glasses, he did not move a muscle. He looked calm and serene as he heard the assistant district attorney read the charges against him. Nor did he respond when his court-appointed attorney, Herbert Alderberg -- who told reporters that his client had indeed shot Lennon -- requested a psychiatric examination for Chapman.

"This defendant is not fully cognizant of what is happening to him at this time," Alderberg said. "I would characterize the man as a very confused individual. He doesn't understand himself." He added that his client had made two previous suicide attempts, including one in the last year with the same gun he had used to kill Lennon.

Assistant District Attorney Kim Hogrefe, speaking before Judge Martin H. rettinger, said Chapman had been fully "cognizant" of his behavior.

The slaying of Lennon, Hogrefe said, had been planned.

The evidence in the case shows, Hogrefe argued, that the murder was a "deliberate, premeditated execution." He noted that Chapman, who is currently unemployed, borrowed "a substantial amount of money -- $2,000 in cash" to make his trip to New York. He had borrowed that money, the prosecutor continued, "to do what he has done." He had acted consciously in a "cool, calm, rational," manner.

Hogrefe told the judge that Chapman had been arrested "approximately" 12 times, including four arrests on charges including kidnapping, abduction and possession of controlled substances. However, two hours later, an embarrassed representative of the district attorney's office returned to court to tell the judge that Hogrefe was wrong. "It appears, at this time, Chapman had no prior arrest record," Barbara Thompson said.

She said that a computer check of Chapman produced information about another man named Chapman, from Texas, with the same birthdate.

Chapman entered no plea, pending psychiatric examination.

Today, as the crowds milled outside Lennon's home, the politicians and celebrities began the litany of public condolence announcements that mark these occasions. And from within the Dakota a distraught Yoko Ono issued a statement on behalf of herself and her five-year-old son, Sean.

"There is no funeral for John," it read. "Later in the week we will set the time for a silent vigil to pray for his soul. We invite you to participate from wherever you are at the time. We thank you for the many flowers sent to John. But in the future, instead of flowers, please consider sending donations to Spirit Foundation Inc. [1 Battery Park Plaza, N.Y.] which is John's personal charitable foundation. He would have appreciated it very much John loved and prayed for the human race. Please pray the same for him.Love. Yoko and Sean."

The statements from musicians -- including the three members of the Beatles -- were gathered from around the world. From his farm outside London, a pale and shaken Paul McCartney said he couldn't "take it in at the moment" and retreated from the press. A spokesman for Ringo Starr, who had been vacationing in Europe and flew to New York, was "extremely shocked" and "didn't want to say any more." George Harrison, who could not be reached for comment, reportedly canceled a concert and also went into seclusion.

Statements from political leaders also began to rush in, President-elect Ronald Reagan, en route to a visit with Cardinal Terence Cooke, head of the Roman Catholic archdiocese in New York, called the shooting, "a great tragedy." But, he added, that did not diminish his opposition to gun control laws. "I believe in the kind of handgun legislation we have in California. If someone commits a crime and carries a gun when he's doing it, add five to 15 years to his sentence."

President Carter said he was "disstressed by the senseless manner" of Lennon's death.

New York City Mayor Ed Koch also decried the shooting. "We mourn his loss," he said. But it is in the nature of politicians not to be able to resist the opportunity to voice a political view. And so Koch reacted to a story in the London News Standard that referred to Lennon's death as a "meaningless murder" of a sort increasingly typical of new York and of the United States in general "Where freedom to carry guns has brought about monsters."

Koch said, "Are there no monsters in Britain? Ask the people of Ireland." The city, he said, was "very proud that Lennon had chosen to make New York his home."

Chapman arrived in New York during the last week, according to police. On Sunday he checked into the Sheraton Centre, at 52nd and Seventh on the north end of the Times Square strip, a notoriously seamy part of town. He spent little time there, however. sNew York police report that he was seen hanging around the Dakota -- a posh Gothic structure that houses such famous New Yorkers as Lauren Bacall, Leonard Berstein, Roberta Flack and Rex Reed. John Lennon and Yoko Ono owned five apartments in the building.

Chapman was seen Saturday and Sunday, looking for Lennon, asking about him, security guards told police. There was, however, never any thought of asking him to leave. Celebrities are so plentiful inside the fine old apartment building -- where security is ensured by a guard, a doorman, and an iron gate -- that fans, stargazers and autograph hounds are commonplace. a

Chapman was at the Dakota again Monday when Lennon and Ono left for a recording session at a studio called The Record Plant. He carried with him Lennon's latest album, the one Lennon had made with Ono, the one that marked his return to music. It was an affirmation of love, marriage and parenthood, called "Double Fantasy." Chapman asked Lennon to autograph the album. Lennon did.

Later that evening Lennon and his wife returned in their limousine, pulling up in front of the building. There was a driveway within the gate where they might have driven, not leaving their car until safely inside, but they did not. They got out and as he walked toward the doorway, Lennon heard someone call his name.

It was Chapman. "Mr. Lennon," he said.

When Lennon turned, the man shot several times. Lennon stumbled inside the investibule, saying only, "I've been shot," and then collapsed. His assailant, witnesses say, threw down his gun, took a book out of his pocket, and began reading. The book, appropriately, was J. D. Salinger's paean to alienated youth: "The Catcher in the Rye. Around the gunman, there was husteria. Ono was in a state of shock. The doorman called police.

Police took Lennon and a hystical Ono quickly to the hospital. The young police officers, Peter Cullen, and his partner, Steven Spiro, did not know the victim was a celebrity until they got to the emergency room. But they did know that the victim was in trouble and that there was no time to wait for an ambulance.

"He was bleeding out of his mouth and chest. I've been involved with enough other shootings to know it was bad," Cullen said.

Lennon was virtually dead on arrival at the hospital, despite desperate ministrations by doctors who tried to revive him.

"I don't think it would have been possible to resucitate him by any means," said Director of Medical Services Stephen Lynn. "He had lost a great deal of blood."

His body was removed to the medical examiner's office and Ono, with Lennon's producer, David Geffen, returned to the Dakota.

"She was quite distraught," said Lynn, in the clean and careful language of health professionals, "and found it hard to accept."

Officer Cullen, who was with Ono when she learned of her husband's death and who later took her home, was more explicit.

"She was very hysterical. She kept saying, 'Is he going to be all right, is he going to be all right?' I kept trying to calm her down."

Today it's all over, nothing left but the words of the politicians and the musicians, and the tributes on the radio. And, of course, the songs -- perhaps an artist's only true hope for immortality.