Diana, princess of Wales, the popular young wife of Britain's Crown Prince Charles, gave birth tonight to the couple's first child, a son, who is second in line to the British throne.

The baby--whose name has not yet been announced--was born in a west London hospital at 9:03 p.m. London time (4:03 p.m. Washington time) after at least a 16-hour labor which began before dawn Monday.

The child weighs 7 1/4 pounds and cried lustily, according to initial reports. The official notice was posted at Buckingham Palace, home of the infant's grandmother, Queen Elizabeth. The BBC broke in to evening programming with urgent bulletins and live reports from the scene of jubilant crowds.

Well-wishers who had waited all day in front of St. Mary's Hospital in Paddington cheered as word of the birth spread. The crowd chanted "We want Charlie! We want Charlie!" and sang "For He's a Jolly Good Fellow" to honor the baby. Knots of people at the palace gate and in front of televisions across the land joyously toasted this latest installment to Britain's favorite royal romance. Typical of the comments was one from an 11-year-old who said, "I think the princess and Charles are just terrific."

Forty-one-gun salutes were scheduled to be fired at the Tower of London and in Hyde Park to mark the event--which adds another boost to the country's spirits, already bouyed by the recent success of British troops in the Falklands war with Argentina.

Charles, 33, and Diana, 20, chose to have the baby in a neighborhood maternity hospital rather than at the palace, as had been anticipated, because it is not yet their home, a spokesman explained. Instead the couple chose a 12-foot-square private room in the Lindo wing of St. Mary's, which costs 126 pounds 90 pence per day, or about $230.

It was the same hospital used by Charles' sister, Princess Anne, whose two children were born there. Diana's room is decorated in pastel colors, has a cork tile floor and simple furniture--a bed, wardrobe, bedside table, rocker and armchair. The room has a single picture on the wall, a television and washbasin in the corner.

Despite the simple surroundings, the 54-bed wing is bound to become a mecca for status-conscious British mothers.

The birth was assisted by Dr. George Pinker, the Queen's official surgeon-gynecologist, and what was described as "other doctors of the Royal Household."

The exact date the baby was due had never been announced, but Diana had predicted it would come on her 21st birthday, July 1.

Diana's stepgrandmother, Barbara Cartland, exclaimed, "I am delighted she has not got to go on waiting and that it started sooner than we thought. The last month is always the worst . . . Every Englishman and every Englishwoman always wants a son first."

Diana herself was thought to want a boy. During a visit in May to a community center in southeast London, she had told people of her choice.

There were no public indications the baby would come this early, and listeners to morning news programs were surpised to hear that Diana was in labor--the first time in weeks that another British story aside from the Falklands topped the news.

Sunday afternoon, according to British press accounts, Diana met Charles at Windsor Castle on his return from a quick trip to France and drove her husband home, in a black Ford Escort, to the couple's apartment in Kensington Palace. (She wore her seat belt, the Daily Mirror noted approvingly.) By then Diana may have known the baby was imminent because Charles had rushed back from France and cancelled a Windsor polo match.

Just before 5 a.m., Charles and Diana drove to the hospital accompanied only by her bodyguard, according to a terse palace communique.

Throughout the day, radio and television reporters fought gamely to keep on top of the story but had virtually nothing new to report. There were extensive interviews with people in the crowd, some of whom claimed they had come thousands of miles just to be in London for this occasion. Bouquets of flowers were ferried to the premises along with outside greeting cards.

When Charles finally emerged from the hospital after it was over, the mainly youthful crowd was in a near frenzy. His face covered with lipstick marks and showing signs of the long day, he said with a smile, "I'm sorry you all had to wait so long." Asked how he felt, he said he "was relieved and delighted." He said the child had blondish hair, but that he expected it would change color later. Before he was driven away, he good-naturedly cautioned the crowd to "stop making so much noise . . . people are trying to sleep in there."

Details of the birth were kept to a minimum. The Buckingham Palace statement merely said that Diana was "delivered safely" of a baby boy. It was not known, for example, if the couple had been trained in natural or Lamaze childbirth techniques. Diana's sister, Lady Sarah McCorquodale, said her sister had been looking forward to the birth very much. Asked if Diana had taken lessons in relaxation and breathing procedures, she replied, "I certainly hope so."

It was, however, repeatedly stressed that Charles was present throughout the labor.

Diana had quipped that Charles had read so many books on infant care and pregnancy that he considered himself an expert. "He keeps telling me what to do," she said, according to the Press Association.

Reuter, the British news agency, reported tonight that the "Princess of Wales is expected to breast-feed the baby, which means that the child's cot will be in their bedroom or close by."

The fact that the child is a son means that the succession question is straightforward. The infant automatically would ascend to the throne in the case of the death or abdication of his father and grandmother. Had the child been a girl, however, and the couple later had a son, he would take precedence over his older sister. As questions of royalty go, this is a contentious one. A Labor member of Parliament, Michael English, has introduced a bill to make the oldest child heir to the throne, regardless of sex. English said he had written to the 17 Commonwealth nations who regard the queen as their monarch to obtain agreement. Charles and the queen also have been canvased, but their views are not known--and for this generation the problem is now moot.

"It's an inexcusable case of outright sexism," said one young Englishman tonight, whose own son also was born at St. Mary's. "Two of the best monarchs we've had in modern times were women, yet everyone wanted a boy."

Speculation over the boy's name already is rife. One London bookmaker made George the favorite, with James, Charles and Edward following behind.

"Prince Charles is quite a traditionalist in many ways, and I should think he would follow the usual pattern," said Patrick Montague Smith, former editor of Debrett's, the handbook of royalty, to the Press Association. "I would think there are about two dozen boy's names they could choose from," he said. It would not be unusual for the child to be given between three and five Christian names.

The saga of Charles and Diana has captivated Britain since their romance was disclosed 18 months ago. Their wedding last July was a gala affair, and Diana since has been praised widely for her charm and demeanor. In recent polls, she had been voted the country's most popular royal, well ahead of Princess Anne and the queen's sister Margaret and, by some counts, surpassing even the queen.

The British were exceedingly pleased when Diana became pregnant, and she was followed so intensively that the palace officially chastised several popular newspapers for photographing her pregnant in a bikini.

The new baby will get a modern upbringing, according to experts quoted in the British press. Diana has experience as a nursery school teacher, and the couple has retained an experienced 39-year-old woman, Barbara Barnes, as the official nanny. Barnes has been quoted as saying, "I do not see any different problems in bringing up a royal baby. I treat all children as individuals."

Today's birth differed greatly from Prince Charles' own birth on Nov. 14, 1948, in Buckingham Palace. While Diana was seen in public until almost the last minute, Queen Elizabeth had been instructed not to move from the palace just before Charles was born. Medical equipment and staff were brought to the premises, and a special nursery was constructed. The baby was moved there just after his birth.

More than 22 years earlier, on April 21, 1926, the queen was born in the Mayfair home of the present queen mother's parents, the earl and countess of Strathmore. For that occasion, as had been traditional for centuries, the government was represented by the home secretary, who was present in the house to see that all went well. This custom now has been quietly abandoned.