The Reagans' gift to Britain's infant Prince William of Wales, announced yesterday, is a handcrafted child's chair. It is one of 4,200 presents for the baby logged in by Buckingham Palace officials, only a small portion of which are ever likely to be clutched in the royal fist.

"He only has 24 hours in his day," a palace spokesman said, explaining why so many of the rattles, knitted objects, caps and cups would be turned over to charities for sick or underprivileged children. Every offering, however, will be acknowledged by an aide to William's parents, Charles and Diana.

The Reagans' gift, selected by Nancy Reagan, is a reproduction of a Chippendale corner child's chair with a needlepoint seat. The White House noted that both of the first lady's children received needlepoint chairs that became family keepsakes.

The palace said that William's gifts tended to come in two waves -- first arriving after the pregnancy was announced and then after the birth in June. The only difference is that the more recent ones, such as the Reagans', feature the child's name -- carved, sewn, woven, engraved or embossed.

The White House described the needlepoint pattern on the seat of the American gift as a 15-inch square with white dogwood blossoms in the corners and a blue oval in the center, bearing the words "H.R.H. William of Wales June 21, 1982" around the border. At the bottom of the oval is a blue bow signifying Britain's Order of the Garter, the country's foremost order of chivalry. Inside the oval is the prince of Wales coronet, with a pair of interlocking W's underneath for William of Wales.

The design was hand-painted by Aileen Crawford of Needlepoint Designers of Georgetown and was stitched by Ellen Hancock in the curator's office in the White House. The pattern took 73,000 stitches to complete.

The 25-inch-high chair was built by Freeman and Co. of Thomasville, N.C., from Honduras mahogany and bears a silver plaque inscribed:

"To Prince William of Wales

From the President of the United States of America and Mrs. Reagan

June 21, 1982."

There is, of course, a pecking order for presents to the royal family. Gifts from family -- the queen, the queen mother, godparents and so on -- are the most likely to find their way to the nursery, officials said. The palace has not disclosed which members of the royal family gave what to the prince.

Next in line are the offerings of "those known to Prince Charles and Princess Diana" (the Reagans presumably fall into this category).

Then come presents from "neighbors" such as the townspeople of Tetbury, where the couple has a country estate. Their offering was a coral-handled silver rattle with bells and a whistle. After that comes just the ordinary well-wisher. And finally, somewhat disreputably, are those harboring "commercial purposes" behind their gifts.

Amid the fanfare over Charles and Diana's nuptials last summer, routine letters of thanks were dispatched to all businesses that sent offerings. That, the palace spokesman says, proved to be a mistake. Some recipients promptly used the letters as promotional material, and it was decided that where possible those sorts of gifts would be declined in the future.

Queen Elizabeth II accepts presents only from personal friends or organizations that she is connected with. Other members of the royal family have less strict rules, but tend to discourage gift-givers except when there is a glad tiding, which the birth of William, a future king, certainly was.

At the time of Prince Charles' birth in November 1948, Britain was still recovering from the effects of World War II and austerity was in vogue. In his definitive biography of Charles, Anthony Holden writes that Charles' mother received from the United States a ton and a half of diapers, which were distributed to expectant mothers. Britain's linen and woolen drapers institution produced a layette of 55 garments and a few weeks later copies were on sale in U.S. stores. The first recorded gift from his grandmother -- now Queen Mother Elizabeth, great-grandmother of William -- was an ivory-handled rattle.

So austere were the times that even Prince Philip, Charles' father, "came up with some of his own baby clothes for repair." There has apparently been nothing so drastic this time, despite Britain's current economic distress.