While Dad was playing polo and Mom stood nearby doing what she does best -- look smashing -- Britain's precocious Prince William and his younger brother, Prince Harry, amused themselves in the back of an ambulance parked adjacent to the field in Windsor. Wills carefully strapped a willing Harry to a stretcher, administered a mock checkup, then asked, solicitously, ''Are you all right? Are you feeling better now?''

Harry was, and he was not alone. All of Britain is feeling better now about Prince William, the onetime superbrat known in some circles as ''William the Terrible.'' Just days away from his fifth birthday on June 21, he is acting more the part of William the Penitent. He can peaceably play doctor with Harry, 2, when once he might have throttled him with the stethoscope. Nicknamed ''the Basher'' in nursery school, he gets on well with his new chums at the upscale Wetherby School, where he started in January. And faux pas such as sticking his tongue out at weddings and running off with a fireman's helmet, screaming, ''I want it!'' are, for the most part, old news. (He did urinate behind a tree not long ago, but that was under his nanny's supervision.)

''William is a proper little gentleman,'' says his mother, Princess Diana. ''He opens doors for women and calls men 'Sir.' '' Part of Wills's turnaround can be traced to Ruth Wallace, 40, the Waleses' new no-nonsense nanny. It was she who was given more authority by Charles and Diana to discipline Wills; former nanny Barbara Barnes had been somewhat more lenient in her approach. Wallace made it clear that neither she nor her colleague Olga Powell would tolerate public tantrums. When, for example, William wouldn't stay put during a recent polo match, Powell gave him a prolonged verbal thrashing. The little boy burst into tears, which prompted one tabloid to run his picture with the headline, ''His Cryness.''

Perhaps Wills has been tamed simply because he doesn't have the time anymore to act up. Since his twice-a-week nursery-school days ended early last winter, he has been up each weekday morning by 7:30. Then he eats breakfast and is driven by a bodyguard in an unmarked car to Wetherby, less than a mile from Kensington Palace. Though it is probably too soon to judge, he may, like other royals before him, be longer on charm than on smarts. He is an average student at the $1,250-per-term school, where he studies reading (he has mastered ''cat'' and ''dog''), writing (he can print his name) and math, and is also involved in singing and competitive sports. When school lets out at 3:30, there are piano lessons, music-appreciation lessons, private physical-training instruction, and swimming lessons from Mom. William also finds time to play dress-up, frequently donning his Spiderman costume or full combat uniform to oversee his arsenal of military toys.

Then, on weekends, the family heads to Highgrove, their country home in Gloucestershire. (That's where he'll likely spend his birthday.) Wills shares his father's passion for gardening and fishing. He also delights in riding Smokey, his pony, or sitting atop the family tractor, looking as proud and delighted with himself as if he were already on the throne.

There is time enough for that later. Indeed, knowing that a lifetime of duty awaits him, his parents have tried to shield him from unnecessary public scrutiny. But Wills seems to be getting the picture. When his former classmates asked him the name of his new school, he couldn't tell them. Replied Wills: "I'm not allowed to know for security reasons."