London - Princess Diana would have been a "proud grandmother".
Prince William's mother died in a car crash in 1997, but had she lived to see the birth of her first grandchild - born to the prince and Duchess Catherine on Monday - she would have looked forward to her role in bringing the new arrival up.
Tessy Ojo, chief executive officer of the Diana Award scheme - an initiative which recognises teenagers who make contributions to their communities - said on the day of the royal baby's birth: "Today Diana, Princess of Wales, would have been a proud grandmother.
"Her legacy continues through the inspirational work of these young people who carry this honour, set up in her memory, with pride."
Diana's strong maternal instincts
Diana's brother, Earl Spencer, also remembered how she had been born on a day similar to Monday.
He told Hello! magazine: "My father always told us how Diana was born on just such a blisteringly hot day, at Sandringham, in July 1961. It's another very happy summer's day, half a century on. We're all so pleased, it's wonderful news."
Another of the Princess of Wales' friends, Rosa Monckton, remembered how she had guided her through her own pregnancy and how much she doted on children.
She wrote in the Daily Mail newspaper: "What people won't be aware of is how much Diana, with her strong maternal instincts, relished the whole process of pregnancy. Indeed, she embraced any woman she saw who happened to be pregnant.
'It makes me ineffably sad'
"Seeing photographs of the Duchess of Cambridge shopping for baby clothes with her mother made me terribly sad that Diana wasn't around to be part of the ritual and fun of the run-up to the birth.
"Diana was made to be a mother. Her nurturing instinct was the best part of her character. She would have been the most magnificent grandmother and it makes me ineffably sad she will not be a part of the royal baby's life."
The new born Prince of Cambridge still has his maternal grandmother, Carole Middleton, to help bring him up, and both of his grandfathers, Mike Middleton and Prince Charles.
A friend of Charles, 64, thinks he will make a great role model, saying: "He will be doting, and I think he will be surprised how involved he enjoys being as the child gets a little older.
"Charles will be terrific when the child gets to two-plus, though I think that nurturing his grandson will also be a more emotional time for him than people may realise."