William's uncle, Earl Spencer, described his joy at the new royal baby.
He said: "We're all so pleased: it's wonderful news."
The Earl, whose sister was the Duke's mother, Diana, Princess of Wales, added: "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."
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New Zealand have beaten the British and Irish Lions 30-15 in the first Test in Auckland.