LONDON — Prince Harry could barely contain himself. Facing a news camera to announce his son’s birth, he rubbed his hands together, bounced on the balls of his feet and seemed unable to stop himself from grinning, even for a second.

“It’s been the most amazing experience I can ever possibly imagine,” he said, standing in front of the stables at Windsor Castle, where two black horses nodded behind him.

“How any woman does what they do is beyond comprehension,