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"I doubt we'll see anything from Harry," Brown said. "He will have sent good wishes privately. His job at the moment is in Afghanistan and that's where is focus has got to be. But I'm sure he's called in and checked in with his brother."

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Kate Middleton is "continuing to feel better" as she spends her second day at King Edward VII Hospital in London, according to St. James's Palace. She might have to stay several more days to recover from severe nausea related to her pregnancy.

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"The Duchess of Cambridge is continuing to feel better," a palace spokesman said. "She and the duke are immensely grateful for the good wishes they have received. She will remain in hospital at present and will continue to be treated for hyperemesis gravidarum."

William left the hospital at around 5:45 p.m. local time today. He appeared relaxed and smiled at reporters before being driven away.

Prince William has been the only member of the royal family seen visiting Kate in the hospital, where she is being treated.

The Clarence House confirmed to ABC News that Kate will be in the hospital for "several days," and will then require a "period of rest" battling severe morning sickness.