'Tricky few days' for pregnant Kate
The Duke of Cambridge has said his wife has experienced a "tricky few days" with very acute morning sickness, but they are thrilled at her pregnancy.
Speaking during a visit to Oxford University to open its new £21 million China Centre, the Duke said: "She's feeling OK, thanks. It's been a tricky few days - week or so - but obviously we're basically thrilled, it's great news, and early days.
"We're hoping things settle down and she feels a bit better."
Kate had to pull out of the visit to open the China Centre with William as she is suffering from hyperemesis gravidarum, as she did during her first pregnancy.
On the advice of medical staff she remained at Kensington Palace where she is being treated by doctors.
It is understood that Kate's pregnancy has not passed the 12-week stage - a similar position to when she was struck by the illness when pregnant with Prince George.
And there is already speculation that the royal couple's second child could be due in April.
The news was greeted by the Queen and members of both William and Kate's families with joy - they are "delighted" at the news, Kensington Palace said.
And during William's visit to the China Centre, he was inundated with congratulations from staff and students.
The Duke repeatedly said "thank you" to the supportive words as he greeted crowds during a brief walkabout as he made the short journey through St Hugh's College to tour the new building.
William suggested that his wife could be back carrying out official duties in a few weeks when one well-wisher sympathised with Kate's condition and said they wished she could have attended.
The Duke replied: "I know, she wishes she could be here - a few weeks' time."
The full statement announcing the pregnancy said: "Their Royal Highnesses the Duke and Duchess of Cambridge are very pleased to announce that the Duchess of Cambridge is expecting their second child.
"The Queen and members of both families are delighted with the news.
"As with her first pregnancy, the Duchess is suffering from Hyperemesis Gravidarum.
"Her Royal Highness will no longer accompany the Duke of Cambridge on their planned engagement in Oxford today. The Duchess of Cambridge is being treated by doctors at Kensington Palace.''
The opening of Oxford University's new centre was a high profile event attended by China's Ambassador to the UK Liu Xiaoming, other notable members of the UK's Chinese community, and the University's Chancellor Lord Patten.
For the Duchess to cancel her attendance, her illness, which is thought to have started a number of days ago, is likely to have caused some concern but is being well managed.
Like her first pregnancy the onset of the condition has meant news of her second baby has probably been announced earlier than the Cambridges would have planned.
Dame Elish Frances Angiolini, principal of St Hugh's College, focused on the happier side of the announcement during a speech to mark the official opening.
She told the guests during an open air ceremony held in the centre's internal courtyard: "Little did we know just what wonderful news we would also have today."
Dame Elish added: "Our sorrow at the absence of the Duchess is more than compensated for by the great joy of that news for the whole country today."
She added afterwards: "Everybody has been congratulating him, there has been great happiness about it - it was pretty clear he was very, very happy."
William's speech remained focused on the subject of the visit and he praised the centre's world-class facilities which include a library housing a large part of the Bodleian Libraries' Chinese book collection.
But he did mention his wife's absence telling guests: "I'm sorry that Catherine could not join me today. She is sorry to miss it, and she hopes to come back in the future to meet you all for herself."
The pregnancy announcement comes around six weeks after Prince George celebrated his first birthday.
The couple's second child will become fourth in line to the throne, shifting Prince Harry further down the line of succession.
Kate's condition will throw into doubt whether she will be able to attend her first solo overseas tour, set to take place in Malta later this month.
The Duchess' first pregnancy was revealed when she was around eight weeks pregnant after she was admitted to hospital suffering from very acute morning sickness in December 2012.
Hyperemesis gravidarum, which affects 3.5 per 1,000 pregnancies, causes severe vomiting and can lead to dehydration, weight loss and a build-up of toxins in the blood or urine, called ketosis.
A Kensington Palace spokesman said the Duchess's attendance at future events would be decided on a "case by case'' basis.
Kate is scheduled to be among the guests at the opening ceremony of the Invictus Games in London on Wednesday evening, along with William, Harry and the Prince of Wales and Duchess of Cornwall.
The following day she is due to attend a solemn Drumhead service at Lee Valley Athletics Centre with the Duke and Harry, and later with William to watch Invictus competitors taking part in matches and heats.
Kate is due to make her first official solo overseas tour in two weeks' time, from September 20-21.
A spokesman said: "We will be planning this on a case by case basis - it's too early to talk about Malta and Invictus.''
Rumours about a second child have been rife since earlier this year.
William fuelled the speculation in April when he told a woman who presented him with a lace shawl: "You might have to make another one soon.''
The rumours were quashed later when Kate drank wine at a vineyard and took a white-knuckle jet boat ride.
Then in July one bookmaker suspended betting on an announcement.
The news sparked betting on aspects from baby names to the child's hair colour in what bookmakers described as "the biggest novelty market of the year''.
It generated excitement around the globe, with the hashtag "royalbaby'' trending worldwide and in the UK.
Former England rugby star Mike Tindall, husband of William's cousin Zara Phillips, said he found out about the new baby when it broke on the news. He told talkSport: "I just sent them a message saying it was nice to hear the news on the radio."