Prince William And Catherine, Duchess of Cambridge, Expecting Third Child

Kensington Palace officials announced Monday that the Duchess is pregnant but that the former Kate Middleton was not feeling well enough to attend an engagement later in the day.

As with her other two pregnancies, the duchess is suffering from hyperemesis gravidarum, or acute morning sickness. She is being cared for at the royal couple’s apartment in London’s Kensington Palace.

The sickness failed to dampen the buoyant mood among the royals, however.

“The queen and members of both families are delighted with the news,” the palace said in a statement.

No details were immediately available about when the third baby is due, though the duchess is less than 12 weeks pregnant. That would put the due date somewhere between mid-March and mid-June.

William and Kate, both 35, already have two children: Prince George, 4, and Princess Charlotte, 2.

The announcement comes as the royal couple prepared to mark another milestone for their young family: Prince George is scheduled to start school Thursday at Thomas’s Battersea in south London.

Their choice of a south London school indicated that the royal couple was settling into their Kensington Palace apartment, having moved recently from their Norfolk home Anmer Hall

Betting agencies were quick to start offering odds on possible names for the soon-to-be addition to the House of Windsor.

Paddy Power offered 8-to-1 odds on Alice and 10-to-1 odds on Arthur. Also popular is Diana, after Prince William’s mother, particularly given the timing of the announcement.

William and Kate took a leading role in marking the 20th anniversary of Diana’s death last week. The couple, joined by William’s brother, Prince Harry, toured the garden of Kensington Palace to commemorate the princess’s contributions to their family and the many charities she supported.

“Given the recent anniversary, there’ll be plenty of interest in the name Diana if the baby is a girl,” Paddy Power said.

When asked on a royal tour in Singapore in 2012 about how many children he wanted, William said he was “thinking about having two.”

More recently, during a royal tour of Poland, Kate joked about a third child when she was given a cuddly toy designed to soothe tiny babies.

Kate thanked the well-wisher for the present and turned to William.

“We will just have to have more babies,” she said, laughing.

Kate is the eldest of three siblings, and reportedly had a very happy childhood. William and Harry are the only children of Prince Charles and Princess Diana.

Some visitors to the palace Monday were taken aback by the news. Elizabeth Hopkins, 79, from west London was delighted and said Britain needs lots of royal children.

“They’re lovely and, you know, going around with a lot of children brings out the best in people as well,” she said. “And they’ve obviously very happy children and in a happy group, so I think it’s all the best for them.”

Others said the world would be watching.

Katherine Redo, 34, who lives in London but is originally from Metairie, Louisiana, held tight to her squirming 2-year-old daughter, Annabelle, and said she believed many people in the United States would be happy for the royal couple.

“It’s sweet because usually it’s just an heir and a spare and they’re having a third,” she said. “It just gives the idea or the impression that they’re just even more the sweetest, perfect little family.”