4 December 2012 Last updated at 11:08 ET

William visits pregnant Kate on second day in hospital

Prince William walked swiftly past journalists

The Duke of Cambridge has returned to visit his pregnant wife, who is in hospital for a second day with severe morning sickness.

Prince William spent Monday with Catherine after her admission led to the couple announcing her pregnancy.

The duchess, who is thought to be less than 12 weeks pregnant, is expected to remain at King Edward VII hospital in central London for several days.

The news has prompted congratulations from across the UK and the world.

No due date has been announced for the baby, which will be third in line to the throne after Prince Charles and Prince William.

Royal gynaecologist Alan Farthing and his predecessor Marcus Setchell visited the hospital on Tuesday afternoon.

Mr Setchell is the duchess's main doctor and is "clearly being advised" by Mr Farthing, the BBC's royal correspondent Peter Hunt has said.

Earlier, Prince William arrived at the private hospital in a green Land Rover, heading straight in to see his wife without speaking to the media.

Families 'delighted'

The duchess is suffering from hyperemesis gravidarum, which causes severe nausea and vomiting, and the main danger is dehydration.

Dr Peter Bowen-Simpkins, medical director at London Women's Clinic, said: "People who get it get intractable vomiting and may lose as much as 10% of their body weight and become very dehydrated.

At the scene Peter Hunt Royal correspondent

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A normally sedate street in the heart of London has been transformed, temporarily, into a live broadcast location for reporters from the UK and abroad.

The King Edward VII private hospital provides the backdrop, but little else.

Royals, like others, are never keen to offer a running commentary on their medical condition.

Prince William arrived without glancing at the journalists across the road. Their presence is a potentially painful reminder of how so much of his private life is played out very publicly.

William is now, once again, with his wife. She's likely to be receiving fluids, intravenously, to address the acute morning sickness she's suffering from.

The duchess, who's in the early stages of her pregnancy, will be treated at the hospital for several days and then continue to convalesce at home.

• Read more from Peter

"When this occurs the simple treatment is to get fluids into them - and usually they feel considerably better."

Dr Bowen-Simpkins also said the condition was "more common with a multiple pregnancy", adding the couple "would know by now whether there were twins there or not".

Catherine and William, who are both 30, were married at Westminster Abbey in April 2011.

In a statement on Monday, St James's Palace said members of both the Royal Family and the Middleton family were "delighted with the news".

"As the pregnancy is in its very early stages, Her Royal Highness is expected to stay in hospital for several days and will require a period of rest thereafter," the statement added.

St James's Palace would not be drawn on when the royal couple had become aware of the pregnancy, only saying "recently", but it is understood the palace announcement was prompted by the duchess's medical condition.

The Queen, Prince Charles and other members of the Royal Family had been told about the pregnancy only earlier in the day.

Prince William's brother, Prince Harry, who is serving with the Army in Afghanistan, is thought to have been told in an email.

Prime Minister David Cameron wrote on Twitter that he was "delighted by the news...They will make wonderful parents."

Labour leader Ed Miliband also tweeted: "Fantastic news for Kate, William and the country. A royal baby is something the whole nation will celebrate."

Right to the throne

Severe morning sickness

It is not uncommon for pregnant women to experience morning sickness, particularly during the first few months of pregnancy.

But some women (around one in every 200) experience severe nausea and vomiting, which continues throughout pregnancy.

This condition is known as hyperemesis gravidarum or HG and needs specialist treatment and often requires a stay in hospital.

The main danger is dehydration - it can be difficult to keep enough fluid down orally.

Doctors can treat HG with medication to help ease the nausea. HG is unlikely to cause harm to your baby. However, if it causes weight loss during pregnancy there is an increased risk that your baby may be born with a low birth weight.

• Severe morning sickness can be 'traumatic'

Among those to offer congratulations from further afield were US President Barack Obama and his wife Michelle.

In October 2011, Commonwealth leaders agreed to change succession laws so that the daughter of any future UK monarch will have the same right to the throne as a son.

Under current laws, if a girl was born first to the couple, she would lose her place in line to the throne if a boy was born later.

The law has not yet been altered but a Cabinet Office spokesman said formal consent was expected "very shortly" and ministers have indicated that the legislation will apply to any royal births from the date of the leaders' decision.

The monarch is also head of the armed forces, supreme governor of the Church of England, head of state of the UK and 15 other Commonwealth countries.