LONDON – The business of monarchy has always been stacked in favor of men. Not any more — or so the British government promises.

The first child of Prince William and his wife, Kate, will be born a king or a queen in waiting, under changes to succession rules designed to overturn centuries of tradition and give daughters the same rights as sons.

Deputy Prime Minister Nick Clegg pledged Tuesday that the law on succession would be changed at the “earliest opportunity.” He said “whether the baby is a boy or a girl, they will have an equal claim to the throne.”

“Born to rule, be it a boy or a girl” proclaimed the Daily Mail, which noted that the baby had “already made royal and constitutional history” even before it is born.

Not so fast, caution others.

A royal saga needs a touch of uncertainty, and experts point out that despite politicians’ promises, the law giving males primacy in succession has not yet been changed — and the clock is ticking.

“We know that the wishes of politicians are written in water,” said royal historian Robert Lacey. “Law only becomes law when the law is made — and the law has not been made.”

Meanwhile, the Duchess of Cambridge — the former Kate Middleton — was “continuing to feel better” Tuesday as she spent a second day in a London hospital being treated for acute morning sickness, St. James’s Palace said. William visited his wife in the hospital for several hours, as photographers and camera crews from around the world camped outside, eager for news on the royal pregnancy. Officials said earlier the duchess was not yet 12 weeks pregnant.

Congratulations poured in from around the world at the good news, which follows Kate and William’s lavish royal wedding in 2011 and Queen Elizabeth II’s Diamond Jubilee celebrations this year.

Officials say Kate and William’s baby will displace Prince Harry, William’s younger brother, as third in line to the throne — and the child will stay there, even if she is a princess who later acquires a younger brother.

For centuries, preference was given to male heirs, so a first-born princess would be leapfrogged in the succession by a younger brother. Thus, there have been 35 kings of England since the Norman Conquest in 1066, but only seven queens.