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Duchess Kate's alleged due date has come and gone and still no royalbaby, but stepmother-in-law Camilla said today the new third-in-line tothe throne is expected by the end of the week.

Camilla, theDuchess of Cornwall, was at a public engagement in Cornwall with herhusband, grandfather-to-be Prince Charles, when she made an impromptuspeech at a children's hospice they were visiting.

"We are all just waiting by the telephone. We are hopeful that by the end of the week he or she will be here," she said, according to media coverage of their engagement.

Itwas the strongest indication so far of when the Duchess of Cambridge'sfirst baby would arrive, as the United Kingdom waited impatiently in thehottest temperatures of the year and the media sweltered and yawned atthe London hospital stakeout.

The duchess wasn't even in London this weekend, when the baby wassupposed to be due. She got out of town and went to her parents' estatein rural Bucklebury about 50 miles or an hour's drive outside London,the British media reported.

Ifnecessary, there is a contingency plan to give birth at a hospital nearBucklebury, but St. Mary's Hospital in London is the preferred venue.Meanwhile, the palace press office remained silent today on the royalbaby; the plan is to alert the media only after Kate has checked intothe hospital and started labor.

"It's Monday and a sunny start tothe week. Still no sign of The Duchess let alone a baby," tweeted DickieArbiter, a former royal press secretary now working as a royalcommentator.

The Cambridge apartment at Kensington Palace, Nottingham Cottage, was too warm, anonymous palace sourcestold reporters, while her parents' $8 million mansion isair-conditioned and has a pool. Temperatures in the city were nearing 90degrees, unusually hot for the U.K.

Father-to-be Prince Williamwas out of town, too. He spent the weekend with his brother, PrinceHarry, playing in polo games on Saturday and Sunday to raise money fortheir charities. Although William was said to be prepared to returnquickly if Kate went into labor, apparently that wasn't anticipated tohappen on either Saturday or Sunday.

The due date for this babyhas always been unclear. The palace said only "mid-July." Kate herselfmentioned July 13 to someone who asked during an engagement. Her mother,Carole Middleton, was quoted as saying the baby would be a Leo, meaning born after July 23.

Butbabies, royal or not, rarely arrive exactly when expected, adding tothe uncertainty and rampant media speculation. One paper quoted Britain's National Health Service on how to induce labor (have sex). And a reporter on Twitter calculatedthat Kate would be due July 27 if she were six weeks pregnant at thetime she was hospitalized for acute morning sickness in December.

Thewaiting journalists have little else to do but tweet about what theyknow and don't know. "#GreatKateWait continues as sun goes down over the#Lindo Wing," tweeted Sky News royals correspondent Paul Harrison latetoday. The Lindo Wing is the private wing of St. Mary's, and it's whereWilliam was born 31 years ago.

Arbiter, who's been watching themedia mob and its tangle of stepladders and camera equipment outside St.Mary's, says bored photographers - some have been camped out since July1 - amuse themselves by sticking jokey little signs - "for sale" - ontheir equipment.

"Media tagging to break the monotony of waiting around - 'for sale, take me away, ladder if success'," Arbiter tweeted

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