The judge said that the adjournment was needed to consider new information presented by the prosecution.
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The judge agreed to an adjournment but said the trial would resume on 24 April.
The adjournment debate, led by by-election winner Andy Sawford, is on energy intensive industries.
The MP secured an adjournment debate on the issue, due to take place in Parliament later.
The adjournment order was made after an application from Eton, tribunal chairman Richard Byrne said.
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It is the fourth adjournment of the hyponatraemia public inquiry in less than a year.
Following discussions, the three judges agreed to the prosecution's adjournment request and postponed the appeal until October.
Miss Boothroyd also stressed the need for greater parliamentary scrutiny through select committees, questions and adjournment debates.
Hugo Groves, representing the club, asked for the adjournment of a winding-up petition by HM Revenue and Customs.
The adjournment comes as the Conservative-Liberal Democrat coalition promised a fresh look at extradition arrangements between the countries.
After a brief adjournment, Judge Murphy called the parties back into the courtroom and remanded Cunningham in custody.
The day ends with an adjournment debate led by Stoke MP Tristram Hunt on misleading origin of country labelling.
Then watch out for the adjournment debate, when the Conservative Stephen Barclay will discuss the regulation of health professionals.
But the commission rejected the request for a two-week adjournment, saying its work needed to be completed with speed.
After stating his name and address, solicitor Michael Reed applied for an adjournment.
He recently secured an adjournment debate in the House of Commons about country of origin markings for manufactured products.
And the Commons day ends with an adjournment debate, led by the Conservative David Amess, about experimentation on animals.
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And, despite being handed a six-week adjournment in their tax bill case, the Conference still want to talk to City.
That's followed by the usual pre-recess adjournment debate - a chance for MPs to raise the issue of their choice.
The day's debates end with an adjournment debate on supermarkets and public land in Scotland, led by Labour's Michael McCann.
And the day ends with an adjournment debate led by the former Prime Minister, Gordon Brown, on Remploy Marine Fife.
Judge Lord Menzies apologised to the eight women and seven men for the adjournment and said he hoped proceedings would resume on Monday.
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And the adjournment debate is on UK exposure to high carbon investment - led by the Green MP Caroline Lucas.
It followed the last formal act of Preston's Guild celebrations which was the adjournment of the Guild Court until 2032.
This followed an earlier adjournment to allow the Irish Prime Minister Enda Kenny to attend a jobs announcement and leaders' questions.
The final event is an adjournment debate on energy infrastructure and the UK supply chain, led by the Conservative, Peter Aldous.
On the other hand, it is by no means certain that Royal would pull out in the event of an adjournment.
The adjournment resolutions that they have passed allows them to come back every four days in the House and pass legislation.
Business in the chamber ends with an adjournment debate led by the Reading MP Alok Sharma on rail ticketing and overcrowding.
"The adjournment creates additional tension and has a bad effect on the health of the defendants, " said defence lawyer Vladimir Sheitanov.
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