LONDON (Reuters) - Prince Charles's new wife Camilla appeared for the first time on Saturday on the balcony of Buckingham Palace, an iconic setting for royal appearances before the British public. Camilla, the Duchess of Cornwall, was taking part in her first Trooping the Colour ceremony as a member of the royal family to mark Queen Elizabeth's official birthday. During the procession Camilla rode in a carriage with her step-son Prince William. In an annual ceremony dating back to the early 1700s, the queen inspected the red-coated troops of the Household Division on Horse Guards Parade in London's Whitehall district....