The Duke and Duchess of Cambridge meet artist Paul Emsley after viewing the newly-commissioned portrait of The Duchess of Cambridge at the National Portrait Gallery in central London, Friday Jan. 11, 2013. AP Photo/PA, John Stillwell LONDON (AP) - Palace officials say Prince William and the former Kate Middleton's first baby is due in July and that her condition is improving. The Duchess of Cambridge, as she is formally known, had been hospitalized earlier in her pregnancy for acute morning sickness. Officials said Monday she is feeling better. She made a rare public appearance last week and appeared to be healthy. The infant would be third in line for the British throne.