His granddaughter has been painted here, somewhere; he knows it. They have to have painted her. As he had always suspected would occur, Elizabeth has grown to be very influential in the Wizarding World. She is now Hogwarts headmistress, and she assured him years ago that upon her appointment to Head she would commission the painting of a portrait.
Therefore, Phineas has spent his morning storming about the other portraits, demanding to know where his dear Elizabeth has been placed, but each subject of every painting has yet to know the location of his granddaughter.
"Where is the painting of Elizabeth Burke?" he asks for the hundredth time, now directing his question towards a pair of monks hunched over a bubbling cauldron.
"She happens to have been placed on the Secondary Staircase," says one of the monks, a middle-aged man with a deep, booming voice.
"Thank you, my dear man," says Phineas with a polite but half-hearted bow before he walks quickly towards the portraits on the Secondary Staircase, locating Elizabeth immediately. He's walking ever faster as he approaches her, and then he envelops his granddaughter in a hug for the first time in thirty years.