The Chestermarke Instinct by J.S. Fletcher

As they turned out of the Market-Place into the street leading to the police-station, Lord Ellersdeane and his companions became aware of a curious figure which was slowly preceding them -- that of a very old man whose massive head and long white hair, falling in thick shocks about his neck, was innocent of covering, whose tall, erect form was closely wrapped about in a great, many-caped horseman's cloak which looked as if it had descended to him from some early Georgian ancestor. In one hand he carried a long staff; the other clutched an ancient folio; altogether he was something very much out of the common, and Neale, catching sight of him, nudged Betty Fosdyke's elbow and pointed ahead.

"One of the sights of Scarnham! " he whispered. "Old Batterley, the antiquary. Never seen with a hat, and never without that cloak, his staff, and a book under his arm. You needn't be astonished if he suddenly stops and begins reading his book in the open street -- it's a habit of his."