"Ah!" I cried. "Then he left here with his beard shaven clean! He intended to disguise himself!" "No doubt, sir," replied the man, who seemed a particularly intelligent fellow. "Because, earlier in the day, while crossing the corridor, I had noticed him standing near the lift. He then had a full beard. I recollected the clothes he was wearing." "Did he talk to you?" "Very little, sir. He seemed a gloomy, rather silent man." That was all he could tell me, though he declared that the gentleman had seemed very agitated and upset while he was being shaved. His hair was also cut, and his moustache trimmed. "Did it alter his appearance much?" I inquired. "Very greatly, sir. I should scarcely have known him when he left here." "And you told nobody?" "It is not my business to pry into customers' affairs," responded the man, and very justly; "but I took good note of his countenance." What he told me was certainly remarkable. The whole of the facts were, indeed, astounding. While the unfortunate Professor lay dead in his laboratory in London he was, at the same time, here, in Edinburgh, making an attempt at disguise, and sending a reassuring telegram to his daughter! That Professor Greer had been killed there was not the slightest doubt-- killed, too, behind locked doors, in circumstances which themselves formed a complete and inscrutable mystery. Then, if so, who was this man who had left London with the Professor's luggage, had arrived in Edinburgh, and whom the hotel-servants and others had identified by his portrait? If he were not the Professor, then who could he have been? One thing was certain, he could not have been the actual assassin. Yet if not, why had he taken such pains to disguise his appearance? The theory of Greer having a double I put aside at once. Doubles only exist in the realms of fiction. Here, however, I was dealing with hard, solid facts. Each phase of the intricate problem became more and more complicated as I endeavoured to analyse it. That grey, wintry afternoon I wandered about the damp streets of Edinburgh, gazing aimlessly in the shop windows, and afterwards sat for a full hour upon a seat in the deserted public gardens below the Castle, thinking and wondering until the gloomy twilight began to creep on, and the lights along Princes Street commenced to glimmer. Then, rising, I set off again across the North Bridge, and through High Street and Johnstone Terrace to the Caledonian Station, and by George Street and St. Andrew's Street back to the Waverley, a tour of the centre of the city. I was merely killing time, for I had decided to take the night express back to King's Cross. When I re-entered the hotel it was nearly seven o'clock, and, as I did so, the porter at the revolving door in Princes Street touched his cap and informed me that the hairdresser desired to see me again.