“Well,” he said, “fifty pounds is not a great deal of money. Some unknown person—possibly, as you suggest, Mr. Jacks—is willing to give fifty pounds to discover your whereabouts. I, on the other hand, am giving a thousand guineas to keep you here as my guest. The odds do not seem even, do they?”

“Put in that way,” Dr. Whiles admitted, “they certainly do not. But there is another thing which has come into my mind.”

The Prince smiled and helped himself to one of the very excellent cigarettes which had been provided for the delectation of his visitor.

“Pray treat me with every confidence, Dr. Whiles,” he said. “Tell me exactly what is in your thoughts.”

“Well, then, I will,” the doctor answered. “Sitting here with nothing particular to do, one has plenty of leisure to think. For the first time, I have seriously tried to puzzle out what Mr. Inspector Jacks really wanted with me, why he came down to ask me about the person whom I treated for injuries resulting from a bicycle accident one Wednesday evening not long ago, why he took me up to London to see if I could identify that person in a very different guise. I have tried to put the pieces together and to ask myself what he meant by it all.”

“With so much time upon your hands, Dr. Whiles,” the Prince remarked, “you can scarcely fail to have arrived at some reasonable explanation.”

“I don’t know whether it is reasonable or not,” the doctor answered, “but the obvious explanation is getting on my nerves. There are two things which I cannot get away from. One is that I cannot for the life of me imagine your riding a bicycle twelve or fifteen miles north of London between eleven o’clock and midnight; and the other—”

“Come, the other?” the Prince remarked encouragingly.

“The other,” the doctor continued, “is the fact that within half a mile of my house runs the main London and North Western line.”

“The London and North Western Railway line,” the Prince repeated, “and what has that to do with it?”