“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?”

“This much,” the doctor answered, “that on that very night, about half an hour before your—­shall we call it bicycle accident?—­the special train from Liverpool to London passed along that line.  You will remember the tragic occurrence which took place before she reached London, the murder of the man Hamilton Fynes.  If you read the report of the evidence at the inquest, you will notice the engine driver’s declaration that the only time on the whole journey when he travelled at less than forty miles an hour was when passing over the viaduct and before entering the tunnel which is plainly visible from my house.”

“This is very interesting,” the Prince remarked, “but it is not new.  We have known all this before.  Perhaps, though, some fresh thing has come into your mind connected with these happenings.  If so, please do not hesitate.  Let me hear it.”

“It is a fresh thing to me,” the doctor said,—­“fresh, in a sense, though all the time I have had an uneasy feeling at the back of my head.  I know now what it was which brought Inspector Jacks to see me.  I know now what it was he had at the back of his head concerning the man who met with a bicycle accident at this psychological moment.”

“Inspector Jacks is a very shrewd fellow,” the Prince said.  “I should not be in the least surprised if you were entirely right.”

The doctor moved restlessly in his chair.  His eyes remained on his companion’s face, as though fascinated.

“Can’t you understand,” he said, “that Inspector Jacks is on your track?  Rightly or wrongly, he believes that you had something to do with the murder on the train that night.”

The Prince nodded amiably.  He seemed in no way discomposed.

“I feel convinced,” he said, “that you are right.  I agree with you.  I believe that Inspector Jacks has had that idea for some little time now.”

The doctor gripped the sides of his chair and stared at this man who discussed a matter so terrible with calm and perfect ease.

“Yes, I have felt that more than once,” the Prince continued.  “My presence upon the spot at that precise moment with injuries which had to be explained somehow or other, was, without doubt, unfortunate.”

The two men sat for several moments without further speech.  The doctor’s features seemed to reflect something of the horror which he undoubtedly felt.  The Prince appeared only a trifle bored.

“So that is why,” the former exclaimed hoarsely, “I have been appointed your physician in chief!”

“I had given you the credit, my dear doctor,” the Prince said smoothly, “of having arrived at that decision some time ago.  To a man of your perceptions there can scarcely have been any question about it at all.  Besides, even Princes, you know, do not give fees of a thousand guineas for nothing.”