“Having now got our young man, without his ticket, into the carriage in which the elder man and the young woman are travelling, it is not difficult to imagine that a violent scene ensued.  It is possible that the pair were also Americans, which is the more probable as the man carried a weapon—­an unusual thing in England.  If our supposition of incipient mania is correct, the young man is likely to have assaulted the other.  As the upshot of the quarrel the elder man shot the intruder, and then made his escape from the carriage, taking the young lady with him.  We will suppose that all this happened very rapidly, and that the train was still going at so slow a pace that it was not difficult for them to leave it.  A woman might leave a train going at eight miles an hour.  As a matter of fact, we know that this woman did do so.

“And now we have to fit in the man in the smoking carriage.  Presuming that we have, up to this point, reconstructed the tragedy correctly, we shall find nothing in this other man to cause us to reconsider our conclusions.  According to my theory, this man saw the young fellow cross from one train to the other, saw him open the door, heard the pistol-shot, saw the two fugitives spring out on to the line, realized that murder had been done, and sprang out himself in pursuit.  Why he has never been heard of since—­whether he met his own death in the pursuit, or whether, as is more likely, he was made to realize that it was not a case for his interference—­is a detail which we have at present no means of explaining.  I acknowledge that there are some difficulties in the way.  At first sight, it might seem improbable that at such a moment a murderer would burden himself in his flight with a brown leather bag.  My answer is that he was well aware that if the bag were found his identity would be established.  It was absolutely necessary for him to take it with him.  My theory stands or falls upon one point, and I call upon the railway company to make strict inquiry as to whether a ticket was found unclaimed in the local train through Harrow and King’s Langley upon the 18th of March.  If such a ticket were found my case is proved.  If not, my theory may still be the correct one, for it is conceivable either that he travelled without a ticket or that his ticket was lost.”

To this elaborate and plausible hypothesis the answer of the police and of the company was, first, that no such ticket was found; secondly, that the slow train would never run parallel to the express; and, thirdly, that the local train had been stationary in King’s Langley Station when the express, going at fifty miles an hour, had flashed past it.  So perished the only satisfying explanation, and five years have elapsed without supplying a new one.  Now, at last, there comes a statement which covers all the facts, and which must be regarded as authentic.  It took the shape of a letter dated from New York, and addressed to the same criminal investigator whose theory I have quoted.  It is given here in extenso, with the exception of the two opening paragraphs, which are personal in their nature: