“But we know that depression of the arch of the foot is brought about by standing for long periods.  Continuous pressure on a living structure weakens it, while intermittent pressure strengthens it; so the man who stands on his feet continuously develops a flat instep and a weak calf, while the professional dancer or runner acquires a high instep and a strong calf.  Now there are many occupations which involve prolonged standing and so induce the condition of flat foot:  waiters, hall-porters, hawkers, policemen, shop-walkers, salesmen, and station officials are examples.  But the waiter’s gait is characteristic—­a quick, shuffling walk which enables him to carry liquids without spilling them.  This man walks with a long, swinging stride; he is obviously not a waiter.  His dress and appearance in general exclude the idea of a hawker or even a hall-porter; he is a man of poor physique and so cannot be a policeman.  The shop-walker or salesman is accustomed to move in relatively confined spaces, and so acquires a short, brisk step, and his dress tends to rather exuberant smartness; the station official patrols long platforms, often at a rapid pace, and so tends to take long strides, while his dress is dignified and neat rather than florid.  The last-mentioned characteristics, you see, appear in the subject of our analysis; he agrees with the general description of a stationmaster.  But if we therefore conclude that he is a stationmaster, we fall into the time-honoured fallacy of the undistributed middle term—­the fallacy that haunts all brilliant guessers, including the detective, not only of romance, but too often also of real life.  All that the observed facts justify us in inferring is that this man is engaged in some mode of life that necessitates a good deal of standing; the rest is mere guess-work.”

“It’s wonderful,” said Polton, gazing at the now distant figure; “perfectly wonderful.  I should never have known he was a stationmaster.”  With this and a glance of deep admiration at his employer, he took his departure.

“You will also observe,” said Thorndyke, with a smile, “that a fortunate guess often brings more credit than a piece of sound reasoning with a less striking result.”

“Yes, that is unfortunately the case, and it is certainly true in the present instance.  Your reputation, as far as Polton is concerned, is now firmly established even if it was not before.  In his eyes you are a wizard from whom nothing is hidden.  But to return to these little pieces, as I must call them, for the lack of a better name.  I can form no hypothesis as to their use.  I seem to have no ‘departure,’ as the nautical phrase goes, from which to start an inquiry.  I haven’t even the material for guess-work.  Ought I to be able to arrive at any opinion on the subject?”

Thorndyke picked up one of the pieces, fingering it delicately and inspecting with a critical eye the flat base on which it stood, and reflected for a few moments.