“So they did. But a careful scrutiny of the photographs convinced my friend that this was not a single series of footprints, made by one man, but two series, made by two different men. The first series started from the bank and ended at the gate. The second series started from the gate and ended on the heath.”

  “Then the footprints were not all alike?”

  “That,” replied Thorndyke, “depends on what we mean by ‘alike.’ If you had taken any one footprint from any part of the whole series and compared it with any other corresponding footprint – right or left – in any other part of the series, you would have said that they were undoubtedly prints of the same foot.”

  “Do I understand you to mean that every footprint in the whole series was exactly like every other footprint of the same side?”

  “Yes. Every right footprint was exactly like every other right footprint, and the same with the left. That is, considered as individual footprints.”

  “Then I don’t see how your friend could have made out that the whole series of footprints, all indistinguishably alike, consisted of two different series, made by two different men.”

  Thorndyke chuckled. “It is quite a subtle point,” he said, “and yet perfectly simple. I am a little surprised that it had not occurred to Mr White, who seems to have been an acute and ingenious man. You see, the difference was not between the individual footprints but between certain periodic characters in the two series.”

  “I don’t think I quite follow you,” said Pottermack.

  “Well, let us follow my legal friend’s procedure. I have told you that his object in examining these photographs was to ascertain whether footprints in series present any periodic or recurrent characters that might be of evidential importance. Now, a glance at these photographs showed him that these footprints must almost certainly present at least one such character. They were the prints of shoes with rubber soles of a highly distinctive pattern and circular rubber heels. Now, Mr Pottermack, why does a man wear circular rubber heels?”

  “Usually, I suppose, because if he wears ordinary leather heels he wears them down all on one side.”

  “And how do the circular heels help him?”

  “In the case of circular heels,” Pottermack replied promptly, “the wear does not occur all at one point, but is distributed round the whole circumf –”

  He stopped abruptly with his mouth slightly open and looked at Thorndyke.

  “Exactly,” said the latter, “you see the point. A circular heel is secured to the shoe by a single, central screw. But it is not a complete fixture. As the wearer walks, the oblique impact as it meets the ground causes it to creep round; very slowly when the heel is new and tightly screwed on, more rapidly as it wears thinner and the central screw-hole wears larger. Of course, my friend knew this, but he now had an opportunity of making his knowledge more exact and settling certain doubtful points as to rapidity and direction of rotation. Accordingly he proceeded, with the ribbon of photographs and the ordnance map before him, to follow the track methodically, noting down the distances and the rate and direction of rotation of each heel.

  “His industry was rewarded and justified within the first dozen observations, for it brought to light a fact of considerable importance, though it does not happen to be relevant to our case. He found that both heels revolved in the same direction – clockwise – though, of course, since they were in what we may call ‘looking-glass’ relation, they ought to have revolved in opposite directions.”

  “Yes,” said Pottermack, “it is curious, but I don’t see what its importance is.”

  “Its importance in an evidential sense,” replied Thorndyke, “is this: the anomaly of rotation was evidently not due to the shoes but to some peculiarity in the gait of the wearer. The same shoes on the feet of another person would almost certainly have behaved differently. Hence the character of the rotation might become a test point in a question of personal identity. However, that is by the way. What concerns us is that my friend established the fact that both heels were rotating quite regularly and rather rapidly. Each of them made a complete rotation in about a hundred and fifty yards.

  “My friend, however, did not accept this result as final, but continued his observations to ascertain if this regular rate of rotation was maintained along the whole of the track. So he went on methodically until he had examined nearly half of the ribbon. And then a most astonishing thing happened. Both the heels suddenly ceased to revolve. They stopped dead, and both at the same place.

  “Now, the thing being apparently an impossibility, my friend thought that he must have made some error of observation. Accordingly he went over this part of the ribbon again. But the same result emerged. Then, abandoning his measurements, he went rapidly along the whole remaining length of the ribbon to the very end, but still with the same result. Throughout the whole of that distance, neither heel showed the slightest sign of rotation. So it came to this: the photographs from number 1 to number 92 showed both heels rotating regularly about once in every hundred and fifty yards; from number 93 to number 197 they showed the heels completely stationary.

  “My friend was profoundly puzzled. On the showing of the photographs, the heels of this man’s shoes, which had been turning quite freely and regularly as he walked, had, in an instant, become immovably fixed. And both at the same moment. He tried to think of some possible explanation, but he could think of none. The thing was utterly incomprehensible. Then he turned to the ordnance map to see if anything in the environment could throw any light on the mystery. Searching along the row of dots for number 93 he at length found it – exactly opposite the gate in the wall.

  “This was a decidedly startling discovery. It was impossible to ignore the coincidence. The position was that this man’s heels had been turning freely until he reached the gate; after passing the gate his heels had become permanently fixed. The obvious suggestion was that this mysterious change in the condition of the heels was in some way connected with the gate. But what could be the nature of the connection? And what could be the nature of the change in the shoes?

  “To the first question the suggested answer was that the man might have gone in at the gate; and while he was inside, something might have happened to his shoes which caused the heels to become fixed. But still the difficulty of the shoes remained. What could cause revolving heels to become fixed? To this question my friend could find no answer. The possibility that the heels had been taken off and screwed on again more tightly would not have explained their complete immobility; and, in fact, they had not been. The screws showed plainly in many of the photographs, and the position of their slots in all was identical. The footprints in the second series – those past the gate – were in every respect the exact counterparts of those in the first series – those from the town to the gate. The only condition that my friend could think of as agreeing with the physical facts was that which would have occurred if the prints in the second series had been made, not by the shoes themselves but by some sort of reproductions of them, such as plaster casts or casts in some other material.”

  “That sounds rather a far-fetched suggestion,” remarked Pottermack.

  “It does,” Thorndyke agreed; “and in fact my friend did not entertain it seriously at first. He merely noted that the appearances were exactly such as would be produced by making impressions with casts; in which, of course, since the soles and heels would be all in one piece, no movement of the heels would be possible. But, Mr Pottermack, we must bear in mind whose footprints these were. They were the footprints of a man who had disappeared in the most mysterious and unaccountable manner. The whole affair was highly abnormal. No reasonable explanation was possible either of the disappearance or of the singular character of the footprints. But in the absence of a reasonable explanation, it is admissible to consider an unreasonable one, if it agrees with the known facts. The cast theory did agree with the physical facts, and, on reflection, my friend decided to adopt it as a working hypothesis and see what came of it.

  “Now, if the footprints from the gate to the heath were counterfeits of Black’s footprints, made with shoes the soles and heels of which were mechanical reproductions of the soles and heels of Black’s shoes, it followed that the wearer of these shoes was not Black, but some other person, in which case Black’s own footprints ended at the gate. This at once got rid of the most unaccountable feature of the disappearance – the nocturnal flight out into the country; for if his footprints ended at the gate he must have gone in. But there was nothing at all abnormal about his calling at a house quite close to, and, in fact, almost in the town, from which he could have easily gone to keep his appointment with his creditor. Thus far, the hypothesis seemed to simplify matters.

  “But it not only followed that Black must have gone in at the gate, it followed that he could never have come out. For the footprints that went on were not his, and there were no footprints going back towards the town.”

  “He might have come out another way; by the front door, for instance,” Pottermack suggested.

  “So he might,” Thorndyke agreed, “under different circumstances. But the counterfeit footprints showed that he did not. For if the continuing footprints were counterfeits, made by some other person, what could have been their purpose? Clearly their purpose could have been no other than that of concealing the fact that Black had gone in at the gate. But if he had come out of the premises, there could have been no reason for concealing the fact that he had gone in.

  “If, however, he did not come out, then, obviously, he remained inside. But in what condition? Was he alive and in hiding? Evidently not. In the first place, he had no occasion to hide, since he could have gone back to the bank and replaced the money. But the conclusive evidence that he was not in hiding was the counterfeit footprints. No mechanical reproduction of the shoes would have been necessary if Black had been there. Black’s own shoes would have been borrowed and used to make the false footprints. But, obviously, the whole set of circumstances was against the supposition that he could be alive. If the evidence was accepted that he went in and was never seen again, the most obvious inference was that he had been made away with. And this inference was strongly supported by the troublesome and elaborate measures that had been taken to conceal the fact that he had gone in at the gate. Accordingly my friend adopted the view, provisionally, that Mr Black had been made away with by some person inside the gate, hereinafter referred to as the tenant.

  “But the adoption of this view at once raised two questions. First, how came it to be necessary to make reproductions of the dead man’s shoes? Why did not the tenant simply take the shoes off the corpse and put them on his own feet? If he had done this, if he had made the false footprints with the dead man’s own shoes, the illusion would have been perfect. No detection would have been possible. Why had he not done it? The shoes themselves could have presented no difficulty. They were large shoes, and large shoes can, with suitable preparation, be worn even by a small man.

  “The answer that suggested itself was that, for some reason, the shoes were not available; that by the time that the necessity for the false footprints had been perceived, the shoes had in some way become inaccessible. But how could they have become inaccessible? Could the body have been buried? Apparently not. For it would have been much less trouble to dig up a body and recover the shoes than to make a pair of reproductions of them. Could it have been burned? Evidently not. Apart from the extreme difficulty of the operation, there had not been time. The false footprints were made on the very night of the disappearance, since they were traced by the police the next morning.

  “The possibility that the body might have been conveyed away off the premises had to be borne in mind. But it was highly improbable, for many obvious reasons; and it did not dispose of the difficulty. For it would surely have been easier and quicker to go – at night – and retrieve the shoes than to make the counterfeits. Indeed, when my friend considered the immense labour that the making of those reproductions must have entailed, to say nothing of the great expenditure of time, just when every moment was precious, he felt that nothing but the absolute physical impossibility of getting access to the original shoes would explain their having been made.

  “Now, what conditions would have rendered those shoes totally inaccessible? Remember the circumstances. Inasmuch as the sham footprints were found on the following morning, they must have been made that night. But before they could be made, the counterfeit soles must have been made, and the making of them must have been a long and tedious piece of work. It therefore followed that the tenant must have begun work on them almost immediately after the death of Mr Black. From this it followed that the body of Mr Black must have been immediately disposed of in such a way as at once to become inaccessible.

  “What methods of disposing of a body would fulfil these conditions? My friend could think of only three, all very much alike: the dropping of the body down a dene-hole, or into a cess-pit, or into a disused well. Any of these methods would at once put the body completely out of reach. And all these methods had a special probability in this particular case. The great difficulty that confronts the would-be murderer is the disposal of the body. Hence the knowledge that there was available a means of immediately, securely, and permanently hiding the body might be the determining factor of the murder. Accordingly, my friend was strongly inclined to assume that one of these three methods was the one actually employed.

  “As to the particular method, the question was of no great importance. Still, my friend considered it. The idea of a dene-hole was at once excluded on geological grounds. Dene-holes are peculiar to the chalk. But this was not a chalk district.

  “The cess-pit was possible but not very probable; for if in use, it would be subject to periodical clearance, which would make it quite unsuitable as a hiding-place, while cess-pits which become superseded by drainage are usually filled in and definitely covered up. A well, on the other hand, is often kept open for occasional and special use after the laying on of a pipe service.”

  “Your friend,” remarked Pottermack, “seems to have taken it for granted that a well actually existed.”

  “Not entirely,” said Thorndyke. “He looked up an older map and found that this house had formerly been a farmhouse, so that it must once have had a well; and as it now fronts on a road in which other houses have been built and which is virtually a street, it is pretty certainly connected with the water-service. So that it was practically certain that there was a well, and that well would almost certainly be out of use.

  “And now, having deduced a reason why the counterfeit soles should have been necessary, he had to consider another question. If the original shoes were inaccessible, how could it have been possible to make the counterfeits, which were, apparently, casts of the originals? At first it looked like an impossibility. But a little reflection showed that the footprints themselves supplied the answer. Mr Black’s own footprints on the path were such perfect impressions that a little good plaster poured into selected samples of them would have furnished casts which would have been exact reproductions of the soles and heels of Mr Black’s shoes. Possibly there were equally good footprints inside the premises, but that is of no consequence. Those on the footpath would have answered the purpose perfectly.

  “I may say that my friend tested this conclusion and got some slight confirmation. For if the false footprints were impressions of reproductions, not of the original shoes but of some other footprints, one would expect to find the accidental characters of those particular footprints as well as those of the shoes which produced them. And this appeared to be the case. In one of the points of the star on the left heel a small particle of earth seemed to have adhered. This was not to be found in Black’s own footprints, but it was visible in all the footprints of the second series, from the gate to the heath. And the fact that it never changed along the whole series suggested that it was really a part of the cast, due to an imperfection in the footprint from which it was made.

  “That brings us to an end of my friend’s train of reasoning in regard to the actual events connected with Mr Black’s disappearance. His conclusions were, you observe, that Mr Black went in at the gate; that he was thereafter made away with by some person inside whom we have called the tenant; that his body was deposited by the tenant in some inaccessible place, probably a disused well; and that the tenant then made a set of false footprints to disguise the fact that Mr Black had gone in at the gate.

  “The questions that remained to be considered were: first, What could be the tenant’s motive for making away with Mr Black? and second, Who was the tenant? But before we deal with his inferences on those points, I should like to hear any observations which you may have to make on what I have told you.”

  Mr Pottermack pondered awhile on what he had heard, and as he reflected, he laid a disparaging hand on the teapot.

  “It is rather cool,” he remarked apologetically; “but such as it is, can I give you another cup?”

  “Prolonged exposition,” Thorndyke replied with a smile, “is apt to have a cooling effect upon tea. But it also creates a demand for liquid refreshment. Thank you, I think another cup would cheer, and we can dispense with the inebriation.”

  Mr Pottermack refilled both the cups and put down the teapot, still cogitating profoundly.

  Chapter Eighteen

  The Sundial has the Last Word

  “Your legal friend,” Mr Pottermack said at length, “must be a man of extraordinary subtlety and ingenuity if he deduced all that you have told me from the mere peculiarities of a set of footprints, and only photographs at that. But what strikes me about it is that his reconstruction was, after all, pure speculation. There were too many ‘ifs.’”

  “But, my dear Mr Pottermack,” exclaimed Thorndyke, “it was all ‘ifs.’ The whole train of reasoning was on the plane of hypothesis, pure and simple. He did not, at this stage, assume that it was actually true, but merely true conditionally on the facts being what they appeared to be. But what does a scientific man do when he sets up a working hypothesis? He deduces from it its consequences, and he continues to pursue these so long as they are consistent with the facts known to him. Sooner or later, this process brings him either to an impossibility or a contradiction – in which case he abandons the hypothesis – or to a question of fact which is capable of being settled conclusively, yes or no.