I glanced back as we reached the entrance to the footpath. The rider had turned in the saddle and was staring back at us. “We seem to have aroused his curiosity,” I remarked.

“Indeed,” returned Holmes. “He appeared uncommonly keen to send us off in another direction, although whether he had any purpose in so doing, or is simply ill-mannered, we can only speculate.”

The pathway through the woods rose gently at first, then levelled off, meandering among the thickly growing bushes and trees, but never far from the gurgling stream on our right. The canopy of foliage overhead was in some places very dense and cast the wood into gloomy shade, but elsewhere the sunshine pierced the gloom and sent shafts of light down to the woodland floor. Presently, a side path branched off to the right, and passing by stepping stones across the stream, vanished among the undergrowth beyond.

“That must be the path to the Topley Grange Estate,” remarked Holmes.

Ahead of us, to the right, I spied the shimmer of water through the trees, and a moment later we came upon the boggy, reed-girt margin of the pool. In shape it was long and narrow, being scarcely more than twenty-five feet across, but a good sixty or seventy in length. At the other end, the pool was fringed by willow trees, their slender branches dipping into the water, but at the lower end, on the side where we stood, was a flat open area of damp, mossy turf, and on the other side a tangle of brambles and briars. Just by the patch of turf, another side path went off to the left and climbed steeply up the wooded valley side.

“This is evidently the way from Oakbrook Hall,” said Holmes, looking up the steeply sloping path. At the top of the hill, which marked the limit of the wood, a bright rectangle of sunlight indicated where the path emerged from the shade of the trees into open country.

“It does not appear a very well-used path,” I remarked.

“Why so?”

“The space where the grass is worn away on that path is considerably narrower than on this one,” I replied. “The obvious conclusion is that fewer feet have passed upon that one than upon this.”

“There, I regret, you fall into a popular error,” observed my friend. “In fact, it makes little difference to the width of a path whether it is lightly or heavily used.”

“You speak as if you have made a special study of the matter,” said I with a chuckle.

“As a matter of fact I have,” said he, to my very great surprise.

“You are surely in jest!”

“Not at all. During my second year at college, I became interested in this very question, as a result of certain observations I had made of the pathways that were most frequented by the undergraduates. It is one of those many matters to which the answer has always been assumed without verification and, as it turns out, assumed quite erroneously. The history of human knowledge is littered with such false assumptions. You will no doubt recall, for instance, that before Galileo, it was universally believed that if two objects identical in all respects save their weight are dropped from a height, the heavier of the two will strike the ground first. That esteemed gentleman alone considered the matter worth verifying. He therefore performed the experiment and discovered that the universal belief was quite mistaken: the two objects strike the ground at precisely the same moment. It is, as I remarked the other day, always worthwhile verifying universally held opinions for oneself. My interest in footpaths having been aroused, I made many score of measurements and calculations, and reached certain very definite conclusions. Among the chief of these is that the amount of human traffic on a footpath has no significant effect on the width of that path, and that a footpath’s width is in fact almost entirely dependent upon the moisture of the ground. To put it simply, if the ground is wet, the path will become muddy, and in stepping to the side to avoid the mud, those who use it will widen it accordingly. The wetter the ground, the wider the path, even if it is used by only a few people each day. It is the same with pathways used by animals: I have seen sheep tracks in dry heathland, which were rutted almost a foot deep by constant use, but were scarcely three or four inches in width. The average width of the paths in the university grounds, incidentally, was exactly nine and five-eighths inches.”

“I cannot but admire your thoroughness and precision,” I remarked with a chuckle. “How was your research received?”

“Alas! I regret to say that my treatise, Upon the Properties of Footpaths Occurring Naturally in Various Terrain, with some notes upon the effects of seasonal variation, failed to arouse any great enthusiasm among the college tutors.”

“Perhaps,” I ventured, “they considered that however intellectually sound the research, it nevertheless constituted somewhat superfluous knowledge.”

“If so, they were in error, and seriously so. We can never tell what use the future will make of our present research. Very often, it is the work that is highly praised upon publication and which satisfies current expectations that ultimately proves of no worth. The work that is done for its own sake, on the other hand, without any consideration of the prevailing fashion, and without, perhaps, any immediately obvious application, generally proves in the end to be of most benefit to mankind. Should anyone wish to avail themselves of the fruit of my labours, they will find it handsomely bound in black buckram in the college library – row ‘J’, as I recall.”

All the time he had been speaking, he had been pacing up and down the margin of the pool, peering this way and that, as if his aim was to view the scene of the old tragedy from every possible angle. Then, breaking off a long stick from a fallen tree, he took himself across the stepping stones and through a tangle of brambles and briars to the other side of the pool. There the brambles were growing close to the water’s edge, their branches trailing into the pool in several places, and I watched as he pushed his way through this undergrowth and made his way along the bank, poking with his stick into the depths of the water as he went. After a while he paused, broke off a small piece from the end of his stick and tossed it into the pool, then watched closely as it drifted slowly upon the surface of the water. He repeated this experiment several times, with increasingly larger pieces of wood, throwing them further out into the centre of the pool each time. At length, evidently satisfied with these experiments, he returned to where I was sitting on the fallen tree.

“There are no brambles on this side of the water, and nor does it appear that there ever have been,” said he. “The ground here is probably too wet for them. Therefore, anyone collecting blackberries would have to do so on the far side, where the ground is firmer and the bushes are growing thickly. The brambles are very close to the water’s edge there, however, leaving little space for anyone to stand, but of course they may not have been quite so close three years ago.”

“Perhaps the narrowness of the gap between the brambles and the water is what caused the girl to slip,” I suggested.

“Perhaps so,” said he in an abstracted tone. For some time he stood in silence, his chin in his hand and his brow drawn down in a frown of concentration as he stared across the water at the tangled undergrowth on the far side, as if he would penetrate the veil of time and see for himself exactly what had occurred in that fateful spot three years ago.

The wood was very quiet, the only sound the constant soft splash of the water as it left the pool and spilled over the stones in the stream below. All at once, however, there came the robust voice of a man singing, somewhere higher up the wood. There was a curious, nasal quality to the voice, and its accent was undoubtedly a rustic one. As its owner approached, I caught some of the words of the song, the subject of which appeared to be “going to the fair”. Holmes looked round in surprise as a large, powerfully built man came into view higher up the path, at the far end of the pool, clapping his hands as he walked along. He was a young man, little more than two-and-twenty at the outside, I judged, and he was clad in a coarse, loose-fitting shirt, knee breeches and leather gaiters. His face was ruddy and shining, and upon it was an expression of openness and good-natured simplicity.