herlock Holmes has been an interest of mine for a long while. I have always enjoyed "The Game," the sleuthing pastime of dissecting the stories for clues to people and events either omitted purposely by Dr. Watson, or unknown by or kept from the good doctor. We get to play the great detective ourselves.
Illustration: Holmes and Watson, Silver Blaze
My Works on Sherlock Holmes
Why Sherlock Holmes Taps His Fingers: My definitive investigation into the reason, wholly unsuspected by Dr. Watson, that Holmes occasionally broke into spates of finger tapping. The explanation also reveals how Holmes produced a most impressive mental calculation--the speed of the train the pair were traveling on to solve the case of Silver Blaze (in the scene illustrated above).
Scenes That Didn't Make It #1: The text of a scene in a Sherlock Holmes story, submitted by Dr. Watson to his literary agent, Sir Arthur Conan Doyle, that was rejected by said agent. Keep in mind here that in the stories, a person is said to be "in a brown study" when they are in a state of absorption or abstraction. ("hey, I don't get it..." click here for spoiler)
Scenes That Didn't Make It #2: Another text of a scene in a Sherlock Holmes story, submitted by Dr. Watson to his literary agent, Sir Arthur Conan Doyle, that was once again rejected by said agent. ("hey, I don't get this one either.." click here for spoiler)
The Bicycle Deduction--A Tiresome Business: In "The Adventure of the Priory School" Sherlock Holmes deduces the direction that a bicycle had traveled from bicycle tracks left in the mud.
"This track, as you perceive, was made by a rider who was going from the direction of the school."
"Or towards it?"
"No, no, my dear Watson. The more deeply sunk impression is, of course, the hind wheel, upon which the weight rests. You perceive several places where it has passed across and obliterated the more shallow mark of the front one. It was undoubtedly heading away from the school."
Later readers have pointed out that in fact the rear wheel would obliterate the front wheel at crossings as Holmes says, but this would happen regardless of the direction that the bicycle was traveling. Conan Doyle admitted this error later, which only demonstrates that Watson misinterpreted Holmes on this point. It is indeed possible to determine a bicycle's direction of travel from its tracks, although Holmes apparently skirted the explanation to avoid the burden of a tiresome lecture to Watson.
A solution is described in a book of mathematical gems titled Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries (Dolciani Mathematical Expositions), by Joseph D. E. Konhauser, Dan Velleman, and Stan Wagon. I'm not going to reproduce their explanation, but if you click on the book name above (the Amazon.com link), click on the "Search in this book" link under the cover photo, and type in "Holmes", you can then click on the "Page 1" shortcut to read the problem and the "Page 64" shortcut to read the solution on pages 63-64. (You now have to log in to Amazon to read this second link.)
The idea is that the front wheel can turn to and fro somewhat independently of the rear wheel, but the direction of the rear wheel is always toward the base of the front wheel, and always the same distance from it. So the tangent from any point on the rear wheel track will always intersect the front wheel track, and in the direction of travel the distance to this intersection is always the same front-to-rear wheel distance. The solution in the book contains explanatory figures, something Holmes was perhaps unwilling to sketch for Watson. Given that the figures in the book were created using Bezier curves and symbolic differentiation in Mathematica, I can't say I blame him.
But of course I have my own theory of what Holmes was up to here, and as usual I haven't seen it documented. My premise is that the front wheel of a bicycle turns to and fro more when going uphill and is straighter when going downhill. The idea is that a rider slows down while struggling to go uphill, possibly even standing on the pedals, and therefore the front wheel swivels left and right more often than when going downhill, when you generally coast more and worry about speeding up. If the landscape was even slightly hilly where Holmes made his deduction, it would have been quite possible to tell where the bicycle was going uphill rather than downhill, thereby indicating the direction of travel. The "several places" Holmes points out where the rear wheel passes over the front wheel track could, it seems to me, be an indication of how much more the front wheel was swiveling at that spot. Then whichever way was uphill at that location was the direction the bicycle was traveling. Since the landscape is described as a moor, it seems more likely that it was a rise rather than a hill, demonstrating once again the keenness of Holmes' observational skills.
My brother, who wishes to remain nameless in this, has suggested another possibility--that a slipping rear tire might have thrown a bit of mud backward and thereby revealed the direction of travel of the bicycle. A promising lead.