Simanaitis Says
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HOLMES PEDALS HIMSELF INTO A CORNER
HOW DID HOLMES deduce a cyclist’s direction of travel? This continues yesterday’s discussion here, ”Pedaling It All Over (Victorian) Town. ”
In “The Adventure of the Priory School,” Holmes says to Watson, “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.”
Or perhaps not.
Holmes and Watson know for sure which direction this particular cyclist is traveling. (Note the pair hiding behind the rock.) But what about in general? Image by Sidney Paget from the Strand Magazine, 1904.
“Which Way Did The Bicycle Travel?” is an essay in The New Annotated Sherlock Holmes: The Complete Short Stories (2 Vol. Set)
Sir Arthur Ignatius Conan Doyle, 1859–1930, Scottish writer, physician and literary agent for Dr. John H. Watson’s chronicles of consulting detective Sherlock Holmes. Photograph by Walter Benington, 1914.
Even Watson’s literary agent Arthur Conan Doyle gets an oar in the water, er… tyre on the ground: “I had so many remonstrances upon this point, varying from pity to anger, that I took out my bicycle and tried.” He found the tracks were the same, whichever way his cycle was heading.
However, being a good literary agent, Conan Doyle strove for damage control: “On the other hand the real solution was much simpler, for on an undulating moor the wheels make a much deeper impression uphill and more shallow one downhill, so Holmes was justified of his wisdom after all.”
Really?
At times, there is an easy solution, but it depends on a specific type of tire. The first pneumatic tires were slicks, until symmetric tread patterns were introduced to improve grip. Then companies such as Dunlop designed their pattern with advertising in mind.
Note the DUNLOP TYRE tread pattern. No problem of directionality here.
However, in “The Adventure of the Priory School,” Holmes had no such aid. He examines a bicycle by match light and Watson says, “I heard him chuckle as the light fell upon a patched Dunlop tyre.”
Holmes and Watson examine a bicycle tire in “The Adventure of the Priory School.” Image by Sidney Paget, Strand Magazine, 1904.
The accompanying Sidney Paget illustration shows the tire in question is an early treadless version. Its patched Dunlop nature determines bicycle ownership, but nothing more.
Indeed, “Which Way Did The Bicycle Travel?” offers an assessment in 2005 that is coincident with that appearing in a “Wordplay” column of The New York Times, December 15, 2014. In the latter, Gary Antonick queries ”Was Sherlock Holmes Correct?”
Briefly, as literary agent Conan Doyle admits, he was not. However, one of Antonick’s respondents offers a means of deducing the bicycle’s direction of travel by its tracks alone:
“We can distinguish the hind wheel from the front one by the average curvatures of the two tracks with the former being higher than the latter. These alone do not provide clues to the heading of the bicycle. However, the distance between the centers of the wheels is bounded by a small interval, depending on the angle of the front steering column makes with the vertical.”
Tire tracks in the snow. This and the following image from “Was Sherlock Holmes Correct?” The New York Times, December 15, 2014.
“So,” the argument continues, “for an arbitrary point of the hind wheel track, there should always be a point on the front wheel track on the tangent line emanating from that former point having the distance between them falling in the aforementioned interval. There is only a very small probability that the tracks are so symmetric so as for either direction to satisfy this condition.”
“In our case,” the respondent concludes, “the bicycle was therefore moving to the left.” Note the tangents from the rear wheel track and the lengths to their interceptions with the front wheel track.
Tangents to curves are part of differential calculus, and there’s also a wonderful video of this technique at Mathematical Impressions: Bicycle Tracks, by George Hart.
Respecting the efforts of Watson’s literary agent Conan Doyle, and the veracity of The New York Times, Mr. Antonick, his respondent and Mr. Hart, I confess I still find Holmes’ technique an elegant one. A pity it doesn’t work. ds
© Dennis Simanaitis, SimanatisSays.com, 2016
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