\section{Bicycle tracks}

C. Dennis Thron has called attention to the following passage from
{\em The Adventure of the Priory School}, by Sir Arthur Conan Doyle:
\begin{quotation}
`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.'

\end{quotation}

\begin{problems}
\item
Discuss this passage.  Does Holmes know what he's talking about?
%
% January 2006:  Removing some of the `fluff'.  PGD
%
%\item
%Try to come up with a method for telling which way a bike has gone
%by looking at the track it has left.
%There are all kinds of possibilities
%here.
%Which methods do you honestly think will work, and under what
%conditions?
%For example, does your method only work if the bike has passed through a
%patch of wet cement?
%Would it work for tracks on the beach?
%Tracks on a patch of dry sidewalk between puddles?
%Tracks through short, dewy grass?
%Tracks along a thirty-foot length of brown package-wrapping paper,
%made by a bike whose tires have been carefully coated with mud, and which
%has been just ridden long enough before reaching the paper
%so that the tracks are not appreciably
%darker at one end of the paper than the other?
\item
Try to determine the direction of travel for the idealized bike tracks
in Figure \ref{bike}.
\fg{bike}{Which way did the bicycle go?}
\item
Try to sketch some idealized bicycle tracks of your own.
You don't need a computer for this;
just an idea of what the relationship is between the track of the
front wheel and the track of the back wheel.
How good do you think your simulated tracks are?
\item
Go out and observe some bicycle tracks in the wild.
Can you tell what way the bike was going?
Keep your eye out for bike tracks, and practice until
you can determine the direction of travel quickly and accurately.
%\item
%Tell your friends about this problem.
%Don't give them the answers; just the questions.
%Let them think for themselves.
%Let them stew a little.
%See what they come up with.
%You can give them a little help, if need be,
%once they've spent enough time thinking about it for themselves
%to appreciate the problem.
%Make sure that they, too, finally master this useful trick
%of bike direction-finding.
\end{problems}
