It would be out of place here to give the working of the
little problem, but I append the rough numerical results in a table.
[Table as referred to above].
The epitome of the whole is this:--1. If you can only answer the question
A, you must seek for the lost path by the tedious circle plan; or, what
is the same, and a more manageable way of setting to work, by travelling
in an octagon, each side of which must be equal to four-fifths of P D.
(See fig. 2.)
[Fig. 2].
That is to say, look at your compass and start in any direction you
please; we will say to the south, as represented in the drawing. Travel
for a distance, P D; then supposing you have not crossed the path, turn
at right angles, and start afresh--we will suppose your present
direction to be west--travel for a distance 4/10 of P D, which will take
you to 1; then turn to the N.W. and travel for a distance 8/10 of P D,
which will take you to 2; then to the N. for a similar distance, which
will take you to 3; and so on, till the octagon has been completed. If
you know B to eight points, and not C, adopt the L M system; also, if you
know A and C, and B to within thirteen points (out of the sixteen that
form the semicircle), you may still adopt the L M system; but not
otherwise. A rough diagram scratched on the ground with a stick would
suffice to recall the above remarks to a traveller's recollection.
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