E. on the one side of
that direction, or to the N.W. on the other, he knows the direction to
within eight points. Similarly he is sure to twelve points, if his
limits, on either hand, are E.N.E. and W.N.W. respectively.
C requires no further explanation.
Now, if a man can answer all three questions, A, B, to within eight
points of the compass, and C, he is four and a half times as well off as
if he could only answer A; as will be seen by the following
considerations. A knowledge of B in addition to A, is of only one-third
the use that it would be if C also were known.
1. Let P (fig. 1) be the point where the traveller finds himself at
fault, and let P D to be a distance within which the path certainly lies;
then the circle, E D F, somewhere cuts the path, and the traveller
starting from P must first go to D, and then make the entire circuit, D E
H F D, before he has exhausted his search. This distance of P D + D E H F
D = P D + 6 P D nearly, = 7 P D altogether, which gives the length of
road that the man must be prepared to travel over who can answer no other
than the question A. Of course, P D may cut the path, but I am speaking
of the extreme distance which the lost man may have to travel.
[Sketch as described above].
Supposing that question B can be answered as well as question A, an that
the direction of the line of road lies certainly within the points of the
compass, P S and P R.
Pages:
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417