e of this adjustable square, and this will also be of
service to us in measuring heights of objects, as well as directing our
course. It is now nine o'clock, and you will see that our pole (A)
throws a shadow to the southwest. Supposing now, we direct the first leg
of our journey to that large tree (C), to the west of us. If, now, we
put one leg (D) of our rule along the shadow line, and the other leg (E)
along the sight of the line (F), which goes to the tree, we shall find
that the distance across between the ends of the bevel square is just
two feet. It happens in this case that the tree (C) is due west from our
observation point; so we have at nine o'clock each morning a means
whereby we can always determine the true east and west."

"But supposing we lose our reckoning during the day, on account of
cloudy weather, or by going through the forest, where we cannot make
observations?"

[Illustration: _Fig. 6. SIGHTING THE DIRECTION_]

"We could, probably, travel an entire day in one general direction,
without being more than a few miles out of our course, north or south,
and our direction immediately made out the next day."

"Wouldn't it be a good idea to prepare angles at different times of the
day, in the forenoon and in the afternoon?"

"That is the proper thing to do, so as to enable you to make
observations from the angles at all times. A chart could then be made
from that which would show at a glance what the value of each angle is."

"We shall certainly have to do that; but what interests me as much is,
to know how far we have traveled. Can we also tell that by the sun?"

"Yes; but to do so will depend on the accuracy of the observation. For
the present, with only a single instrument, the bevel square, we must be
content to make our calculations exactly at midday, when the shadow
points due south. Or, in the northern hemisphere, when the shadow points
due north. I want you, in the meantime, to think over that problem, as
it is a very interesting one, and we will take it up when we are not so
tired."

CHAPTER IV

THE DISAPPEARANCE OF THE YAKS

It was a relief to get on fairly even ground again, where it would not
be necessary to make turns and twists around all sorts of obstructions,
to say nothing of ravines and water courses. On the evening of the
fifteenth day, calculations showed that they were halfway back from the
point farthest west, but they still had no knowledge of their distance
fro