et due west, for he is raised above the horizon by atmospheric
refraction, before he has really reached it in the morning, and he
remains raised above it after he has really passed below--understanding
the word "really" to relate to his actual geometrical direction. Thus,
at true spring and autumn, the sun rises slightly to the north of east,
and sets slightly to the north of west. The atmospheric refraction is
indeed so marked, as respects these parts of the sun's apparent course,
that it must have been quickly recognized. Probably, however, it would
be regarded as a peculiarity only affecting the sun when close to the
horizon, and would be (correctly) associated with his apparent change of
shape when so situated. Astronomers would be prevented in this way from
using the sun's horizontal position at any season to guide them with
respect to the cardinal points, but they would still consider the sun,
when raised high above the horizon, as a suitable astronomical index (so
to speak), and would have no idea that even at a height of sixty degrees
above the horizon, or seen as in direction D A, Fig. 1, he is seen
appreciably above his true position.

Adopting this method--the shadow method--to fix the latitude of the
pyramid's base, they would conceive the sun was sixty degrees above the
horizon at noon, at true spring or autumn, when in reality he was
somewhat below that elevation. Or, in other words, they would conceive
they were in latitude 30 deg. north, when in reality they were farther north
(the mid-day sun at any season sinking lower and lower as we travel
farther and farther north). The actual amount by which, supposing their
observations exact, they would thus set this station north of its proper
position, would depend on the refractive qualities of the air in Egypt.
But although there is some slight difference in this respect between
Egypt and Greenwich, it is but small; and we can determine from the
Greenwich refraction tables, within a very slight limit of error, the
amount by which the architects of the great pyramid would have set the
centre or the base north of latitude 30 deg., if they had trusted solely to
the shadow method. The distance would have been as nearly as possible
1125 yards, or say three furlongs.

Now, if they followed the other method, observing the stars around the
pole, in order to determine the elevation of the true pole of the
heavens, they would be in a similar way exposed to error arisin