ld be observing a
body at twice as great an elevation. The error would be, in fact, in
this case, about 1 mile 1512 yards.

It seems not at all unlikely that astronomers, so skilful and ingenious
as the builders of the pyramid manifestly were, would have employed both
methods. In that case they would certainly have obtained widely
discrepant results, rough as their means and methods must unquestionably
have been, compared with modern instruments and methods. The exact
determination from the shadow plan would have set them 1125 yards to the
north of the true latitude; while the exact determination from the
Pole-star method would have set them 1 mile 1512 yards south of the true
latitude. Whether they would thus have been led to detect the effect of
atmospheric refraction on celestial bodies high above the horizon may be
open to question. But certainly they would have recognized the action of
some cause or other, rendering one or other method, or both methods,
unsatisfactory If so, and we can scarcely doubt that this would actually
happen (for certainly they would recognize the theoretical justice of
both methods, and we can hardly imagine that having two available
methods, they would limit their operations to one method only), they
would scarcely see any better way of proceeding than to take a position
intermediate between the two which they had thus obtained. Such a
position would lie almost exactly 1072 yards south of true latitude 30 deg.
north.

Whether the architects of the pyramid of Cheops really proceeded in this
way or not, it is certain that they obtained a result corresponding so
well with this that if we assume they really did intend to set the base
of the pyramid in latitude 30 deg., we find it difficult to persuade
ourselves that they did not follow some such course as I have just
indicated--the coincidence is so close considering the nature of the
observations involved. According to Professor Piazzi Smyth, whose
observational labours in relation to the great pyramid are worthy of all
praise, the centre of the base of this pyramid lies about 1 mile 568
yards south of the thirtieth parallel of latitude. This is 944 yards
north of the position they would have deduced from the Pole-star method;
1 mile 1693 yards south of the position they would have deduced from the
shadow method; and 1256 yards south of the mean position between the two
last-named. The position of the base seems to prove beyond all
possibil