d in
that way and no other. It has been by unsound reasoning of this kind
that nine-tenths of the absurdities have been established on which
Taylor and Professor Smyth and their followers have established what may
be called the pyramid religion.

All we can fairly assume as probable from the evidence, in so far as
that evidence bears on the results of _a priori_ considerations, is that
the builders of the great pyramid preferred the Pole-star method to the
shadow method, as a means of determining the true position of latitude
30 deg. north. They seem to have applied this method with great skill
considering the means at their disposal, if we suppose that they took no
account whatever of the influence of refraction. If they took refraction
into account at all they considerably underrated its influence.

Piazzi Smyth's idea that they knew the _precise_ position of the
thirtieth parallel of latitude, and also the _precise_ position of the
parallel, where, owing to refraction, the Pole-star would appear to be
thirty degrees above the horizon, and deliberately set the base of the
pyramid between these limits (not exactly or nearly exactly half-way,
but somewhere between them), cannot be entertained for a moment by any
one not prepared to regard the whole history of the construction of the
pyramid as supernatural. My argument, let me note in passing, is not
intended for persons who take this particular view of the pyramid, a
view on which reasoning could not very well be brought to bear.

If the star method had been used to determine the position of the
parallel of 30 deg. north latitude, we may be certain it would be used also
to orient the building. Probably indeed the very structures (temporary,
of course) by which the final observations for the latitude had been
made, would remain available also for the orientation. These structures
would consist of uprights so placed that the line of sight along their
extremities (or along a tube perhaps borne aloft by them in a slanting
position) the Pole-star could be seen when immediately below or
immediately above the pole. Altogether the more convenient direction of
the two would be that towards the Pole-star when below the pole. The
extremities of these uprights, or the axis of the upraised tube, would
lie in a north-and-south line considerably inclined to the horizon,
because the pole itself being thirty degrees above the horizon, the
Pole-star, whatever star this might be, would