such slant stones corresponding to the
size of the passage elsewhere, so as to make the four surfaces of the
passage perfectly plane from its greatest depth below the base of the
pyramid to its aperture, close to the surface to be formed eventually by
the casing stones of the pyramid itself.

Now, in this part of his work, the astronomical architect could scarcely
fail to take into account the circumstance that the inclined passage,
however convenient as bearing upon a bright star near the pole when that
star was due north, was, nevertheless, not coincident in direction with
the true polar axis of the celestial sphere. I cannot but think he would
in some way mark the position of their true polar axis. And the natural
way of marking it would be to indicate where the passage of his
Pole-star _above_ the pole ceased to be visible through the slant tube.
In other words he would mark where a line from the middle of the lowest
face of the inclined passage to the middle of the upper edge of the
mouth was inclined by twice the angle 3 deg. 42' to the axis of the passage.
To an eye placed on the optical axis of the passage, at this distance
from the mouth the middle of the upper edge of the mouth would (_quam
proxime_) show the place of the true pole of the heavens. It certainly
is a singular coincidence that at the part of the tube where this
condition would be fulfilled, there is a peculiarity in the construction
of the entrance passage, which has been indeed otherwise explained, but
I shall leave the reader to determine whether the other explanation is
altogether a likely one. The feature is described by Smyth as "a most
singular portion of the passage--viz., a place where two adjacent
wall-joints, similar, too, on either side of the passage, were vertical
or nearly so; while every other wall-joint, both above and below, was
_rectangular_ to the length of the passage, and, therefore, largely
_inclined_ to the vertical." Now I take the mean of Smyth's
determinations of the transverse height of the entrance passage as 47.23
inches (the extreme values are 47.14 and 47.32), and I find that, from a
point on the floor of the entrance passage, this transverse height would
subtend an angle of 7 deg. 24' (the range of Alpha Draconis in altitude when
on the meridian) at a distance 363.65 inches from the transverse mouth
of the passage. Taking this distance from Smyth's scale in Plate xvii.
of his work on the pyramid ("Our Inheritance i