d be opened out from the slant
tunnel. The vertical boring, which need not be wider than necessary to
allow a plumb-line to be suspended down it, would enable the architects
to determine the point vertically below the point of suspension. The
slant tunnel would give the direction of the true north, either from
that point or from a point at some known small distance east or west of
that point.[19] Thus, a line from some ascertained point near the mouth
of the vertical boring to the mouth of the slant tunnel would lie due
north and south, and serve as the required guide for the orientation of
the pyramid's base. If this base extended beyond the opening of the
slant tunnel, then, by continuing this tunnelling through the base tiers
of the pyramid, the means would be obtained of correcting the
orientation.

This, I say, would be the course naturally suggested to astronomical
architects who had determined the latitude in the manner described
above. It may even be described as the only very accurate method
available before the telescope had been invented. So that if the
accuracy of the orientation appears to be greater than could be obtained
by the shadow method, the natural inference, even in the absence of
corroborative evidence, would be that the stellar method, and no other,
had been employed. Now, in 1779, Nouet, by refined observations, found
the error of orientation measured by less than 20 minutes of arc,
corresponding roughly to a displacement of the corners by about 37-1/2
inches from their true position, as supposed to be determined from the
centre; or to a displacement of a southern corner by 53 inches on an
east and west line from a point due south of the corresponding northern
corner. This error, for a base length of 9140 inches, would not be
serious, being only one inch in about five yards (when estimated in the
second way). Yet the result is not quite worthy of the praise given to
it by Professor Smyth. He himself, however, by much more exact
observations, with an excellent altazimuth, reduced the alleged error
from 20 minutes to only 4-1/2, or to 9-40ths of its formerly supposed
value. This made the total displacement of a southern corner from the
true meridian through the corresponding northern corner, almost exactly
one foot, or one inch in about twenty-one yards--a degree of accuracy
rendering it practically certain that some stellar method was used in
orienting the base.

Now there _is_ a slanting tunne