[17] This star, called _Thuban_ from the Arabian _al-Thuban_, the
Dragon, is now not very bright, being rated at barely above the fourth
magnitude, but it was formerly the brightest star of the constellation,
as its name indicates. Bayer also assigned to it the first letter of the
Greek alphabet; though this is not absolutely decisive evidence that so
late as his day it retained its superiority over the second magnitude
stars to which Bayer assigned the second and third Greek letters. In the
year 2790 B.C., or thereabouts, the star was at its nearest to the true
north pole of the heavens, the diameter of the little circle in which it
then moved being considerably less than one-fourth the apparent diameter
of the moon. At that time the star must have seemed to all ordinary
observation an absolutely fixed centre, round which all the other stars
revolved. At the time when the pyramid was built this star was about
sixty times farther removed from the true pole, revolving in a circle
whose apparent diameter was about seven times as great as the moon's.
Yet it would still be regarded as a very useful pole-star, especially as
there are very few conspicuous stars in the neighbourhood.

[18] Even that skilful astronomer Hipparchus, who may be justly called
the father of observational astronomy, overlooked this peculiarity,
which Ptolemy would seem to have been the first to recognise.

[19] It would only be by a lucky accident, of course, that the direction
of the slant tunnel's axis and that of the vertical from the selected
central point would lie in the same vertical plane. The object of the
tunnelling would, in fact, be to determine how far apart the vertical
planes through these points lay, and the odds would be great against the
result proving to be zero.

[20] It may, perhaps, occur to the reader to inquire what diameter of
the earth, supposed to be a perfect sphere, would be derived from a
degree of latitude measured with absolute accuracy near latitude 30 deg.
A degree of latitude measured in polar regions would indicate a diameter
greater even than the equatorial; one measured in equatorial regions
would indicate a diameter less even than the polar. Near latitude 30 deg.
the measurement of a degree of latitude would indicate a diameter very
nearly equal to the true polar diameter of the earth. In fact, if it
could be proved that the builders of the pyramid used for their unit of
length an exact subdivision of the pol