s of a circle with
that perimeter, it follows that the height should symbolise the sun's
distance. 'That line, further,' says Professor Smyth (speaking on behalf
of Mr. W. Petrie, the discoverer of this relation), 'must represent'
this radius 'in the proportion of 1 to 1,000,000,000' (or _ten_ raised
to power _nine_), 'because amongst other reasons 10 to 9 is practically
the shape of the great pyramid.' For this building 'has such an angle at
the corners, that for every ten units its structure advances inwards on
the diagonal of the base, it practically rises upwards, or points to
sunshine' (_sic_) 'by _nine_. Nine, too, out of the ten characteristic
parts (viz. five angles and five sides) being the number of those parts
which the sun shines on in such a shaped pyramid, in such a latitude
near the equator, out of a high sky, or, as the Peruvians say, when the
sun sets on the pyramid with all its rays.' The coincidence itself on
which this perverse reasoning rests is a singular one--singular, that
is, as showing how close an accidental coincidence may run. It amounts
to this, that if the number of days in the year be multiplied by 100,
and a circle be drawn with a circumference containing 100 times as many
inches as there are days in the year, the radius of the circle will be
very nearly one 1,000,000,000th part of the sun's distance. Remembering
that the pyramid inch is assumed to be one 500,000,000th part of the
earth's diameter, we shall not be far from the truth in saying that, as
a matter of fact, the earth by her orbital motion traverses each day a
distance equal to two hundred times her own diameter. But, of course,
this relation is altogether accidental. It has no real cause in
nature.[23]

Such relations show that mere numerical coincidences, however close,
have little weight as evidence, except where they occur in series. Even
then they require to be very cautiously regarded, seeing that the
history of science records many instances where the apparent law of a
series has been found to be falsified when the theory has been extended.
Of course this reason is not quoted in order to throw doubt on the
supposition that the height of the pyramid was intended to symbolise the
sun's distance. That supposition is simply inadmissible if the
hypothesis, according to which the height was already independently
determined in another way, is admitted. Either hypothesis might be
admitted were we not certain that the sun's dist