identity of its
angle of ascent with the angle of descent of the passage D C has ever
been given. Most pyramidalists content themselves by assuming, as Sir E.
Beckett puts it, "that the same angle would probably be used for both
sets of passages, _as there was no reason for varying it_," which is not
exactly an explanation of the relation. Mr. Wacherbarth has suggested
that the passages were so adjusted for the purpose of managing a system
of balance cars united by ropes from one passage to another; but this
explanation is open, as Beckett points out, to the fatal objection that
the passages meet at their lowest point, not at their highest, so that
it would be rather a puzzle "to work out the mechanical idea." The
reflection explanation is not only open to no such objections, but
involves precisely such an application of optical laws as we should
expect from men so ingenious as the pyramid builders certainly were. In
saying this, let me explain, I am not commending myself for ingenuity in
thinking of the method, simply because such methods are quite common and
familiar in the astronomy of modern times.

While I find this explanation, which occurred to me even while this
paper was in writing, so satisfactory that I feel almost tempted to say,
like Sir G. Airy of his explanation of the Deluge as an overflow of the
Nile, that "I cannot entertain the slightest doubt" of its validity, I
feel that there ought to be some evidence in the descending passage
itself of the use of this method. We might not find any traces of the
plugs used to stop up, once a year or so, the rock part of the
descending passage. For they would be only temporary arrangements. But
we should expect to find the floor of the descending passage constructed
with special care, and very closely fitted, where the water was to be
received.

Inquiring whether this is so, I find not only that it is, but that
another hitherto unexplained feature of the great pyramid finds its
explanation in this way,--the now celebrated "secret sign." Let us read
Professor Smyth's account of this peculiar feature:--

"When measuring the cross-joints in the floor of the
entrance-passage, in 1865, I went on chronicling their angles, each
one proving to be very nearly at right angles to the axis, until
suddenly one came which was _diagonal_; another, and that was
diagonal too; but, after that, the rectangular position was
resumed. Further, the stone