It is hardly necessary to remind those who have given any attention to the subject of the pyramid that there is precisely such an ascending passage as C A, and that as yet no explanation of the 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:--