A plan would be available, however (not yet noticed, so far as I know, by any who have studied the astronomical relations of the great pyramid), which would have enabled the builders perfectly to overcome this difficulty.
Suppose the line of sight down the entrance passage were continued upwards along an ascending passage, after reflection at a perfectly horizontal surface—the surface of still water—then by the simplest of all optical laws, that of the reflection of light, the descending and ascending lines of sight on either side of the place of reflection, would lie in the same vertical plane, that, namely, of the entrance passage, or of the meridian. Moreover, the farther upwards an ascending passage was carried, along which the reflected visual rays could pass, the more perfect would be the adjustment of this meridional plane.
To apply this method, it would be necessary to temporarily plug up the entrance passage where it passed into the solid rock, to make the stone-work above it very perfect and close fitting, so that whenever occasion arose for making one of the observations we are considering, water might be poured into the entrance passage, and remain long enough standing at the corner (so to speak) where this passage and the suggested ascending passage could meet, for Alpha Draconis to be observed down the ascending passage. Fig. 2 shows what is meant. Here D C is the descending passage, C A the ascending passage, C the corner where the water would be placed when Alpha Draconis was about to pass below the pole. The observer would look down A C, and would see Alpha Draconis by rays which had passed down D C, and had been reflected by the water at C. Supposing the building to have been erected, as Lepsius and other Egyptologists consider, at the rate of one layer in each year, then only one observation of the kind described need be made per annum. Indeed, fewer would serve, since three or four layers of stone might be added without any fresh occasion arising to test the direction of the passage C A.
Fig. 2.
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:—
"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 material carrying these diagonal joints was harder and better than elsewhere in the floor, so as to have saved that part from the monstrous excavations elsewhere perpetrated by some moderns. Why, then, did the builders change the rectangular joint angle at that point, and execute such unusual angles as they chose in place of it, in a better material of stone than elsewhere; and yet with so little desire to call general attention to it, that they made the joints fine and close to that degree that they escaped the attention of all men until 1865 A.D. The answer came from the diagonal joints themselves, on discovering that the stone between them was opposite to the butt end of the portcullis of the first ascending passage, or to the hole whence the prismatic stone of concealment through 3000 years had dropped out almost before Al Mamoun's eyes. Here, therefore, was a secret sign in the pavement of the entrance-passage, appreciable only to a careful eye and a measurement by angle, but made in such hard material that it was evidently intended to last to the end of human time with the great pyramid, and has done so thus far."
Whether Professor Smyth is right in considering that this specially-prepared position of the floor was intended not for any practical purpose, but to escape the notice of the careless, while yet, when the right men "at last, duly instructed, entered the passage," this mysterious floor-sign should show them where a ceiling-stone was movable, on perceiving which they "would have laid bare the beginning of the whole train of those sub-aërial features of construction which are the great pyramid's most distinctive glory, and exist in no other pyramid in Egypt or the world," I leave the reader to judge. I would remark, only, that, if so, the builders of the pyramid were not remarkably good prophets, seeing that the event befell otherwise, the ceiling-stone dropping out a thousand years or so before the floor-sign was noticed; wherefore we need not feel altogether alarmed at their own prediction (according to Professor Smyth), that the end of the world is to come in 1881, even as Mother Shipton also is reported to have prophesied. For my own part, I am quite content with my own interpretation of the secret sign; as showing where the floor of the descending passage was purposely prepared for the reception of water, on the still surface of which the Pole-star of the day might be mirrored for one looking down the ascending passage.