observed or known phenomena. And it may do so for every known case of any Egyptian pyramid, except the great pyramid; and there it explains nothing of what it chiefly consists in. Taking, however, the cases which it does apply to, viz. the profane Egyptian examples, this alleged 'law' pronounces that the sole object of any pyramid was to form a royal tomb-subterranean, as a matter of course-and that operations began by making an inclined descending passage leading down into the rock, and in cutting out an underground chamber at the end of it. The scheme, thus begun below, went on also growing above-ground, every year of the king's reign, by the placing there of a new heap or additional layer of building stones, and piling them, layer above layer, over a central square-based nucleus upon the levelled ground, virtually above the subterranean apartment; and it was finally (that is, this superincumbent mass of masonry) finished off on that king's death by his successor, who deposited his predecessor's body embalmed and in a grand sarcophagus in the underground chamber, stopping up the passage leading to it, cased in the rude converging sides of the building with bevelled casing stones, so as to give it a smooth pyramidal form, and left it in fact a finished Egyptian and Pharaonic pyramid to all posterity; and no mean realisation either of prevailing ideas among some early nations, of burying their monarchs sub montibus altis, in impressive quiet, immovable calm, and deep in the bosom of mother earth."

Although Lepsius states that he discovered this solution of the riddle of pyramidal construction, it was in part suggested earlier by James Wilde, and is thus described in the letterpress accompanying Frith's large photographs of Egypt: "A rocky site was first chosen, and a space made smooth, except a slight eminence in the centre to form a peg upon which the structure should be fixed" (which is absurd). "Within the rock, and usually below the level of the future base, a sepulchral chamber was excavated, with a passage inclined downwards, leading to it from the north." After describing the way in which the work proceeded, the account goes on to say that" in this manner it was possible for the building of a pyramid to occupy the lifetime of its founder, without there being any risk of his leaving it incomplete to any such degree as would afford a valid excuse for his successor neglecting to perform his very moderate part, of merely filling up the angles and smoothing off generally."

This, however, is not precisely the same as Lepsius's law, and is manifestly less complete and less satisfactory.

But in the first place I am not at all disposed to admit that Lepsius's law, even though it explains the manner in which the

pyramids may have been built, is either proved by any evidence cited in its favour, or in turn proves anything respecting the purpose of any of the pyramids. It agrees well with the theory that the pyramids, including, of course, the great one, served as tombs for the several persons to whom they belonged or were assigned. But no one thinks of questioning this, so far as all the pyramids, except the great one, are concerned; and I apprehend that very few share Professor Smyth's faith that King Cheops never was buried, and was never meant to be buried, in the pyramid which bears his name. None of the difficulties of the exclusively tombic theory seem even touched by Lepsius's theory, whether it be accepted or rejected. The construction of the pyramids by single layers year by year, if proved, and if it prove anything, shows that the use of the pyramids related chiefly to the life of those to whom the pyramids were assigned, not solely to their death and burial.

Lepsius's theory is partly based on a circumstance which no astronomer who attentively considers the matter can fail to interpret in one special manner, bearing very significantly on our ideas respecting the purpose for which the pyramids were constructed.

In all the pyramids of Ghizeh there is a slant passage (in some there are two such passages) leading down into the rock, an underground chamber being cut at the end of the passage. Lepsius, of course, like all who regard the astronomical relations fulfilled by the pyramids as of slight importance, pays no special attention to the circumstance that in every case the descending passage passes in a north and south direction, at an angle always of about 26 degrees, and has its entrance always on the northern side. Fig. 2 shows the

FIG. 2. Showing the dimensions of the four chief pyramids, and the position of the inclined passages. position of the descending passages in the four chief pyramids. But if it were not obvious in other ways that astronomical relations were regarded by the builders of the pyramids as of extreme importance, these slant passages would prove it. They show unmistakably (1) that the builders proposed to make the pyramids fulfil certain definite

astronomical conditions; and (2) the method in which the builders effected their purpose.

I have shown in my article on the Religion of the Great Pyramid how an architect, proposing to set a building in a particular latitude, might use either the sun, when due south, or those stars which circle close round the pole, for that purpose; that the better the astronomers were in the days of the pyramid-builders, the more likely they were to prefer the latter, or stellar method, to the former, or solar method; and that if they adopted the solar method the building would be set too far north unless correction were made for the refraction of the atmosphere; while if they adopted the stellar method the building would be set too far south. Wherefore, as we find the centre of the great pyramid set somewhat south of the latitude 30° north which the builders clearly intended to have it to occupy the error being about a mile and a quarter, while, if refraction were wholly neglected, it would have been about a mile and three-quarters-we may infer that the astronomers who superintended the arrangements for fixing the latitude employed the stellar method; that they were exceedingly skilful observers, considering they had no telescopic meridian instruments; and (with less certainty) that they made some correction for atmospheric refraction.

I show also fully in that article that astronomers using the stellar method for that purpose would most certainly employ it to set the sides of the "pyramid's" square base facing as exactly as possible the four cardinal points. One method would certainly present itself, and only one would be at all suitable for this purpose. They would take their pole-star, whatever it might be, and would note its direction when

FIG 3. Showing how the builders of the pyramid probably obtained their base.

how could they mark this direction on their selected base? They could in the first place set up a pointed upright, as AB in fig. 3, at the

middle of the northern edge of the base, and another shorter one, CD, so that at one of the epochs, it would not matter which, an eye placed as at E would see the points c and E in the same straight line as the pole-star s. Then the line DB would lie north and

south.

This would only be a first rough approximation, however. The builders would require a much more satisfactory north and south line than DB. To obtain this they would bore a slant passage in the solid rock, as DG, which should point directly to the pole-star s when due north, starting their boring by reference to the rough north and south line DB, but guiding it as they went on, by noticing whether the pole-star, when due north, remained visible along the passage. But they would now have to make selection between its passage above the pole and its passage below the pole. In using the uprights D and B, they could take either the upper or the lower passage; but the underground boring could have but one direction, and they must choose whichever of the two passages of the star they preferred. We cannot doubt they would take the lower passage, not only as the more convenient passage for observation, but because the length of their boring DG would be less for a given horizontal range FD, if the lower passage of s were taken, than it would be for the upper passage, when its direction would be as DG'.

When they had bored far enough down to have a sufficient horizontal range FD (the longer this range, of course, the truer the north and south direction), they would still have to ascertain the true position of F, the point vertically above G. For this purpose they would get F first as truly as they could from the line DB prolonged, and would bore down from F vertically (guiding the boring, of course, with a plumb-line), until they reached the space opened out at G. The boring FG might be of very small diameter. Noting where the plumb-line let down from F to G reached the floor of the space G, they would ascertain how far F lay to the east or to the west of its proper position over the centre of the floor of this space. Correcting the position of F accordingly, they would have FD the true north and south line.

This method could give results of considerable accuracy; and it is the only method in fact which could do so. When, therefore, we find that the base of the pyramid is oriented with singular accuracy, and secondly that just such a boring as DG exists beneath the base of the pyramid, running three hundred and fifty feet through the solid rock on which the pyramid is built, we cannot well refuse to believe that the slant passage was bored for this purpose, which it was so

well fitted to subserve, and which has been so well subserved in

some way.

Now, if this opinion is adopted, and for my own part I cannot see how it can well be questioned, we cannot possibly accept the opinion that the slant tunnel was bored for another purpose solely, or even chiefly, unless it can be shown that that other purpose in the first place was essential to the plans of the builders, in the second place could be subserved in no other way so well, and in the third place was manifestly subserved in this way to the knowledge of those who made the slant borings. Now, it certainly is the case that, noting the actual position of this slant boring, we can form a shrewd guess at the date of the great pyramid's erection. In the year 2170 B.C., and again (last before that) in the year 3350 B.C., and also for several years on either side of those dates, a certain bright star did look down that boring, or, more precisely, could be seen by any one who looked up that boring, when the star was just below the pole in its circuit round that point. The star was a very important one among the old constellations, though it has since considerably faded in lustre, being no other than the star Alpha of the constellation the Dragon, which formerly was the polar constellation. For hundreds of years before and after the dates 3350 and 2170 B.C., and during the entire interval between those dates, no other star would at all have suited the purposes of the builders of the pyramid; so that we may be tolerably sure this was the star they employed. Therefore the boring, when first made, must have been directed towards this star. We conclude, then, with considerable confidence that it was somewhere about one of the two dates 3350 B.C., and 2170 B.C., that the erection of the great pyramid was begun. And from the researches of Egyptologists it has become all but certain that the carlier of these dates is very near the correct epoch. But though the boring thus serves the purpose of dating the pyramid, it seems altogether unlikely that the builders of the pyramid. intended to record the pyramid's age in this way. They could have done that, if they had wanted to, at once far more easily and far more exactly, by carving a suitable record in one of the inner chambers of the building. But nothing yet known about the pyramid suggests that its builder wanted to tell future ages anything whatever. So far from this, the pyramid was carefully planned to reveal nothing. Only when men had first destroyed the casing, next had found their way into the descending passage, and then had in the roughest and least skilful manner conceivable (even so, too, by an accident) discovered the great ascending gallery, were any of the secrets of this mighty tomb revealed for a tomb and nothing else it has been, ever since Cheops