Each of these pieces was, like the steps of the Pyramid, 21 inches, or 1 cubit, in length;[10] and, according to the evidence we now have, the Lions’ heads were consequently spaced 2 cubits, or 3 feet 6 inches, from the centre of one to the centre of another.
The interest of this measurement lies in the certainty that the inter-columniation was somehow commensurate with it. The usual arrangement in Greek architecture would have been that there should be one Lion’s head over the centre of each column, and one half-way between. This certainly was not the arrangement here, as the columns, which are 3 ft. 6 in. Greek, or exactly 2 cubits in width, in their lower diameter, would then have been only one diameter apart.
It has been suggested that, as the Lions’ heads are so unusually close, the pillars may have been so arranged that one column had a Lion’s head over its centre, and those on each side stood between two Lions’ heads—thus making the intercolumniation 8 ft. 9 in. The first objection that occurs to this view is, that it is unknown in any other examples; that it is contrary to the general principles of the art, and introduces an unnecessary complication; and is, therefore, unlikely. But the great objection is, that it cannot be made to fit in with any arrangement of the Pyramid steps. Let it be assumed, for instance, that the thirty-six columns of the Pteron were so arranged as to give an uneven number each way, so as to have eleven intercolumniations on one side by seven on the other; this would give a dimension of 96 feet 3 inches by 61 feet 3 inches from centre to centre of the angle columns, to which it would be impossible to fit the Pyramid, assuming, from the evidence of the steps, that its sides were in ratio 4 to 5, or nearly so at all events. If, on the contrary, it is assumed that there were 10 intercolumniations by 8, this would give a dimension of 87·6 by 70; and adding 2 ft. 9 in. each way, which we shall presently see was the projection of the first step of the Pyramid beyond the centre of the angle column, we should have for its base 93 feet by 75 feet 6 inches, within which it is impossible to compress it, unless we adopt a tall pyramid, as was done by Mr. Cockerell and Mr. Falkener before the discovery of the pyramid steps, or unless we admit of a curvilinear-formed pyramid, as was suggested by myself. With the evidence that is now before us, neither of these suggestions seems to be for one moment tenable; and as we cannot, with this intercolumniation, stretch the dimensions of the Pteron beyond what is stated above, it must be abandoned.
Advancing 1 cubit beyond this, we come to 6 cubits, or 10 feet 6 inches Greek, as the distance from the centre of one column to the centre of the next;[11] and the Lions’ heads then range symmetrically, one over each pillar, and two between each pair.
At first sight there seems to be no objection to the assumption that one plain piece of the Cymatium may have been inserted between each of the pieces to which were attached the Lions’ heads, or the impress of them. It is true none were found; but as there could be only one plain piece in three, and as only six or seven fragments were found altogether, the chances against this theory are not sufficient to cause its rejection. The real difficulty is, that a Lion’s head exists on a stone 1 cubit from the angle; and, unless the architects adopted a different arrangement at the angles from what they did in the centre, which is, to say the least of it, extremely improbable, it cannot be made to fit with the arrangement. If one plain piece had been found, it would have fixed the distance between centre and centre of column at 10 ft. 6 in. absolutely. As none, however, were found, or at least brought home, we must look for our proofs elsewhere.
The first of these is a very satisfactory one, on the principle of definite proportions above explained. As we have just found that six pyramid steps, or 6 cubits, are equal to one intercolumniation, so six intercolumniations, or 36 cubits, is exactly 63 Greek feet—the “sexagenos ternos pedes,” which Pliny ascribes to the cella or tomb; it is further proved that this was not accidental, by our finding that twice the length of the cella, or 126 Greek feet, or 72 cubits, is, or ought to be, the total length of the building, measured on its lowest step. This, as before mentioned, Mr. Newton quotes, in round numbers, as 127 feet English; but as neither he nor any of those with him had any idea that any peculiar value was attached to this dimension, they measured carelessly and quoted loosely. My own conviction is, that it certainly was 127 ft. 6-3/4 in. English, which would be the exact equivalent of 126 Greek feet. At all events, I feel perfectly certain that the best mode of ascertaining the exact length of the pyramid step would be to divide this dimension, whatever it is, by 72.
Pteron.
Returning to the Pteron: if the columns were ranged in a single row—and no other arrangement seems possible with the evidence now before us—there must have been eleven columns on the longer faces and nine at the ends, counting the angle columns twice, and consequently a column in the centre of each face. This, at least, is the resultant of every conceivable hypothesis that I have been able to try. No other will, even in a remote degree, suit the admitted forms and dimensions of the pyramid: it is that adopted by Lieutenant Smith and Mr. Pullan; and, according to the evidence before us, seems the only one admissible.
Adopting it for the present, the first difficulty that arises is that 10 intercolumniations at 10 ft. 6 in. give 105 feet; to which if we add as before 5 ft. 6 in., or twice 2 ft. 9 in., for the projection of the first step of the pyramid beyond the centres of the columns, we have 110 ft. 6 in., a dimension to which it is almost impossible to extend the pyramid; and, what is worse, with a cella only 63 feet in its longest dimension, it leaves 21 feet at either end, from the centre of the columns to the wall, a space which it is almost impossible could be roofed by any of the expedients known to the Greeks; and the flanks are almost equally intractable. It was this that rendered Lieutenant Smith’s restoration so unacceptable. He boldly and honestly faced the difficulty, and so far he did good service, and deserves all praise. Mr. Pullan’s expedient of cutting 6 inches off each intercolumniation is not so creditable, nor is the result much more satisfactory.