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.