After trying several others, the solution appears to me to lie in the hypothesis that the angle columns were coupled,—or, in other words, half an intercolumniation (5 feet 3 inches) apart from centre to centre.
Should it be asked if there are any other examples of this arrangement, the answer must probably be that there are not; but there is also no other building known with a pyramidal roof, or which, from its design, would so much require strengthening at the angles. The distance between the columns and the front must necessarily be so great,—the height at which they are placed is so considerable,—and the form of the roof so exceptional, that I feel quite certain any architect will admit that this grouping together of the angle columns is æsthetically an improvement.[12]
Although this arrangement may not be found in any Ionic edifice, it is a well-known fact that in every Doric Temple the three columns at the angles are spaced nearer to each other than those intermediate between them, either in the flanks or front. The usual theory is that this was done to accommodate the exigencies of the triglyphs. It may be so, but the Greeks were too ingenious a people to allow any such difficulty to control their designs if they had not thought it an improvement to strengthen the angles of their buildings. We may also again refer to the Lion Tomb at Cnidus (Woodcut, No. 1), where the angle intercolumniations are less than the centre ones, for no conceivable reason but to give apparent strength to that part.
The proof, however, must depend on how it fits with the other parts.
Taking first the flanks, we have 8 whole and 2 half intercolumniations, equal to 94 feet 6 inches Greek, or 48 cubits, or just once and a half the length of the cella; which is so far satisfactory. At the back of the gutter behind the cymatium there is a weather mark which certainly indicates the position of the first step of the pyramid, and, according to Mr. Pullan’s restoration of the order, this mark is 2 ft. 8-1/2 in. beyond the centre of the columns. As there are a great many doubtful elements in this restoration, and as, from the fragmentary nature of the evidence, it is impossible to be certain within half an inch or even an inch either way, let us, for the nonce, assume this dimension to be 2 ft. 9 in. Twice this for the projection either way, or 5 ft. 6 in., added to 94 ft. 6 in., gives exactly 100 Greek feet for the dimension of the lowest step of the pyramid. So far nothing could be more satisfactory; but, if it is of any value, the opposite side ought to be 80 feet,—or in the ratio of 5 to 4.
On this side we have 6 whole and 2 half intercolumniations, or 73 ft. 6 in.,—to which adding, as before, 5 ft. 6 in. for the projection of the step, we obtain 79 feet! If this is really so, there is an end of this theory of restoration on a system of definite proportions; and so for a long time I thought, and was inclined to give up the whole in despair. The solution, however, does not seem difficult when once it is explained. It probably is this: the steps of the Pyramid being in the ratio of 4 to 5, or as 16·8 in. to 21 inches Greek, the cymatium gutter must be in the same ratio, or the angle would not be in the same line with the angles of the steps or of the pedestals, or whatever was used to finish the roof. In Mr. Newton’s text this dimension is called 1 ft. 10 in. throughout; according to Mr. Day’s lithographer it is 1′·88, which does not represent 1 ft. 10 in. by any system of decimal notation I am acquainted with. According to Mr. Pullan’s drawing it scales 2 feet.[13] From internal evidence, I fancy the latter is the true dimension. Assuming it to be so, and that it is the narrowest of the two gutters, the other was of course as 4 is to 5, or as 2 feet to 2 feet 6 inches, which gives us the exact dimensions we are seeking, or 6 inches each way. This I feel convinced is the true explanation, but the difficulty is that, if it is so, there must be some error in Mr. Pullan’s restoration of the order. If we assume that we have got the wider gutter, the other would be 19·2 in., which would be easily adjusted to the order, but would give only 4·8 in. each way, or 1-2/10 in. less than is wanted. It is so unlikely that the Greeks would have allowed their system to break down for so small a quantity as one inch and one-fifth in 40 feet, that we may feel certain—if this difficulty exists at all—that it is only our ignorance that prevents our perceiving how it was adjusted. If it should prove that the cymatium we have got is the larger one, and that consequently this difference does exist, the solution will probably be found in the fact of the existence of two roof stones, with the abnormal dimensions quoted by Mr. Pullan as 10-1/2 inches and 9 respectively. It may be they were 9″ and 10″·2, which would give the quantity wanted. But, whatever their exact dimensions, it is probable that they were the lowest steps of the pyramid; and, if the discrepancy above alluded to did exist, they may have been used as the means of adjusting it. Be all this as it may, I feel convinced that whenever the fragments can be carefully re-examined, it will be found that the exact dimension we are seeking was 80 Greek feet.[14]
There is another test to which this arrangement of the columns must be submitted before it can be accepted, which is, the manner in which it can be made to accord with the width of the cella.
The first hypothesis that one naturally adopts is that the peristyle should be one intercolumniation in width, in other words that the distance between the centres of the columns and the walls of the cella should be 10 feet 6 inches. Assuming this, or deducting 21 Greek feet from the extreme width we have just found above of 73 feet 6 inches, it leaves 52 feet 6 inches for the width, which is a very reasonable explanation of Pliny’s expression, “brevius a frontibus.” It is also satisfactory, as it is in the proportion of 5 to 6, with 63 feet, which is Pliny’s dimension, for the length of the cella. But the “instantia crucis” must be that it should turn out—like the longer sides—just one half the lower step, or rock-cut excavation. What this is, is not so easily ascertained. In his letter to Lord Stratford de Redcliffe, of 3rd April, 1857, Mr. Newton calls it 110 feet; in the text (p. 95) it is called 108; while Lieut. Smith, who probably made the measurement, calls it 107 (Parl. Papers, p. 20). The latter, therefore, we may assume is the most correct. If the above hypothesis is correct, it ought to have been 106·31 English or 105 Greek feet, which most probably was really the dimension found; but as it did not appear to the excavators that anything depended upon it, they measured it, as before, carelessly and recorded it more so.
In the meanwhile, therefore, we may assume that the width of the cella was 52 feet 6 inches, or 30 Babylonian cubits. The width of the lower step on the east and west fronts was 105 Greek feet, or 60 cubits exactly.
Of course this is exactly in the proportion of 5 to 6 with the longer step, which, as we found above, was 72 cubits or 126 Greek feet; and this, as we shall presently see, was the exact height of the building without the quadriga, the total height being 80 cubits or 140 Greek feet.