Assuming this, therefore, we find the height dividing itself into three portions, each of which was 37 ft. 6 in., and two which seem to be 13 ft. 9 in. each. But if this were so, we come to the difficulty that there is no very obvious rule of proportion between these parts, which there certainly ought to be. Even if we add the two smaller ones together we obtain 27 ft. 6 in., which, though nearly, is not quite in the ratio of 3 to 4 to the larger dimension of 37 ft. 6 in. If we add to the first 9 inches we get the exact ratio we require; but by this process increase the height of the building by that dimension, which is impossible.
The explanation of the difficulty may perhaps be found in the fact that the order overlaps the pyramid nearly to that extent, as is seen in the diagram (Woodcut No. 5.) It is by no means improbable that the architects made the pyramid 37 ft. 6 in. from the bottom of the bottom step,—as they naturally would,—and measured the order to the top of the cymatium; and consequently these two dimensions added together did not make 75 feet, but 74 ft. 3 in., or something very near to it.
There is a curious confirmation of this in another dimension which must not be overlooked. At page 24 we found the extreme length of the building to be 126 feet, or 72 Babylonian cubits. This ought to be the height; and so it is, to an inch, if we allow the quadriga to have measured 14 Greek feet. Mr. Newton, it is true, makes it only 13 ft. 3 in. English, but it was necessary for his theory of restoration to keep it as low as possible; and, though it may have been only that height, there are no data to prevent its being higher, nor indeed to fix its dimensions within the margin of a foot. Considering the height at which it was seen, there is everything to confirm the latter dimension, which has besides the merit of being exactly one-tenth of the total height of the building.
From these data we obtain for the probable height of the different parts of the building the following:—
| Ft. | In. | ||
| Height of basement to soffit | 37 | 6 | |
| Entablature of ditto | 14 | 0 | |
| Pteron, to top of cymatium | 37 | 6 | |
| Pyramid | 37 | 6 | |
| Quadriga | 14 | 0 | |
| ——— | |||
| 140 | 6 | ||
| Deduct for overlap | 6 | [17] (9?) | |
| ——— | |||
| 140 | 0 | ||
or exactly 80 Babylonian cubits, which is probably the dimension Hyginus copied out, though either he or some bungling copier wrote “feet” for “cubits,” just as the lithographers have altered all Mr. Pullan’s decimals of a foot into inches, because they did not understand the unusual measures which were being made use of.
There is still another mode in which this question may be looked at. It appears so strange that the architects should have used one modulus for the plan and another for the height, that I cannot help suspecting that in Satyrus’s work the dimensions were called 21 Babylonian or 25 Greek cubits, or some such expression. The difference is not great (9 inches), and it seems so curious that Greek cubits should have been introduced at all that we cannot help trying to find out how it was.
In the previous investigation it appeared that the only two vertical dimensions obtained beyond those quoted by Pliny which were absolutely certain were 126 feet or 72 cubits for the height of the building, and 8 cubits or 14 feet for the quadriga. Now, if we assume thrice 21 cubits for the height, we have 63 cubits, and this with 8 cubits for the quadriga, and 9 for the entablature of the basement, making together 17 cubits, complete the 80 we are looking for. In other words, we return to the identical ratios from which we started, of 17″ and 21″, if these figures represented in inches the dimensions of the steps, as they are always assumed to be by Messrs. Newton, and Pullan, and Smith. If it were so, nothing could be more satisfactory; but, to make the ratio perfect, the last dimension, instead of 9 cubits, ought to be 8·8; so that we should get a total of 4 inches too short, instead of being in excess, as it was by the last calculation.
It would, of course, be easy to apportion this as one inch to each of the four parts; but that is inadmissible in a building planned with such exactitude as this, and I therefore merely state it in order to draw to it the attention of some one cleverer at ratios than I am, confessing that I am beaten, though only by an inch.