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