7. In the architecture of temples, at least, the height either of the shaft or of the full column compares with the complementary height of the order, or of the front, in a ratio of which the terms differ by unity, and the larger term pertains to the columns. For example, the height of the Parthenon column is two parts out of three into which the full height of the order at the flank of the temple is divisible; the remaining part being divided between the entablature and the steps.[8] Mr. Lloyd first publicly explained his theory of the system of proportions used in Greek architecture in a lecture he delivered at the Institute of British Architects in June, 1859, and he afterwards added an appendix to Mr. Cockerell’s work on Egina and Bassæ, explaining specially the proportions of those temples; but the full development of his views, and particularly their relation to the Parthenon, which it appears surpassed all known works in refined and exact application of the system, still unfortunately remains in manuscript. The more direct application of this theory to the design of the Mausoleum will be explained as we proceed, but in the meanwhile it may be asserted that without it many of the dimensions of this celebrated monument might for ever have remained matters of dispute. With its assistance there is scarcely one that may not be ascertained with almost absolute certainty. Another and quite distinct set of ratios was discovered by Colonel Howard Vyse and his architect Mr. Perring, in their explorations of the Pyramids of Egypt. They found, for instance, in the Great Pyramid that the distance Cubits. From the ground-line to the floor of the Queen’s chamber was 40 From the floor of the Queen’s to the floor of the King’s chamber 40 From the floor of the King’s chamber to the apex of the discharging roof 40 From that point to the apex of the pyramid, 40 × 4 160 ——— Making up exactly 280 They also found that the length of the base line was to this dimension in the ratio of 8 to 5, making it 448 cubits or 767·424 feet English exactly. With these two dimensions all the other parts of so simple a figure follow as a matter of course. The bearing of this also on the Mausoleum will be seen in the sequel, though a much more complicated system of ratios was of course necessary either to such a building or to even the very simplest Greek temples. CHAPTER II. _Greek Measures._