_Lastly._—The system of definite proportions in Greek architecture, which is not only most useful in suggesting forms, but also most valuable in rectifying deductions arrived at from other sources. 1. _Scripta._ Among the things written with regard to the Mausoleum, by far the most important is the celebrated passage in Pliny’s Natural History.[2] It is to the following effect: “Scopas had, as rivals in the same age, Bryaxis, and Timotheus, and Leochares, who should be mentioned together, as they were equally employed in the sculptures of the Mausoleum, a sepulchre erected by his wife Artemisia to Mausolus, King of Caria, who died in the second year of the hundred and seventh Olympiad. It was mainly owing to the work of the above-named artists that this building was considered one of the seven wonders of the world. It extends on the north and south 63 feet, but is shorter on the other fronts. The whole circumference is 411 feet. It is raised in height 25 cubits, and is surrounded by 36 columns. This part was called the pteron. The sculptures on the east side were by Scopas, on the north by Bryaxis, on the south by Timotheus, and on the west by Leochares. Before they had finished their work, the Queen Artemisia, who had ordered this building to be constructed in honour of her husband’s memory, died; but they did not on that account cease from their labours till it was entirely finished, regarding it as a monument of their own fame and of art; and to this day the work testifies to their rivalry in merit. A fifth artist was joined to them; for above the pteron there was a pyramid equal in height to the lower part, with 24 steps, contracting into a summit, like that of a meta. On the top of all this was a quadriga in marble, made by Pythis. These being added, the height of the whole work was equal to 140 feet.” It is easy to see what difficulties were involved in this description. How, in the first instance, was it possible that a building which was only 63 feet in length in plan, and shorter on the other sides, could be 411 feet in circumference? and, in regard to height, what substantive was to be supplied after “inferiorem”? If “partem,” it might apply to the pteron, which is the only part mentioned in the previous description; but the logic seemed to require “pyramidem,” and if so, what was it? If either, how was the whole height of 140 feet to be made up?