There is one other point which must be carefully attended to in any attempt to restore the Mausoleum, which is the ratio between Greek and English measures. Those quoted by Pliny are in the former, of course; those obtained by the excavations are in the latter; and every result is vitiated and worthless without due attention to the difference. The length of a Greek foot may be attained most directly by comparison with the Roman. From the researches of the best antiquaries as summed up by Niebuhr, the length of the Roman foot was ·972 English—a result confirmed by Mr. Penrose’s careful independent investigation. Now, as it is known that the ratio between the Greek foot and the Roman was as 25 to 24, we arrive at the result of 101·25 English feet equal to 100 Greek. Mr. Penrose obtained a slightly different result from his measurement of the upper step of the Parthenon. The front was known or assumed to be exactly 100 Greek feet; it gave 101·341, or about one inch in excess in 1200. As the flanks were to the front in the ratio of 4 to 9, this ought to have given 228·019. It was found to be 228·166, or nearly two inches in excess. But, on the other hand, it is admitted that the term Hecatompedon in Greek authors seems always to apply to the Naos and not to the step; and this, as measured by Mr. Penrose, including the transverse wall, gave 101·222, or a little under the other—the mean between the two being almost exactly identical with the measure derived from the Roman foot. In consequence of this the preference will be given throughout the following pages to the ratio of 101·25, or 101 ft. 3 in. English, as being equal to 100 Greek feet. Turning from this to the measurement of the steps of the Pyramid, which, as mentioned above, is one of the most important elements for the restoration which have been brought to light by the recent excavations, we find their dimensions quoted throughout by Lieut. Smith, Mr. Pullan, and Mr. Newton as 1´ 9´´, or 21 inches English for the wider, and 1´ 5´´, or 17 English inches for the narrower step. The first thing that strikes one on considering this is, that it is a most wonderful coincidence that these dimensions should come out so exactly in English measures, without any fraction either way. On any moderate calculation of chances the odds are at least 100 to 1 against this being the case. The suspicion that there is an error somewhere is confirmed by observing that, though so very nearly in the ratio of 4 to 5, they are not exactly so; but if we try with the lower number we find 4 : 5 :: 17 : 21·25, or within the minutest fraction of 21 Greek inches. If we adopt 17·01 English inches for the shorter, we have 21·2625, or exactly 21 Greek inches, for the latter.