Note 18 — GREECE.

“A stadium measures 600 Greek feet, and eight stadia make a Roman mile; 606 feet and 9 inches English are equal to a stadium. This is a well known fact, requiring no proof. But it is a very debatable question, as to whether the ancients, when reckoning by stadia, always adopted the measure of the Olympian stadium, or whether we have sometimes to understand others. The latter opinion has been very generally spread by the moderns, especially in consequence of an error committed by the excellent D’Anville. It very often occurs, that the distances mentioned by the ancients are irreconcilable with modern measurements; whence it has been inferred that sometimes different stadia must be meant, and the statement that the Pythian stadium was shorter than the Olympian, appeared to support this supposition. But there is no other hypothesis which has been set forth equally often, and is yet so devoid of all foundation: the ancient writers do not furnish a single passage in support of the assertion; an endless confusion, moreover, would be introduced into all statements, if we were to suppose that the ancients reckoned according to different stadia without informing their readers of it. Wherever the stadia mentioned are irreconcilable with correct measurements, the cause is no other but either an error in our calculation, or some inaccuracy in the statements of the ancients, which arose in a very natural manner; for the high-roads in Greece were, not like those of the Romans, made in a straight line, but had various turnings, because they had been gradually formed out of the common paths across the fields. In some instances, on the other hand, it has been found that, where the ancients were charged with inaccuracy, too much confidence has been placed in modern travellers, so that the statements of the ancients are, after all, not as inaccurate as some have supposed.

“A question of the highest importance in history and geography is that concerning the proportion which the side of the pyramid bears to the measured degree of the earth and to the Egyptian cubit—a question to which French mathematicians, who were no scholars, have first directed attention. These numbers are such exact multiples of one another, that we must either assume the most marvellous coincidence, or else an artificial calculation. The immortal Laplace set great value upon this discovery, and inferred from it that the elements of mathematical geography were known at a very early time. When the new French system of measures was introduced, the measure of a degree was taken as the standard, and thus the framers of the new system arrived at the same foundation as the ancients. When a degree of latitude was measured in Egypt, the result was perfectly safe; but the French wanted to establish a measure for the whole world, and in this case it is illegitimate to make use of the degree of latitude, for though in a metre the inaccuracy was not great, yet it was so in larger measures. The ancients proceeded from degrees which were not too large, and could be measured with accuracy. Now the degree is a multiple of the Greek stadium, as it is of the Egyptian measure: 600 Greek feet make a stadium, 600 stadia make an equatorial degree, that is, 360,000 Greek feet make a degree; and this system of measurement is derived from Egypt. As the Egyptian foot was larger than an ordinary human foot, the Greeks invented the fable, that the foot of Heracles had been taken as the standard in measuring the stadium. The pace of the Romans is likewise an ideal measure, for it is the thousandth part of one seventy-fifth of a degree.”