Arrian's Voyage Round the Euxine Sea/Appendix

THE learned Bishop of St. Asaph, Dr. Horsley, in a note annexed to Dr. Vincent's Account of the Voyage of Nearchus, has expressed himself to be of a different opinion, respecting the length of the stadium, from the one above specified. I shall take the liberty of examining briefly his Lordship's arguments; and must request the reader's patience, if I repeat some part of what has been urged in the foregoing Dissertation.

He begins with observing, that the circumference of the earth amounted, according to Eratosthenes's calculation, to 252,000 stadia; and, according to Aristotle, to 400,000 stadia; and infers from thence that the stadium of Aristotle was to the stadium of Eratosthenes as 252 is to 400, or very nearly as five to eight.

But this proposition takes it for granted that Aristotle and Eratosthenes agreed in opinion respecting the dimensions of the earth, and differed only in respect to their estimations of the measure which each of them respectively employed; a position which can by no means be admitted.

​It does not appear on what grounds Aristotle^[1], or rather the mathematicians of his age, estimated the circumference of the earth to be 400,000 stadia: but this is certain, that Eratosthenes, did not borrow his calculations from them, but formed his opinion from observations of his own, which are yet preserved. He attempted this arduous task by an actual measurement of a segment of a great circle on the globe, making his computation upon the whole by uniting observations made in the heavens with a corresponding distance, measured (as it was supposed to be) on a meridian of the earth.

The segment of the meridian, which he fixed on for this purpose,was that between Alexandria and Syene, the distance between which places he is said to have measured, and found to be 5000 stadia. He also found that the angle of the meridian shadow upon the scaphia or sun-dial at Alexandria was equal, at the smmer sositice, to ⁠1/50⁠ part of the circle; and that there was no shadow from the gnomon at Syene at the same period of time, and at the same instant of the day.

Supposing then Alexandria and Syene to lie under the same meridian, he concluded that the distance between them was ⁠1/50⁠ part of a great circle of the earth; and this distance being (as was supposed) by measure, 5000 stadia, the whole circumference of the earth must: be of course 250,000 stadia. But in the account of this process, which is accurately detailed by Cleomedes, not a ​word occurs respecting the calculation of Aristotle, who, I believe, however great in other instances, had not much skill in astronomy. Dr. Long laments "that the Babylonia Observations, a treasure almost inestimable, and which he neither knew how to make use of himself, nor so much of their value as to induce him to use the necessary means for their preservation, for the use of those who did, had not fallen into the hands of Eudoxus, rather than into those of Aristotle."

There is then neither proof nor presumption that Eratosthenes accommodated his calculation to that of Aristotle; or that the itinerary stadium was less in the time of Arisiotle than it was in that of Eratosthenes ^[2]. But I fear we can place no great confidence either in the observations or in the measurements of Eratosthenes. He thought that Alexandria and Syene lay under the same meridian; whereas they are found to differ by a space equal to 100 minutes of latitude, equal nearly to 115% English miles, Alexandria being so much to the west of Syene. The difference of latitude is about 7° 20′; so that the real distance between the two places is about 521 English miles, equal nearly to 4552 Olympic stadia.

This falls short of Eratosthenes's calculation by 448 stadia, equal to 51 English miles: but we must consider that the distance laid down by Eratosthenes is the one found by measurement, which must exceed the difference of latitude, since the measurers ​did not discover that the two places lay under different meridians. The numbers of Eratosthenes above specifed were not however acquiesced in by succeeding astronomers, since Marinus and Ptolemy allotted, as Dr. Blair observes, no more than 3600 stadia^[3] to that distance; as the seven degrees twelve minutes (a calculation of the latitude not very different from that of Mr. D'Anville before-mentioned) amounted exactly to that number on the proportion of 500 stadia to a degree; which, Ptolemy tells us, was agreeable to mensurations allowed and acknowledged.

The learned Prelate's calculations in the next paragraph are rather incorrect. He states the proportion of the Roman foot to the English to be as 97: 100; whereas it appears from Greaves, whose measurement the Bishop seems to have adopted, to be only 967: 1000; which makes a difference of nearly ⁠1/134⁠ part, and amounts nearly to 16 feet in the space of an English mile; which, although an inconsiderable difference in small distances, is necessary to be taken into account in the estimation of large extents; and this error, by over-rating the length of the Roman foot, vitiates in some measure his subsequent calculations.

This appears in the next sentence of his Lordship's observations; where he urges, "that if eight Olympic stadia were equal to a Roman mile, and that Polybius's addition of ⅓ of a stadium was an error of his own, arising from the difference between the Roman and the Olympic foot, then one Olympic stadium would be 506.25 feet, London measure;" which computation over-rates ​the length of the stadium by one foot and 875 decimal parts, equal to 22.5 inches, amounting to more than 15 feet in the extent of an Englsih mile.

The Bishop next lays it down, that the opinion of the Greek foot being to the Roman in the proportion of 25 to 24 was erroneous, though current among the Romans themselves. But it is difficult to suppose that persons of rank, science, and education among the Romans were ignorant of the difference between the Greek and the Roman foot, when we consider the intimate connection which subsisted between the two countries; or that Pliny, perhaps the most learned and philosophical man of the age in which he lived, and who, as appears from works of his, published by himself, and still extant, bestowed much labour on geographical researches, would assign 625 feet to a stadium, when he must know that 600 only was the-proper quantity, and that too in a passage, wherein he was speaking of the stadium only, without any reference to the mile.,

Nor can I admit with the learned Prelate, that the Romans, even in their popular valuation of the Greek measures, would be apt to reckon eight Olympic stadia to be exactly equal to their own mile, taking no account of the fraction mentioned by Polybius, supposing that such an addition was necessary to complete the true extent of the mile.

Can we suppose this to have been the case with those persons to whom the care of the mensuration of these distances was committed, when we are told by Polybius, not at second-hand, as in the quotation from Strabo, but in a passage now extant in his ​original works, "that the distances between places were distinctly and accurately marked and divided by the Romans into portions of eight stadia each?"

Would it have been consistent with the character of these mensores terrarum ^[4], persons of rank entrusted with this charge by public authority, to have neglected one part in twenty-five of the distance which they were directed to measure, which, in large extents, would have amounted to a considerable spacel Thus Herodotus tells us, that the circumference of the lake Morris amounted to 3000 stadia; which extent is estimated by Mucianus, a person of the greatest: authority, and frequently appealed to by Pliny, to be 450 m. p. which is eight stadia, and no more, to a mile. Had the third part of a stadium been added, it would have amounted only to 432 m. p. or about 18 miles short of Mucianus's calculation; a space too large to be properly overlooked in any survey that pretends to accuracy.

Again, Pliny tells us, that the 252,000 stadia, which Eratosthenes computed to be the circumference of the earth, amounted in Roman measure to 31,500 m. p. This, it is obvious, is no more than eight stadia to a mile; and it is surely very improbable, if Pliny had known (as he must have done, had it really been the case) that ⅓ of a stadium was necessary to be added to make up the ​mile, that he did not take such an additional quantity into the account, where it would make so great a difference.

Two hundred and fifty-two thousand stadia, at eight stadia and one-third to the mile, amount only to 30,240 m. p. which is 1200 m. p. short of Pliny's calculation. Can we then suppose that Pliny, on whose scientific character it is needless to enlarge, would knowingly have passed over, as not worthy notice, a space, which, at 75 m. p. to a degree, amounts nearly to 17 degrees of latitude, or about 1153 English miles?

But the learned Prelate would do well to consider, that Pliny is not the only Roman writer who has assigned 625 feet to the stadium. Columella, in a part of his work above cited, which was written professedly to explain the præcepta mensurarum, allots the same number with Pliny, both of paces and of feet; and Censorinus, Frontinus, together with the authors of the treatise de Limitibus, and that de Mensuris, preserved among the Rei Agrarian Auctores, all concur in giving the same description of this measure. Is it possible to suppose writers of such rank and accuracy all uniting in the same mistake, respecting a circumstance of such common occurrence? Is it not more reasonable and more natural to suppose the meaning of Polybius to be, that the stadium, measured by 600 Roman feet, would be defective one part in 24, compared with its length, if measured by the same number of Greek feet; and that therefore it would be necesssary to add ⁠1/24⁠ part, or 25 additional Roman feet, to make up the deficiency? and that these 25 feet were really added, the testimonies above produced demonstrate.

​The Olympic foot, we are expressly told by Aulus Gellius, exceeded the common foot in the same proportion as the foot of Hercules exceeded in length the foot of an ordinary man; and this difference appears to be in the proportion of 25 to 24.

It is proper to remark, that all the Greek writers, who describe they Olympic or itinerary stadium, and who might be supposed to reckon by Greek feet, as Herodotus, Hero, and Suidas, concur in assigning to this measure 600 feet. On the other hand, all the Latin or Roman writers, to whom the Roman foot was more familiar, who describe the stadium in use among the Romans, uniformly ascribe to it the measure of 625 feet. Yet we have no reason to think that the Greek and the Roman stadium were of different dimensions.

The Greek foot, as deduced by Mr. Stuart, from measurements of different parts of the Hecatompedon at Athens, exhibits, as I have before shewn, as nearly as possible, allowing for small inaccuracies in the mensuration, and perhaps for some in the construction of the building itself, the proportion of 25 to 24, as compared with the Roman foot described by Mr. Greaves to be sculptured on the marble monument of Cossutius at Rome; which proportion coincides with the difference of the number of feet assigned to the stadium by the Greek, and that assigned to the same measure by the Latin or Roman writers. If Hercules was taller than other men, "aliorum procerius," as it is expressed by Aulus Gellius, the measure taken from his foot, supposing that to be in proportion with the rest of his body, must exceed the usual measure of length; and of course fewer Herculean feet than-feet of the usual size would be required to make up a given length. To this ​we may add, that the proportion of 25 to 24 is no extravagant or improbable excess of stature above that of ordinary men, for one so celebrated for strength, activity, and other athletic exercises, as Hercules is reported to have been.

Supposing the height of an ordinary man to be five feet ten inches, English measure, the addition of a 24th part will make that of Hercules to have been rather under six feet and one inch, which is no extraordinary height, though superior to the common standard of mankind.