De Facie Quae in orbe Lunae Apparet

Here Apollonides broke in. Then by the moon herself, he said, do you people think it possible that any clefts and chasms cast shadows which from the moon reach our sight here; or do you not reckon the consequence, and shall I tell you what it is? Please listen then, though it is not anything unknown to you. The diameter of the moon measures twelve digits in apparent size at her mean distance[*](cf. Cleomedes, ii. 3. 95 (p. 172. 25-27 [Ziegler]); on this measurement of 12 digits cf. Heath, Aristarchus of Samos, p. 23, n. 1.); and each of the black and shadowy spots appears greater than half a digit and consequently would be greater than one twenty-fourth of her diameter. Well then, if we should suppose that the circumference of the moon is only thirty thousand stades and her diameter ten thousand each of the shadowy spots on her would in accordance with the

assumption measure not less than five hundred stades.[*](Apodonides exaggerates for the sake of his point, for 500 stades is 1/20 not 1/24 of 10,000: but he has guarded himself by saying that each of the spots is more than half a digit and so more than 1/24 of the diameter. On the other hand, he intends his estimate of the moon’s size to err, if at all, on the side of conservatism: cf. only thirty thousand stades. Such small figures, even as minima, are remarkable, however. Cleomedes (ii. 1. 80-81 [pp. 146. 25-148. 3, Ziegler]) gives 40,000 stades as the lunar diameter, basing this upon the assumption that the earth is twice as large as the moon and has a circumference of 250,000 stades according to the measurement of Eratosthenes and a diameter therefore of more than 80,000 stades. Plutarch adopted the same figure for the terrestrial diameter (see 925 D supra) but supposed this and the terrestrial circumference to be three times those of the moon (see 923 B supra and note d there), figures which should have given him more than 26,000 stades as the lunar diameter. According to Hultsch, however, Posidonius must have calculated the lunar diameter to be 12,000 stades (cf. Abhand. K. Gesell. Wissensch. zu Göttingen, Phil.-Hist. Kl., N.F. i, No. 5, p. 38), which by the usual approximation would have given 36,000 stades for the lunar circumference; and Apollonides minimal estimate may have been based upon these figures. For the common rough approximation 3-1 as the relation of circumference to diameter cf. Archimedes, Arenarius, ii. 3 (Opera Omnia, ii, p. 234. 28-29 [Heiberg]).) Consider now in the first place whether it is possible for the moon to have depths and corrugations so great as to cast such a large shadow; in the second place why, if they are of such great magnitude, we do not see them. Then I said to him with a smile: Congratulations for having discovered such a demonstration. Apollonides. It would enable you to prove that both you and I are taller than the famous sons of Aloeus,[*](Otus and Ephialtes: cf. Exilio, 602 d; Iliad, v. 385-387; Odyssey, xi. 305-320; Apollodorus, Bibliotheca, i. 7. 4. 2-4.) not at every time of day to be sure but early in the morning particularly and in late afternoon, if, when the sun makes our shadows enormous. you intend to supply sensation with this lovely reasoning that, if the shadow cast is large, what casts the shadow is immense. I am well aware that neither of us has been in Lemnos; we have both, however, often heard this line that is on everyone’s lips:

Athos will veil the Lemnian heifer’s flank.[*](The verse, which comes from an unidentified tragedy of Sophocles, is elsewhere quoted with καλύπτει or σκιάζει and with πλευρά or νῶτα (cf. Nauck, Trag. Graec. Frag.² , p. 299, frag. 708). For the shadow of Athos cast upon Lemnos cf. Pliny, Nat. Hist. iv. 12 (23). 73; Apollonius Rhodius, i. 601-604; Proclus, In Timaeum, 56 B (i, p. 181. 12 ff. [Diehl]).)

The point of this apparently is that the shadow of the mountain, extending not less than seven hundred stades over the sea,[*](Proclus (loc. cit.) says that this is the distance of Lemnos from Athos, Plutarch rather that it is the length of the shadow cast by the mountain. According to Eustathius (Ad Iliadem, 980. 45 ff.), Athos is 300 stades distant from Lemnos, according to Pliny (loc. cit.) 87 Roman miles (unless this is a scribal error for XXXXVII). The actual distance is said to be about 50 miles; and Athos, which is 6350 feet high, could cast a shadow for almost 100 miles over open sea.) falls upon a little bronze heifer; [but it is not necessary, I presume,] that what casts the shadow be [seven hundred stades] high, for the reason that shadows are made many times the size of the objects that cast them by the remoteness of the light from the objects.[*](In this Plutarch is guilty either of an error or of an intentional sophism; cf. Class. Phil. xlvi (1951), p. 145.) Come then, observe that, when the moon is at the full and because of the shadows depth exhibits most articulately the appearance of the face, the sun is at his maximum distance from her. The reason is that the remoteness of the light alone and not the magnitude of the irregularities on the surface of the moon has made the shadow large. Besides, even in the case of mountains the dazzling beams of the sun prevent their crags from being discerned in broad daylight, although their depths and hollows and shadowy parts are visible from afar. So it is not at all strange that in the case of the moon too it is not possible to discern accurately the reflection and illumination, whereas the juxtapositions of the shadowy and brilliant parts by reason of the contrast do not escape our sight.