Part 24

The mathematical account of the movements of the moon has its history. As we have seen, it was early realized that she revolved round and near the earth in a circular orbit. Soon it appeared that there were irregularities in this movement. The ‘First Anomaly’, a difference of speed observed at different parts of the orbit, was well understood by Hipparchus. It could be expressed, so as to ‘save the phenomena’, by either of two methods, both resting on the assumption that no curve except a circle was admissible, and both superseding the ingenious but cumbrous arrangement of ‘concentric Spheres’ known to Aristotle. One was that of ‘movable eccentrics’, where the orbit of the planet was round a point outside the earth, itself shifting. The other, which prevailed, and was finally adopted by Ptolemy, was that of epicycles, circles described round points in the primary orbit, by means of which the planet’s motion could be retarded or quickened at will, and its position modified. By this device, the visible _movement_ could be, and was, recorded with great accuracy, but sometimes at the expense of physical truth. Thus the epicyclic arrangement for the moon’s orbit involved, if closely looked into, the consequence that her distance from us at nearest must be half that at the farthest, and her angular diameter double! Kepler, after the work of a lifetime (1571-1630), discovered the cause of this ‘anomaly’ in the shape of the orbit, which is elliptical, not circular, and substituted ‘eccentricity’ for ‘anomaly’ as the key-word. Newton (1642-1727) proved that a body revolving round another _must_ move in an ellipse, with the larger body at one focus. Thus the wheel had come full circle, and physical and mathematical inquiry met after two thousand years of separation. The ‘Second Anomaly’ due to the action of the sun (the ‘Evection’) was indicated by Hipparchus, worked out as a phenomenon by Ptolemy, and its physical cause explained by Newton. The inclination of the moon’s path to the sun’s was known to Hipparchus as 5°, and the recession of her nodes was familiar to him. A third anomaly now known as ‘Variation’ is instructive because its discovery has been claimed for an Arabian astronomer of about A.D. 1000. After an exhaustive discussion during the last century (1836-71), it seems to be proved that the claim rested upon a mistake, and that the sole credit is due to Tycho Brahe (see Dreyer, p. 252). In fact, whatever in astronomy does not belong to modern science is Greek, after allowing for what the Greeks may have learnt in early ages from Chaldaeans or Egyptians. The Romans contributed nothing, the Indians learnt much from scientific men who accompanied Alexander, and used it skilfully, but did not advance it. And the modern makes a really continuous whole with the ancient Greeks, for it is not only astronomy which should be considered, but the essential preliminaries, such as the study of the Conic Sections, which, in its geometrical form, is purely Greek.

One authority to whom Plutarch twice refers by name requires special mention. This was Aristarchus of Samos, who belongs to the middle or later part of the third century B.C. He is the author of a work on ‘The Sizes and Distances of the Sun and Moon’ which is extant. It was well edited by Wallis for the Oxford Press in 1688, and more recently (1913) and in a modern form, by Sir Thomas Heath, F.R.S., who has prefixed an invaluable history of astronomy prior to Aristarchus. The book is rigorously mathematical, and contains six ‘hypotheses’, and eighteen propositions deduced from them. The second of the hypotheses, ‘That the earth is in the relation of a point and centre to the sphere in which the moon moves’, is quoted by Plutarch, apparently as being accepted by Hipparchus. The sixth, ‘That the moon subtends one-fifteenth part of a sign of the Zodiac (i. e. 2°)‘, raises a curious point which is fully considered by Sir T. Heath. That Aristarchus should at any time have thus exaggerated (multiplied by four) a measurement which seems open to some sort of simple observation, and have based good work upon it, seems very strange, firstly, because he must have considered the matter, (since he is aware that the same figure may stand for sun and moon); and, secondly, because Archimedes (287-212 B.C.), whose knowledge and good faith are beyond question, says that ‘Aristarchus discovered that the sun appeared to be about one seven hundred and twentieth part of the circle of the Zodiac (30´)‘, which is roughly correct.[302]

The fourth hypothesis runs: ‘That when the moon appears to us halved, its distance from the sun is then less than a quadrant by one-thirtieth of a quadrant (i.e. is 87°).’ From this is directly deduced (Hypothesis 6 is not here used) Prop. 7, an elaborate proof that ‘the distance of the sun from the earth is greater than eighteen times, but less than twenty times, the distance of the moon from the earth’, quoted by Plutarch in c. 10. The fact assumed does not appear to be open to observation; perhaps Aristarchus, or a predecessor, arrived at it by comparing the average times taken by the moon over the first and second quarters of her orbit. The true (theoretical) figure is 89° 50´. The sequel is very interesting. Hipparchus, a century later, adopted the result in calculating the parallax of the sun, which he found to be 3´ of arc (more than twenty times too much). This was adopted by Ptolemy in the second century A.D., and remained the official estimate until nearly A.D. 1700, though both Hipparchus and Kepler had protested, the latter stating as his opinion that the parallax could not be greater than one minute of arc, or the distance less than twelve millions of miles. Shortly before A.D. 1700 improved knowledge of the orbit and distances of Mars enabled the sun’s parallax to be reduced to 9-1/2 seconds of arc, and his distance stated at eighty-seven millions of miles, which is not very inadequate. It was a great achievement of Aristarchus, though he led the world into error, to state a reasoned figure at all, and to think in such mighty units.

His cosmical speculation is even more daring. It is known to us from this Dialogue (c. 6) and also from Archimedes, who records it in his (extant) _Arenarius_ without comment. Aristarchus proposed to ‘disturb the hearth of the universe’ by his hypothesis that the heaven of the stars is fixed, while the earth has a daily motion on her axis and an annual motion round the sun. It was a brilliant intuition, possible in an age of comparatively simple knowledge, which could not easily have been advanced when the complexity of the several orbits was increasingly realized (see Dreyer, pp. 147-8). Dr. Dreyer (p. 145) makes the interesting suggestion that Aristarchus took the idea from some early form of the system of ‘movable eccentrics’, and, further (p. 157), that if that system had prevailed against that of epicycles, it must have flashed, sooner or later, upon some bright mind, that there was one eccentric point, namely, one in the sun, central to the orbits of all the planets.

It is to be observed that ‘Heraclides of Pontus’ (at one time a pupil of Plato’s) discovered the movement of the two inner planets round the sun. It is possible (as contended by Sciaparelli) that he believed all the planets to move round the sun, and the sun round the earth, in fact anticipated Tycho Brahe. Further, there is a statement that he anticipated Aristarchus as to the movement of the earth; but Sir T. Heath, who examines the evidence very fully, concludes that the evidence has been misread. Aristarchus certainly contended for the diurnal rotation of the earth, but this was rejected by Hipparchus and passed out of account for many centuries.

The history of the emergence of the heliocentric theory has a curiously close counterpart in that of the circulation of the blood. Harvey communicated his discovery to the College of Physicians on April 17, 1616, but he had kept it back for twelve years out of deference to the great and deserved authority of Galen, which it was dangerous to dispute, as Copernicus held back his ‘Treatise of Revolutions’ for thirty years, because it was very dangerous, even for the nephew of a Bishop, himself the Canon of a cathedral far north of the Alps, to question the findings of Ptolemy. ‘Yet for years the profession had been in latent possession of a knowledge of the circulation. Indeed a good case has been made out for Hippocrates, in whose works occur some remarkably suggestive sentences’ (see _The Growth of Truth_, the Harveian Oration of 1906, by Sir William Osler, M.D., F.R.S.). Bacon, who ‘writes philosophy like a Lord Chancellor’—i.e. seeks to eliminate error from facts stated, and then to apply the law (see De Morgan, _Bundle of Paradoxes_, p. 50)—, would have none of the Copernican hypothesis. Nor would Sir Thomas Browne, though he preferred Dr. Harvey’s discovery ‘to that of America’. But truth will out, at her own time and through the ministers of her choice.

Behind the horseplay of the Stoics and Academics, on the subject of the centre of the universe and the laws which light and heavy bodies obey, there seems to lie some real groping after a general cosmic law, such as gravitation. Thus the earth and the moon draw bodies, each from its own surface to its own centre, and if the earth draws the moon, it is as a part of herself, once ejected and now reclaimed.

There is no direct evidence of the time or place when this Dialogue is supposed to take place, nor of the date of its composition. Much of the matter is common to it with the Dialogue _On the cessation of the Oracles_, one passage of which has been thought (by Adler) to be an extract from it. Lamprias takes the principal place in both, and Plutarch is not present, at least under his own name. The solar eclipse mentioned in c. 19 as recent would give a clue if it could be identified. Ginzel (_Spezieller Kanon_) has selected three for special consideration, viz., those of April 30, A.D. 59, March 20, A.D. 71, and January 5, A.D. 75. By the kindness of J. K. Fotheringham, Esq., D.Litt., Fellow of Magdalen College, who has made the laborious computation, I am able to state the respective magnitude of these eclipses at Chaeroneia as 11·08, 11·82, 10·38 (totality = 12). Thus Ginzel’s preference for No. 2 is confirmed; it was there a large partial eclipse, and the time of greatest phase was 11 hours 4·1 minutes local solar time. Several stars would become visible, 66/67 of the sun’s diameter being obscured; a few might be visible during No. 1, none during No. 3.

PERSONS OF THE DIALOGUE

1. SEXTIUS SYLLA, the Carthaginian, mentioned in the _Life of Romulus_ (c. 15) as ‘a man wanting neither learning nor ingenuity’, who had supplied Plutarch with a piece of archaeological information. Elsewhere (_De cohib. ira_, c. 1) he is addressed as ‘O most eager Sylla!’ In another Dialogue he declines to be led into a discussion on all cosmology by answering the question ‘whether the egg or the bird comes first?’ (_Sympos._ 2, 3).

He has a story, or myth, to tell about the moon, which he is impatient to begin. This story, which he had heard from a friend in Carthage, is mainly geographical in interest. The details remind us of those quoted from Pytheas about his journeys to Britain and the Northern Seas. The whole conception of the globe is clearly earlier than that of Ptolemy (see especially as to the Caspian Sea, c. 26). The myth also introduces us to the worship of Cronus as practised at Carthage, and connects it with the wonders of the moon, and her place in the heavenly system.

In c. 17 SYLLA raises a good point, about the half-moon, which was being passed over.

2. LAMPRIAS, a brother, probably an elder brother, of Plutarch directs the course of the conversation, and himself expounds the Academic view, referring to Lucius for his recollections of a recent discussion at which both had been present, when the Stoic doctrines on physics had been criticized.

In some of the Symposiacs and other dialogues Lamprias takes a similar place; in others both brothers take part. Lamprias probably died early.

‘Evidently a character, a good trencherman, as became a Boeotian, one who on occasion could dance the Pyrrhic war dance, who loved well a scoff and a jest ... and who, if he thrust himself somewhat brusquely into discussions which are going forward, was quite able to justify the intrusion.’—Archbishop Trench.

3. APOLLONIDES, astronomer and geometrician; perhaps the latter would be the more correct designation. In another Dialogue (_Sympos._ 3, 4) a ‘tactician’ of the name appears.

As Apollonius, the great mathematician (living about 200 B.C.) was also a geometrician who contributed to astronomical theory, not himself an astronomer, it seems likely that the name Apollonides has been coined by Plutarch for ‘one of the clan of Apollonius’, i. e. a young professor of geometry. Apollondes is treated rather brusquely by Lamprias, certainly with less respect than Menelaus. He seems to have cast in his lot with the Stoics in their physical opinions.

4. ARISTOTLE, a Peripatetic. Perhaps the name was given to him to mark the School to which he belonged. In the Dialogue _On the Delays in Divine Punishment_ an ‘Epicurus’ is a representative Epicurean.

5. PHARNACES, a Stoic, who sturdily supports his physical creed against all comers.

6. LUCIUS, an Etruscan pupil of Moderatus the Pythagorean, spoken of in one place (_Sympos._ 8, 7 and 8) as ‘Lucius our comrade’. He is elsewhere reticent as to the inner Pythagorean teaching, but is courteous and ready to discuss ‘what is probable and reasonable’.

Kepler is inclined to complain of his professorial tone and longwindedness in the present Dialogue. This is hardly fair, as he is for the most part reporting a set discourse heard elsewhere, and that by request. Lamprias has to give him time to remember the points (c. 7). In c. 5 he asks that justice may be done to the Stoics. He associates himself with the Academics on physical matters.

7. THEON (see Preface, p. xii), represents literature (as he does in other Dialogues, notably in that on the _E at Delphi_). He is a welcome foil to the more severe disputants. In c. 24 he interrupts by moving the previous question—‘Why a moon at all?’ and is congratulated on the cheerful turn which he has given to the discussion. Theon may sometimes recall to readers of Jules Verne’s pleasant _Voyage autour de la lune_ the sallies of Michel Ardan the poet.

8. MENELAUS, a distinguished astronomer who lived and observed at Alexandria. Observations of his, which include some taken in the first year of Trajan, A.D. 98, are recorded by Ptolemy (_Magna Syntaxis_, 7, 3, p. 170) and other writers.

ANALYSIS

[The opening chapters are lost. There must have been an introduction of the speakers, with some explanation as to time and place, a reference to a set discussion at which some of the speakers had been present, and a promise of Sylla to narrate a myth, bearing upon the moon and her markings, which he had heard in Carthage. This conversation had taken a turn, prematurely as SYLLA thinks, towards the mythical or supernatural aspects of the moon.] But see note (1) on p. 309.

c. 1. It is agreed that the current scientific or quasi-scientific views on the markings of the moon’s face shall be first considered, then the supernatural.

cc. 2-4. LAMPRIAS mentions

(i) The view that the markings are due to weakness of human eyesight. This is easily refuted.

(ii) The view of Clearchus, the Peripatetic, that they are caused by reflexion of the ocean on the moon’s face. But ocean is continuous, the markings are broken; they are seen from all parts of the earth, including ocean itself (and the earth is not a mere point in space, but has dimensions of its own); and, thirdly, they are not seen on any other heavenly body.

c. 3. The mention of Clearchus brings up the view, adopted from him by the Stoics, that the moon is not a solid or earth-like body, but is fire or air, like the stars. This view had been severely handled in the former conference.

c. 6. PHARNACES complains that the Academics always criticize, never submit to be criticized. Let them first answer for their own paradox in confusing ‘up’ and ‘down’, if they place a heavy body, such as the moon is now said to be, above. LUCIUS retorts: ‘Why not the moon as well as the earth, a larger body, yet poised in space?’ PHARNACES is unconvinced.

cc. 7-15. To give Lucius time to remember his points, LAMPRIAS reviews the absurd consequences from the Stoic tenet that all weights converge towards the centre of our earth. Why should not every heavy body, not earth only, attract its parts towards its own centre? Again, if the moon is a light fiery body, how do we find her placed near the earth and immeasurably far from the sun, planets, and stars? How can we assume that earth is the middle point of the Whole, that is, of Infinity? Lastly, allow that the Moon, if a heavy body, is out of her natural place. Yet why not? She may have been removed by force from the place naturally assigned to her to one which was better. Here the tone of the speaker rises as he lays down, often following the thought and the words of Plato’s _Timaeus_, the theory of creative ‘Necessity’ and ‘The Better’.

c. 16. LUCIUS is now ready to speak, but ARISTOTLE intervenes with a reference to the view, held by his namesake, that the stars are composed of something essentially different from the four elements, and that their motion is naturally circular, not up or down. LUCIUS points out that it is degrading to the moon to call her a star, being inferior to the stars in lustre and speed, and deriving her light from the sun. For this, the view of Anaxagoras and of Empedocles, is the only one consistent with her phases as we see them (not that quoted from Posidonius the Stoic).

cc. 17, 18. To an inquiry from SYLLA whether the difficulty of the half-moon (i. e. how does reflexion, being at equal angles, then carry sunlight to the earth, and not off into space beyond us?) had been met, Lucius answers that it had. The answer given was: (i) Reflexion at equal angles is not a law universally admitted or true; (ii) there may be cross lights and a complex illumination; (iii) it may be shown by a diagram, though this could not be done at the time (such a diagram is supplied by Kepler), that some rays would reach the earth; (iv) the difficulty arises at other phases also. He repeats the argument drawn from the phases as we see them; and ends with an analogy: Sunlight acts on the moon as it does on the earth, not as on the air; therefore the moon resembles earth rather than air.

c. 19. This is well received, and LUCIUS refers (a second analogy) to solar eclipses, and in particular to a recent one, to show that the moon, like the earth, can intercept the sun’s light, and is therefore, like it, a solid body. The fact that the track of the shadow is narrow in a solar eclipse is explained.

c. 20. LUCIUS continues his report, and describes in detail what happens in a lunar eclipse. If the moon, he concludes, were fiery and luminous, we should only see her at eclipse times, i. e. at intervals, normally of six months, occasionally of five.

c. 21. PHARNACES and APOLLONIDES both rise to speak. APOLLONIDES raises a verbal point about the word ‘shadow’; PHARNACES observes that the moon does show a blurred and fiery appearance during an eclipse, to which LAMPRIAS replies by enumerating the successive colours of the moon’s face during eclipse, that proper to herself being dark and earth-like, not fiery. He concludes that the moon is like our earth, with a surface broken into heights and gullies, which are the cause of the markings.

c. 22. APOLLONIDES objects that there can be no clefts on the moon with sides high enough to cast such shadows. LAMPRIAS replies that it is the distance and position of the light which matter, not the size of objects which break it;

c. 23. And goes on himself to supply a stronger objection—that we do not see the sun’s image in the moon—and the answer. This is twofold: (_a_) general, the two cases differ in all details; (_b_) personal to those who, like himself, believe the moon to be an earth, and to have a rough surface. Why should we see the sun mirrored in the moon, and not terrestrial objects or stars?

c. 24. Sylla’s myth is now called for, and the company sits down to hear it. But THEON interposes: Can the moon have inhabitants or support any life, animal or vegetable? If not, how is she ‘an earth’, and what is her use?

c. 25. Theon’s sally is taken in good part, and gravely answered at some length by LAMPRIAS.

c. 26. The mention of life on the moon calls up SYLLA, who again feels that he has been anticipated. He begins his myth, heard from a stranger met in Carthage, who had himself made the northward voyage and returned. Once in every thirty years (or year of the planet Saturn) an expedition is sent out from Carthage to certain islands in the Northern Atlantic where Cronus (Saturn) reigns in banishment. The stranger had charged Sylla to pay special honour to the moon,

cc. 27-29. instructing him as to the functions of Persephone in bringing about the second death—the separation of mind from soul—which takes place on the moon, and the genesis of ‘daemons’,

c. 30. to whom are assigned certain functions on earth. SYLLA commends the myth to his hearers.

OF THE FACE WHICH APPEARS ON THE ORB OF THE MOON

I. Here Sylla said:[303] ‘All this belongs to my story, and comes [Sidenote: 920 B] out of it. But I should like to ask in the first place whether you really backed on to those views about the moon’s face which are in every one’s hand and on every one’s lips.’ ‘Of course we did,’ I answered, ‘it was just the difficulty which we found in these which thrust us off upon the others. In chronic diseases, patients grow weary of the common remedies and plans of treatment, and turn to rites and charms and dreams. Just so in obscure and perplexing enquiries, when the common, received, familiar accounts are not convincing, [Sidenote: C] we cannot but try those which lie further afield; we must not despise them, but simply repeat to ourselves the spells which the old people used, and use all means to elicit the truth.

II. ‘To begin, you see the absurdity of calling the figure which appears in the moon an affection of our eyesight, too weak to resist the brightness, or, as we say, dazzled; and of not observing that this ought rather to happen when we look at the sun, who meets us with his fierce strong strokes. Empedocles has a pretty line giving the difference between the two:

_The sun’s keen shafts, and moon with kindly beams._

Thus he describes the attractive, cheerful, painless quality of her light. Further, the reason is given why men of dim and weak eyesight do not see any distinct figure in the moon; [Sidenote: D] her orb shines full and smooth to them, whereas strong-sighted persons get more details, and distinguish the features impressed there with clearer sense of contrast. Surely the reverse should happen if it were a weakness and affection of the eye which produced the image; the weaker the organ the clearer should be the appearance. The very irregularity of the surface is sufficient to refute this theory; this image is not one of continuous and confluent shadow, but is well sketched in the words of Agesianax: [Sidenote: E]

_All round as fire she shines, but in her midst, Bluer than cyanus, lo, a maiden’s eye, Her tender brow, her face in counterpart._