INTRODUCTION
Plutarch’s Dialogue on The Face in the Moon is not a scientific treatise, and its author would have disclaimed any intention of writing to advance science. It is discussion for the sake of discussion, the ‘good talk’ of which Plutarch wished that Athens should have no monopoly, any more than she had when the Boeotian Simmias and Cebes were among the trusted friends of Socrates, or, later, when ‘plain living and high thinking’ could be exhibited in lofty perfection in the Theban home of Epaminondas. A mixed company, which includes an astronomer, another mathematician, a literary man, and professed philosophers (there is no Epicurean here), with Lamprias, Plutarch’s brother, for president, discusses the movements and physical nature of the moon, from many points of view. Reference is made throughout to a previous discussion at which Lamprias, and Lucius, another of the speakers, had been present, when a person called ‘Our Comrade’ had dealt faithfully with the Peripatetic view, endorsed by the Stoics, that the moon is not of substance like our earth, but is a fiery or starlike body. This discussion had wandered into mystical theories as to the moon’s office in the birth and death of human souls, and her connexion with ‘daemons’. Sylla has joined the present company with a myth to relate bearing on these deep subjects, which had come to him at Carthage as a traveller’s tale. Its production is delayed until the end of the Dialogue, which it closes after the manner of a Platonic myth; the phrases with which it is opened and dismissed may be compared with those of the Gorgias. This double device, of referring part of the matter to a former conversation (as the E at Delphi is a recollection of an old discourse by Ammonius), and part to a new and strange tale, skilfully relieves this elaborate Dialogue. Some difficulty is caused by the imperfect, or doubtful, condition of the text of the opening chapter, as no complete explanation seems to be given as to the place or time of the former discussion. Probably this abruptness is intentional, but the text requires careful attention.
Perhaps this Dialogue throws more light on the views about the solar system accepted or under discussion in the first century of our era than a scientific treatise could have done. No reference is made to the great astronomical work of Ptolemy, which belongs to the second century, and closed most questions until the sixteenth. The estimate, e.g. of the moon’s distance (56 earth’s radii) is not Ptolemy’s (59). Some of the geographical details, as that of the Caspian Sea, seem to show that Ptolemy’s geographical work was not known to the Author.
It may be useful to enumerate some of the simpler of the accepted views about the heavens :
(1) That the earth is a Sphere was known to Pythagoras and allowed by Plato (Phaedo 110 B), and affirmed by Aristotle, De Caelo, 2, 14, 297 b 18. The moon, and, according to Aristotle, the stars, are also spherical.
(2) That the moon derived her light from the sun was a discovery due to Anaxagoras (fifth century B.C.).
(3) The true cause of eclipses was known to the Pythagoreans, and is stated by Aristotle, and, with more precision, by Posidonius.
(4) The inclination of the equator to the sun’s path is stated by Oenopides of Chios (a little after Anaxagoras).
(5) That the moon revolves round the earth at a moderate distance is stated by Empedocles.
(6) The other planets (including the sun) revolve round the earth at a distance vastly less than that of the fixed stars. (No actual estimate of the distances or sizes is given even by Ptolemy, who is not able to state a parallax for any, or an angular diameter.)
(7) That the planets share in the (apparent) daily motion of the stars, and also have an (apparent) motion of their own in the reverse direction was held by Pythagoras.
All these refer to physical facts and can be stated without the use of mathematical language, though many of the discoverers were expert mathematicians. Gradually, and certainly from the time of the great astronomer Hipparchus (about 130 B.C.), attention came to be fixed upon the accurate mathematical interpretation of observed apparent facts; in a favourite phrase, the object was ‘to save the phenomena’, irrespective of physical and actual fact.
In the case of the moon, the two lines of inquiry are less sharply divided than in that of other bodies. Very correct statements as to her size and distance from the earth may be gathered from Plutarch’s Dialogue. A guess is even hazarded that she is lighter than the earth, bulk for bulk, because of the action of fire in the past.
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.