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.