Great Astronomers - Robert Stawell Ball (the little red hen ebook .TXT) 📗
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conclusion that they were all fixed on one spherical surface,
though we are not informed as to the material of this marvellous
setting which sustained the stars like jewels.
Nor should we hastily pronounce this doctrine to be absurd. The
stars do appear to lie on the surface of a sphere, of which the
observer is at the centre; not only is this the aspect which the
skies present to the untechnical observer, but it is the aspect in
which the skies are presented to the most experienced astronomer
of modern days. No doubt he knows well that the stars are at the
most varied distances from him; he knows that certain stars are
ten times, or a hundred times, or a thousand times, as far as
other stars. Nevertheless, to his eye the stars appear on the
surface of the sphere, it is on that surface that his measurements
of the relative places of the stars are made; indeed, it may be
said that almost all the accurate observations in the observatory
relate to the places of the stars, not as they really are, but as
they appear to be projected on that celestial sphere whose
conception we owe to the genius of Ptolemy.
This great philosopher shows very ingeniously that the earth must
be at the centre of the sphere. He proves that, unless this were
the case, each star would not appear to move with the absolute
uniformity which does, as a matter of fact, characterise it. In
all these reasonings we cannot but have the most profound
admiration for the genius of Ptolemy, even though he had made an
error so enormous in the fundamental point of the stability of
the earth. Another error of a somewhat similar kind seemed to
Ptolemy to be demonstrated. He had shown that the earth was an
isolated object in space, and being such was, of course, capable
of movement. It could either be turned round, or it could be
moved from one place to another. We know that Ptolemy
deliberately adopted the view that the earth did not turn round;
he had then to investigate the other question, as to whether the
earth was animated by any movement of translation. He came to the
conclusion that to attribute any motion to the earth would be
incompatible with the truths at which he had already arrived. The
earth, argued Ptolemy, lies at the centre of the celestial sphere.
If the earth were to be endowed with movement, it would not lie
always at this point, it must, therefore, shift to some other part
of the sphere. The movements of the stars, however, preclude the
possibility of this; and, therefore, the earth must be as devoid
of any movement of translation as it is devoid of rotation. Thus
it was that Ptolemy convinced himself that the stability of the
earth, as it appeared to the ordinary senses, had a rational
philosophical foundation.
Not unfrequently it is the lot of the philosophers to contend
against the doctrines of the vulgar, but when it happens, as in
the case of Ptolemy’s researches, that the doctrines of the vulgar
are corroborated by philosophical investigation which bear the
stamp of the highest authority, it is not to be wondered at that
such doctrines should be deemed well-nigh impregnable. In this
way we may, perhaps, account for the remarkable fact that the
theories of Ptolemy held unchallenged sway over the human
intellect for the vast period already mentioned.
Up to the present we have been speaking only of those primary
motions of the heavens, by which the whole sphere appeared to
revolve once every twenty-four hours. We have now to discuss the
remarkable theories by which Ptolemy endeavoured to account for
the monthly movement of the moon, for the annual movement of the
sun, and for the periodic movements of the planets which had
gained for them the titles of the wandering stars.
Possessed with the idea that these movements must be circular, or
must be capable, directly or indirectly, of being explained by
circular movements, it seemed obvious to Ptolemy, as indeed it had
done to previous astronomers, that the track of the moon through
the stars was a circle of which the earth is the centre.
A similar movement with a yearly period must also be attributed to
the sun, for the changes in the positions of the constellations in
accordance with the progress of the seasons, placed it beyond
doubt that the sun made a circuit of the celestial sphere, even
though the bright light of the sun prevented the stars in its
vicinity, from being seen in daylight. Thus the movements both of
the sun and the moon, as well as the diurnal rotation of the
celestial sphere, seemed to justify the notion that all celestial
movements must be “perfect,” that is to say, described uniformly
in those circles which were the only perfect curves.
The simplest observations, however, show that the movements of the
planets cannot be explained in this simple fashion. Here the
geometrical genius of Ptolemy shone forth, and he devised a scheme
by which the apparent wanderings of the planets could be accounted
for without the introduction of aught save “perfect” movements.
To understand his reasoning, let us first set forth clearly those
facts of observation which require to be explained. I shall take,
in particular, two planets, Venus and Mars, as these illustrate,
in the most striking manner, the peculiarities of the inner and
the outer planets respectively. The simplest observations would
show that Venus did not move round the heavens in the same fashion
as the sun or the moon. Look at the evening star when brightest,
as it appears in the west after sunset. Instead of moving towards
the east among the stars, like the sun or the moon, we find, week
after week, that Venus is drawing in towards the sun, until it is
lost in the sunbeams. Then the planet emerges on the other side,
not to be seen as an evening star, but as a morning star. In
fact, it was plain that in some ways Venus accompanied the sun in
its annual movement. Now it is found advancing in front of the
sun to a certain limited distance, and now it is lagging to an
equal extent behind the sun.
[FIG. 1. PTOLEMY’S PLANETARY SCHEME.]
These movements were wholly incompatible with the supposition
that the journeys of Venus were described by a single motion of
the kind regarded as perfect. It was obvious that the movement
was connected in some strange manner with the revolution of the
sun, and here was the ingenious method by which Ptolemy sought to
render account of it. Imagine a fixed arm to extend from the
earth to the sun, as shown in the accompanying figure (Fig. 1),
then this arm will move round uniformly, in consequence of the
sun’s movement. At a point P on this arm let a small circle be
described. Venus is supposed to revolve uniformly in this small
circle, while the circle itself is carried round continuously by
the movement of the sun. In this way it was possible to account
for the chief peculiarities in the movement of Venus. It will be
seen that, in consequence of the revolution around P, the
spectator on the earth will sometimes see Venus on one side of the
sun, and sometimes on the other side, so that the planet always
remains in the sun’s vicinity. By properly proportioning the
movements, this little contrivance simulated the transitions from
the morning star to the evening star. Thus the changes of Venus
could be accounted for by a Combination of the “perfect” movement
of P in the circle which it described uniformly round the earth,
combined with the “perfect” motion of Venus in the circle which it
described uniformly around the moving centre.
In a precisely similar manner Ptolemy rendered an explanation of
the fitful apparitions of Mercury. Now just on one side of the
sun, and now just on the other, this rarely-seen planet moved like
Venus on a circle whereof the centre was also carried by the line
joining the sun and the earth. The circle, however, in which
Mercury actually revolved had to be smaller than that of Venus, in
order to account for the fact that Mercury lies always much closer
to the sun than the better-known planet.
[FIG. 2. PTOLEMY’S THEORY OF THE MOVEMENT OF MARS.]
The explanation of the movement of an outer planet like Mars could
also be deduced from the joint effect of two perfect motions. The
changes through which Mars goes are, however, so different from
the movements of Venus that quite a different disposition of the
circles is necessary. For consider the facts which characterise
the movements of an outer planet such as Mars. In the first
place, Mars accomplishes an entire circuit of the heaven. In this
respect, no doubt, it may be said to resemble the sun or the moon.
A little attention will, however, show that there are
extraordinary irregularities in the movement of the planet.
Generally speaking, it speeds its way from west to east among the
stars, but sometimes the attentive observer will note that the
speed with which the planet advances is slackening, and then it
will seem to become stationary. Some days later the direction of
the planet’s movement will be reversed, and it will be found
moving from the east towards the west. At first it proceeds
slowly and then quickens its pace, until a certain speed is
attained, which afterwards declines until a second stationary
position is reached. After a due pause the original motion from
west to east is resumed, and is continued until a similar cycle of
changes again commences. Such movements as these were obviously
quite at variance with any perfect movement in a single circle
round the earth. Here, again, the geometrical sagacity of Ptolemy
provided him with the means of representing the apparent movements
of Mars, and, at the same time, restricting the explanation to
those perfect movements which he deemed so essential. In Fig. 2
we exhibit Ptolemy’s theory as to the movement of
Mars. We have, as before, the earth at the centre, and the sun
describing its circular orbit around that centre. The path of Mars
is to be taken as exterior to that of the sun. We are to suppose
that at a point marked M there is a fictitious planet, which
revolves around the earth uniformly, in a circle called the
DEFERENT. This point M, which is thus animated by a perfect
movement, is the centre of a circle which is carried onwards
with M, and around the circumference of which Mars revolves
uniformly. It is easy to show that the combined effect of these
two perfect movements is to produce exactly that displacement of
Mars in the heavens which observation discloses. In the position
represented in the figure, Mars is obviously pursuing a course
which will appear to the observer as a movement from west to east.
When, however, the planet gets round to such a position as R, it
is then moving from east to west in consequence of its revolution
in the moving circle, as indicated by the arrowhead. On the other
hand, the whole circle is carried forward in the opposite
direction. If the latter movement be less rapid than the former,
then we shall have the backward movement of Mars on the heavens
which it was desired to explain. By a proper adjustment of the
relative lengths of these arms the movements of the planet as
actually observed could be completely accounted for.
The other outer planets with which Ptolemy was acquainted, namely,
Jupiter and Saturn, had movements of the same general character as
those of Mars. Ptolemy was equally successful
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