Great Astronomers by Robert Stawell Ball (best ereader for students .txt) 📖

Thus it was that Ptolemy came to the

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