Stargazing: Past and Present. Sir Norman Lockyer
Fig. 2.—The Zodiac of Denderah.
Now let us see how Posidonius a long time afterwards (he was born about 135 years B.C.) applied this conception. He observed that at Rhodes the star Canopus grazed the horizon at culmination, while at Alexandria it rose above it 7½°. Now 7½° is 1 48 of the whole circle; so he found that from the latitude of Rhodes to that of Alexandria was 1 48 of the circumference of the earth. He then estimated the distance, getting 5,000 stadia as the result; and this multiplied by 48 gave him 240,000 stadia, his measure of the circumference of the earth.
When the sun’s yearly course in the heavens had been determined, it was found that it was restricted to that band of stars called the Zodiac, Fig. 2; the sun’s position in the zodiac at any one time of the year being found by the midnight culmination of the stars opposite the sun; this and the apparent and heliacal risings and settings were alone the subjects of observation.
It is obvious, then, that when observations of this nature had gone on for some time, men would be anxious to map the stars, to make a chart of the field of heaven; and such a work was produced by Autolycus three and a half centuries before Christ. We also owe to Autolycus and Euclid, who flourished about the same time (300 B.C.), the first geometrical conceptions connected with the apparent motions of the stars.
In the theorems of Autolycus there is a particular reference to the twelve parts of the zodiac, as denoted by constellations. The following are the most important propositions which he lays down:—
1. “The zodiacal sign occupied by the sun neither rises nor sets, but is either concealed by the earth or lost in the sun’s rays. The opposite sign neither rises nor sets, i.e., visibly, i.e., after sundown, but it is visible during the whole night.
2. “Of the twelve signs of the zodiac, that which precedes the sign occupied by the sun rises visibly in the morning; that which succeeds the same sign sets visibly in the evening.
3. “Eleven signs of the zodiac are seen every night. Six signs are visible, and the five others, not occupied by the sun, afterwards rise.
4. “Every star has an interval of five months between its morning and its evening rising, during which time it is visible. It has an interval of at least thirty days—between its evening setting, and its morning rising—during which time it is invisible.” (That is, the space passed over by the sun in its annual path is such that a star which you see on one side of the sun, when the sun rises at one time, would be seen a month afterwards on the other side of the sun.)
Autolycus makes no mention of the planets. Their irregular movements rendered them unsuited to the practical object which he had in view. He is, however, stated by Simplicius, as quoted by Sir G. C. Lewis to have proposed some hypothesis for explaining their anomalous motions, and to have failed in his attempt.
Euclid carries the results arrived at in this early pre-telescopic age much further; in a little-known treatise, the Phenomena,[3] he thus sums up the knowledge then acquired:—
“The fixed stars rise at the same point, and set at the same point; the same stars always rise together, and set together, and in their course from the east to the west they always preserve the same distance from one another. Now, as these appearances are only consistent with a circular movement, when the eye of the observer is equally distant from the circumference of the circle in every direction (as has been demonstrated in the treatise on Optics), it follows that the stars move in a circle and are attached to a single body, and that the vision is equally distant from the circumference.
Fig. 3.—Illustration of Euclid’s statements. P the star between the Bears. D D´ the region of the always visible. C B A the regions of the stars which rise and set.
“A star is visible between the Bears, not changing its place, but always revolving upon itself. Since this star appears to be equally distant from every part of the circumference of each circle described by the other stars, it must be assumed that all the circles are parallel, so that all the fixed stars move along parallel circles, having this star as their common pole.
“Some of these neither rise nor set, on account of their moving in elevated circles, which are called the ‘always visible.’ They are the stars which extend from the visible pole to the Arctic circle. Those which are nearest the pole describe the smallest circle, and those upon the Arctic circle the largest. The latter appears to graze the horizon.
“The stars to the south of this circle all rise and set, on account of their circles being partly above and partly below the earth. The segments above the earth are large and the segments below the earth are small in proportion as they approach the Arctic circle, because the motion of the stars nearest the circle above the earth is made in the longest time, and of those below the earth in the shortest. In proportion as the stars recede from this circle, their motion above the earth is made in less time, and that below the earth in greater. Those that are nearest the south are the least time above the earth, and the longest below it. The stars which are upon the middle circle make their times above and below the earth equal; whence this circle is called the Equinoctial. Those which are upon circles equally distant from the equinoctial make the alternate segments in equal times. For example, those above the earth to the north correspond with those below the earth to the south; and those above the earth to the south correspond with those below the earth to the north. The joint times of all the circles above and below the earth are equal. The circle of the milky way and the zodiacal circle being oblique to the parallel circles, and cutting each other, always have a semicircle above the earth.
“Hence it follows that the heaven is spherical. For if it were cylindrical or conical, the stars upon the oblique circles, which cut the equator, would not in the revolution of the heaven always appear to be divided into semicircles; but the visible segment would sometimes be greater and sometimes less than a semicircle. For if a cone or a cylinder were cut by a plane not parallel to the base, the section is that of an acute-angled cone, which resembles a shield (an ellipse). It is, therefore, evident that if a figure of this description is cut in the middle both in length and breath, its segments will be unequal. But the appearances of the heaven agree with none of these results. Therefore the heaven must be supposed to be spherical, and to revolve equally round an axis of which one pole above the earth is visible and the other below the earth is invisible.
“The Horizon is the plane reaching from our station to the heaven, and bounding the hemisphere visible above the earth. It is a circle; for if a sphere be cut by a plane the section is a circle.
“The Meridian is a circle passing through the poles of the sphere, and at right angles to the horizon.
“The Tropics are circles which touch the zodiacal circle, and have the same poles as the sphere. The zodiacal and the equinoctial are both great circles, for they bisect one another. For the beginning of Aries and the beginning of the Claws (or Scorpio) are upon the same diameter; and when they are both upon the equinoctial, they rise and set in conjunction, having between their beginnings six of the twelve signs and two semicircles of the equinoctial; inasmuch as each beginning, being upon the equinoctial, performs its movement above and below the earth in equal times. If a sphere revolves equally round its axis, all the points on its surface pass through similar axes of the parallel circles in equal times. Therefore these signs pass through equal axes of the equinoctial, one above and the other below the earth; consequently the axes are equal, and each is a semicircle; for the circuit from east to east and from west to west is an entire circle. Consequently the zodiacal and equinoctial circles bisect one another; each will be a great circle. Therefore the zodiacal and equinoctial are great circles. The horizon is likewise a great circle; for it bisects the zodiacal and equinoctial, both great circles. For it always has six of the twelve signs above the earth, as well as a semicircle of the equator. The stars above the horizon which rise and set together reappear in equal times, some moving from east to west, and some from west to east.”
We have given this long extract in justice to the men of old, containing as it does many of those geometrical