Stargazing: Past and Present

by Sir Norman Lockyer

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 principles which all our modern instruments must and actually do fulfil.