The dawn of astronomy / A study of the temple-worship and mythology of the ancient Egyptians

by Sir Norman Lockyer

Among other important results of these movements dependent upon precession we have the various changes in the pole-star from period to period, due to the various positions occupied by the pole of the earth's equator. We thus see how in this period of 25,000 years or thereabouts the pole-stars will change, for a pole-star is merely the star near the pole of the equator for the time being. At present, as we all know, the pole-star is in the constellation Ursa Minor. During the last 25,000 years the pole-stars have been those lying nearest to a curved line struck from the pole of the heavens with a radius equal to the obliquity of the ecliptic, which, as we have seen, is liable to change within small limits; so that about 10,000 or 12,000 years ago the pole-star was no longer the little star in Ursa Minor that we all know, but the bright star Vega, in the constellation Lyra. Of course 25,000 years ago the pole-star was practically the same as it is at present.

Associated with this change in the pole-star, the point of intersection of the two fundamental planes (the plane of the earth's rotation and the plane of the earth's revolution) will be liable to change, and the period will be the same—about 25,000 years. Where these two planes cut each other we have the equinoxes, because the intersection of the planes defines for us the vernal and the autumnal equinoxes; when the sun is highest and lowest half-way between these points we have the solstices. In a period of 25,000 years the star which is nearest to an equinox will return to it, and that which is nearest a solstice will return to it. During the period there will be a constant change of stars marking the equinoxes and the solstices.

The chief points in the sun's yearly path then will change among the stars in consequence of this precession. It is perfectly clear that if we have a means of calculating back the old positions of stars, and if we have any very old observations, we can help matters very much, because the old observations—if they were accurately made—would tell us that such and such a star rose with the sun at the solstice or at the equinox at some special point of ancient time. If it be possible to calculate the time at which the star occupied that position with regard to the sun, we have an astronomical means of determining the time, within a few years, at which that particular observation was made.

Fortunately, we have such a means of calculation, and it has been employed very extensively at different periods, chiefly by M. Biot in France, and quite recently by German astronomers, in calculating the positions of the stars from the present time to a period of 2000 years B.C. We can thus determine with a very high degree of accuracy the latitude, longitude, right ascension, declination, and the relation of the stars to an equinox, a solstice, or a pole, as far back as we choose. Since we have the planes of the equator and ecliptic cutting each other at different points in consequence of the cause which I have pointed out—the attraction of the sun and moon—we have a fixed equator and a variable equator depending upon that. In consequence of the attraction of the planets upon the earth, the plane of the ecliptic itself is not fixed, so that we have not only a variable equator, but also a variable ecliptic. What has been done in these calculations is to determine the relations and the results of these variations.

The calculations undertaken for the special purposes of this book will be referred to later.

A simpler, though not so accurate a method consists in the use of a processional globe. In this we have two fixed points at the part of the globe representing the poles of the heavens, on which the globe may be rotated; when this is done the stars move absolutely without any reference to the earth or to the plane of the equator, but purely with reference to the ecliptic. We have, then, this globe quite independent of the earth's axis, flow can we make it dependent upon the earth's axis? We have two brass circles at a distance of 23½° from each pole of the heavens (north and south); these represent the circle described by the pole of the earth in the period of 25,000 years. In these circles are forty-eight holes in which I can fix two additional clamping screws, and rotate the globe with respect to them by throwing out of gear the two points which produced the ecliptic revolution.

If I use that part of the brass circle which is occupied by our present pole-star, we get the apparent revolution of the heavens with the earth's axis pointing to the pole-star of to-day. If we wish to investigate the position of things, say 8,000 years ago, we bring the globe back again to its bearings, and then adjust the screws into the holes in the brass circles which are proper for that period. When we have the globe arranged to 6000 years B.C. (i.e., 8,000 years ago), in order to determine the equator at that time all we have to do is to paint a line on the globe-in some water-colour, by holding a camel's-hair pencil at the east or west point of the wooden horizon. That line represents the equator 8,000 years ago. Having that line, of course, the intersection of the equator with the ecliptic will give us the equinoxes, so that we may affix a wafer to represent the vernal equinox. Or if we take that part of the ecliptic which is nearest to the North Pole, and, therefore, the N. declination of which is greatest, viz., 23½° N., we have there the position of the sun at the summer solstice, and 23½° S. will give us the position of the sun at the winter solstice. So by means of such a globe as this it is possible to determine roughly the position of the equator among the stars, and note those four important points in the solar year, the two equinoxes and the two solstices. I have taken a period of 8,000 years, but I might just as easily have taken a greater or a smaller one. By means of this arrangement, therefore, we can determine within a very small degree of error, without any laborious calculations, the distance of a star north or south of the equator, i.e., its declination, at any point of past or future time.

The positions thus found, say, for intervals of 500 years, may be plotted on a curve, so that we can, with a considerable amount of accuracy, obtain the star's place for any year. Thus the globe may be made to tell us that in the year 1000 A.D. the declination of Fomalhaut was 35° S., in 1000 B.C. it was 42°, in 2000 it was about 44°, in 4000 it was a little over 42° again, but in 6000 B.C. it had got up to about 33°, and in 8000 B.C. to about 22°.

The curve of Capella falls from 41° N. at 0 A.D. to 10° at 5500 B.C., so we have in these 5500 years in the case of this star run through a large part of that variation to which I have drawn attention.

I have ascertained that the globe is a very good guide indeed within something like 1° of declination. Considering the difficulty of the determination of amplitudes in the case of buildings, it is clear that the globe may be utilised with advantage, at all events to obtain a first approximation.