But it must not be imagined that, even in Egypt, all stars can be observed the moment they are above the horizon. In the morning, especially, there are mists, so that all but the brightest stars are often invisible till they are 1° or 2° high. On this point I quote Biot:—
"Comme le rapporte Nouet, l'astronome de l'expédition française, on n'y aperçoit jamais à leur lever les étoiles de 2° et de 3° grandeur même dans les plus belles nuits, à cause d'une bande constant de vapeurs qui borde l'horizon.[38] Aussi en expliquant le calcul des levers héliaques dans l'Almageste, Ptolémée a-t-il soin de remarquer[39] que les annonces qu'on voudrait faire de ces phénomènes seront toujours très-incertaines, à cause de l'état des couches d'air dans lesquelles on les observe, et à cause de la difficulté optique qu'on éprouve à saisir la première apparition, comme il dit lui-même en avoir fait l'expérience."[40]
Before we begin to consider the question of stars at all, we must be able to describe them—to speak of them in a way that shall define exactly which star is meant. We can in these days define a star according to its constellation, or its equatorial or ecliptic co-ordinates, but all these means of reference were unknown to the earliest observers. Still we may assume that the Egyptians could define some of the stars in some fashion; and it is evident that we here approach a matter of the very highest importance for our subject, to which I shall have to return in a subsequent chapter.
So far as we have been dealing with the sun and the observations of the sun at rising and setting, we have taken for granted that the amplitude of the sun at the solstices does not change; the amplitude of 26° at Thebes for the solstices is practically, though as we have seen not absolutely, invariable for a thousand years; but one of the results of astronomical work is that the stars are known to behave quite differently. In consequence of what is called precession the stars change their place with regard to the pole of the equator; and further, in consequence of this movement, the position of the sun among the stars at the solstices and equinoxes changes also.
In reference to the sun's path we considered what are called the ecliptic and the equatorial co-ordinates. The ecliptic defines the plane in which the earth moves round the sun, and 90° from that plane we have the pole of the heavens; celestial latitude we found reckoned from the plane of the ecliptic north and south up to the pole of the heavens, and celestial longitude was reckoned along the plane of the ecliptic from the first point of Aries. We had also declination reckoned from the equator of the earth prolonged to the stars, and right ascension reckoned along the equator from the first point of Aries.
The pole of the heavens or of the ecliptic, then, we must regard as practically, but not absolutely, fixed; but the pole of the earth's equator is not fixed, it slowly moves round the pole of the heavens. In consequence of that movement there is a change of declination in a star's place.
Going back to the diagram (p. 49), we find that the amplitude of a body rising or setting at Thebes or anywhere else depends upon its declination; so that if from any cause the declination of a star changes, its amplitude must change.
That is the first point where we meet with difficulty, because if the amplitude changes it is the same as saying that the place of star-rising or star-setting changes; that is, a star which rises in the east in a certain amplitude this year will change its amplitude at some future time.
In the last chapter I referred to one of the difficulties of modern inquiries into the orientation of ancient temples, which arises from the fact that the sun has not always, at the solstices, risen or set at exactly the same points of the horizon. We now find ourselves face to face with the fact that the stars do not rise or set at the same points century after century. We saw that the change in the position of the sun on the horizon at the solstices is due to a very small change of obliquity of the ecliptic, so that in a matter of something like 6,000 years the position of the sun at sunrise and sunset on the horizon may be varied by, roughly speaking, 1 degree. But in the case of the stars the matter is very much more serious, because in the course of something like 13,000 years the rising-or setting-places of a star may vary by something like 47° along the horizon north or south.
So that in the cases both of sun and stars there is no real fixity in the places of rising or setting, although of course those who made the first observations and built the first temples were not in a position to know this.