June 4, 1891] 



NATURE 



107 



ON SOME POINTS IN THE EARLY HISTORY 

 OF ASTRONOMY} 



IV. 



FROM what has been stated it is not too much to 

 assume that the Egyptians observed the sun on the 

 horizon. This being so, the chances are that at first they 

 would observe the stars on the horizon too, both stars 

 rising and stars setting; and that is rendered more 

 probable by the very careful way in which early astro- 

 nomers defined the various conditions under which a star 

 can rise or set, always, be it well remembered, in relation 

 to the sun. They spoke of a star as rising or setting 

 achronically, heliacally, or cosmically. 



The cosmic rising meant that the star rose, and the- 

 cosmic setting meant that the star set, at the same moment 

 as the sun — that is, that along the eastern horizon we 

 should see the star rising at the moment of sunrise, 

 or along the western horizon a star setting at the 

 moment of the sun setting. The achronical rising is 

 different from the cosmic in this respect — that we have 

 the star rising when the sun is setting and setting 

 when the sun is rising. Finally we have the heliacal 

 rising and setting ; that is taken to be that the star 

 appeared in the morning a little in advance of the sun- 

 rise, or set at twilight a little later than the sun. The 

 following table from Biot^ should make matters quite 

 clear : — 



Star at eastern horizon. ... Rising. 



True or cosmic Sun rising. 



Morning. ... I Apparent or heliacal. 



Star at western horizon. 



Setting. .. 



True or achronic. 

 Evening. ...I Apparent or heliacal. 



Evening. 



Sun not yet risen, but depressed 

 below horizon sufficiently to 

 enable the star to be seen. 



Sun setting. 



Sun just set, and depressed 

 below horizon sufficiently to 

 enable the star to be seen. 



j' True or cosmic Sun setting. 



Apparent or heliacal. 





Sun set, and depressed below 

 horizon sufficiently to enable 

 the star to be seen. 



Morning. 



True or achronic Sun rising. 



Apparent or heliacal 



Sun not yet risen, but depressed 

 below horizon sufficiently to 

 enable the star to be seen. 



It is Ideler's opinion that, in Ptolemy's time, in the 

 case of stars of the first magnitude, for heliacal risings 

 and settings, if the star and sun were on the same 

 horizon a depression of ii° was taken; if on opposite 

 horizons a depression of 7^. For stars of the second 

 magnitude, these values were 14° and 8^.° But if temples 

 were employed as I have suggested, even cosmic and 

 achronic risings and settings could be observed in the 

 case of the brightest stars. 



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 what star is meant. We 

 can in these days define a star according to its constel- 

 lation 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. 



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 invariable for a thousand 

 years ; but one of the results of astronomical work is that 

 the stars are known to behave quite differently. In con- 

 sequence of what is called precession the stars change 

 their place with regard to the pole of the heavens, and 

 further, in consequence of this movement, the position of 

 the sun among the stars at the solstices and equinoxes 

 changes also. 



In the last lecture we considered what were called the 

 ecliptic and the equatorial co-ordinates. The ecliptic was 

 the plane in which the earth moves round the sun, and 

 90° from that plane we had the pole of the heavens ; 



' Ccntinued from p. 60. 



NO. I 127, VOL. 44] 



celestial latitude we found reckoned from the plane of the 

 ecliptic north and south up to the pole of the heavens, 

 and celestial longitude we reckoned along the plane of 

 the ecliptic from the first point of Aries. We had also 

 declination reckoned from the equator of the earth pro- 

 longed to the stars, and right ascension reckoned along 

 the equator from the first point of Aries. The pole of 

 the heavens then we must regard as fixed, but the pole 

 of the earth is not fixed, but slowly moves round it. In 

 consequence of that movement there is a change o/declma- 

 tion in a starts place. 



Going back to the tables, 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 at any particular place. 



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 rose in the east in a certain amplitude 

 this year will change its amplitude at some future time. 



The real cause of the precession of the stars lies in. 

 the fact that the earth is not a sphere, its equatorial 

 diameter being longer than its polar diameter, so that 

 there is a mass of matter round the equator in excess of 

 what we should get if the earth were spherical. Suppose 

 that matter to be represented by a ring. The ring is 

 differently presented to the sun, one part being nearer 

 than the other, the nearer part being attracted more 

 forcibly. If we take the point where there is the greatest 

 attraction, and draw a line to the least, we can show 

 that the case stands in this way : that the sun's pull 

 may be analyzed into two forces, one of them between 

 the sun and the point in a direction parallel to the 

 line joining the centre of the sun and the centre of the 



' Biot, " Traitd rfKmentaire d' Astronomic physique," 3rd edition, vol. iv. 

 p. 625. 



