A Source Book in Greek Science

Author: Claudius Ptolemy


The Precession of the Equinoxes

Ptolemy, Almagest VII. 1–2. Translation of T. L. Heath, Greek Astronomy

First of all we must premise, as regards the name ("fixed stars"), that, since the stars themselves always appear to keep the same figures and the same distances from each other, we may fairly call them "fixed," but, on the other hand, seeing that their whole sphere on which they are carried round as if they had grown upon it, appears itself to have an ordered movement of its own in the direct order of the signs, that is, towards the east, it would not be right to describe the sphere itself also as "fixed." We find both these facts to be as stated, judging by observations made so far as was possible in a comparatively short period. At an even earlier date Hip-parchus, in consequence of the phenomena which he had recorded, became vaguely aware of the two facts,1 but, as regards the effects over a longer time, what he gave were guesses rather than facts thoroughly established, because he had come across only very few observations of the fixed stars made before his own time, and, indeed, almost the only observations he found recorded were those of Aristyllus and Timocharis,1 and even these were neither flee from doubt nor thoroughly worked out. We, for our part, have found the same result by comparing observations made to-day with those of the earlier time, but the result is now more firmly established by virtue of the fact that the inquiry has now lasted over a longer period, and the recorded data of Hipparchus about the fixed stars, with which our comparisons have mainly been made, have been handed down to us fully worked out. . . .

That the sphere of the fixed stars has a movement of its own in a sense opposite to that of the revolution of the whole universe, that is to say, in the direction which is east of the great circle described through the poles of the equator and the zodiac circle, is made clear to us especially by the fact that the same stars have not kept the same distances from the solstitial and equinoctial points in earlier times and in our time respectively, but, as time goes on, are found to be continually increasing their distance, measured in the eastward direction, from the same points beyond what it was before.

For Hipparchus, in his work "On the displacement of the solstitial and equinoctial points," comparing the eclipses of the moon, on the basis both of accurate observations made in his time, and of those made still earlier by Timocharis, concludes that the distance of Spica from the autumnal equinoctial point, measured in the inverse order of the signs, was in his own time 6° but in Timocharis’ time 8° nearly. His words at the end are: "If then, for the sake of argument, Spica was, longitudinally with respect to the signs, at the earlier date 8° west Of the autumnal-equinoctial point, but is now 6° west of it," and so on.2 And in the case of practically all the other fixed stars the position of which he has similarly compared he shows that there has been the same amount of progression in the direct order of the signs. . . .3

This [i.e., an increase in longitude at the rate of about 1° in 100 years] seems to have been the idea of Hipparchus to judge by what he says, in his work "On the length of the year": "If for this reason the solstices and the equinoxes had changed their position in the inverse order of the signs, in one year, by not less than

their displacement in 300 years should not have been less than 3°."

1 By comparison of his own observations of the position of certain fixed stars with those made some 160 years earlier, Hipparchus showed that there had been a change in longitude, or, what is equivalent, a displacement of the points at which the equator and ecliptic intersect. The displacement was in a direction opposite to the diurnal motion of the universe. On the assumption that the displacement was a uniform one, Hipparchus estimated its extent as at least 36″ a year or 1° a century. This phenomenon, known as the precession of the equinoxes, is in large measure due to the fact that the earth is not a perfect sphere. The sun and moon, by their attraction of the matter at the equatorial bulge, tend to draw the plane of the equator into coincidence with that of the ecliptic. Consequently the earth’s axis does not remain constantly parallel to itself, but very slowly turns about an axis passing through the center of the earth and perpendicular to the earth’s orbit. That is, the celestial pole traces what is approximately a circle whose center is the pole of the ecliptic and angular radius

This circle is traced in a period of about 25,000 years. The extent of the precession is now calculated as approximately 50″ per annum.

The westward displacement of the equinox makes the sun’s path along the ecliptic from one vernal equinox to the next (the tropical year) shorter than the path from a given fixed star back to the same fixed star (the sidereal year). Hipparchus gives the tropical year (Ptolemy, Almagest III. 1) as

less 1/300 of a day, i.e., 365d. 5h. 55m. 12s. (The modern estimate is 365d. 5h. 48m. 46s.)

The discovery of a kind of precession has sometimes been credited to the Babylonian astronomer Kidinnu (probably of the fourth century B.C.). O. Neugebauer, in Journal of Cuneiform Studies 1 (1947) 147, holds this ascription false, and indicates an alternative explanation of the supposed evidence. [Edd.]

1 Aristyllus and Timocharis made observations at Alexandria at the beginning of the third century B.C. [Edd.]

2 If, as seems to be the case, the variation was 2° in about 160 years, the precession would amount to 45″ per annum, a result much more accurate than 36″, given by Hipparchus as a lower limit and adopted by Ptolemy as the true value. [Edd.]

3 Ptolemy then gives as an example the increase in longitude of the star Regulus. Comparing an observation of Hipparchus with one taken by himself, Ptolemy makes the difference in longitude 2°40′ in 265 years, or about 1° in a century. [Edd.]


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Chicago: Claudius Ptolemy, "The Precession of the Equinoxes," A Source Book in Greek Science, trans. T. L. Heath in A Source Book in Greek Science, ed. Morris R. Cohen and I. E. Drabkin (Cambridge: Harvard University Press, 1948), 115–117. Original Sources, accessed July 2, 2022, http://originalsources.com/Document.aspx?DocID=56JSR85842WZNLW.

MLA: Ptolemy, Claudius. "The Precession of the Equinoxes." A Source Book in Greek Science, translted by T. L. Heath, Vol. VII., in A Source Book in Greek Science, edited by Morris R. Cohen and I. E. Drabkin, Cambridge, Harvard University Press, 1948, pp. 115–117. Original Sources. 2 Jul. 2022. http://originalsources.com/Document.aspx?DocID=56JSR85842WZNLW.

Harvard: Ptolemy, C, 'The Precession of the Equinoxes' in A Source Book in Greek Science, trans. . cited in 1948, A Source Book in Greek Science, ed. , Harvard University Press, Cambridge, pp.115–117. Original Sources, retrieved 2 July 2022, from http://originalsources.com/Document.aspx?DocID=56JSR85842WZNLW.