Dodwell: The Obliquity of the Ecliptic

 

CHAPTER SIX

OBSERVATIONS OF THE OBLIQUITY OF THE ECLIPTIC MADE BY THE MEDIAEVAL ARABS AND PERSIANS

 

Numerous observations of the Obliquity of the Ecliptic were made by Arab and Persian astronomers between the years 830 A.D., and 1020 A.D.

The sites of the observations were:

Site Latitude Longitude
Bagdad (Iraq)
33° 21’ N. 44° 28’ E.
Rakka (near the River Euphrates in Syria
35° 57’ N. 39° 55’ E.
Damascus (Syria)
33° 30’ N. 36° 18’ E.
Shiraz (Persia)
29° 30’ N 52° 40’ E.
Edessa (Turkey in Asia)
37° 11’ N. 38° 55’ E.
Cairo (Egypt)
30° 03’  N. 31° 15’ E.

 

The first Arab Observatory at Bagdad, combined with a magnificent Library, and called the “House of Wisdom,” was erected about 820 A.D. by the Seventh Caliph of Bagdad, Al Mamun, son of Haroun al Raschid.  In addition to his celebrated measurement of a degree of latitude on the Earth’s surface, to determine the size of the Earth, Al Mamun also took much trouble to determine the Obliquity of the Ecliptic.

Some authorities give his results as 23° 33’, but the Arabs generally adopted 23° 35’ as the most reliable value.  Ibn Junis reports the following passage from Ebn-Hatem-Alnairizi (some time after the death of al Mamun in 833 A.D.):

The Obliquity of the Ecliptic of the astronomers of Al Mamun is that which still exists in our time.  It was observed by them with great exactness, and although they have not equally succeeded in their observations because of the knowledge which they lacked, nevertheless these observations have been very well made because of the size and excellence of the instruments, and the little difficulty of the operation, and the help which they had.  This obliquity is 23° 35’.

Al Fargani (Alfraganus) about 850 A.D., in his textbook Elements of Astronomy and Chronology, which was very highly thought of in Mediaeval Europe, also gives the value 23° 35’ for the obliquity determined by Al Mamun.  The Obliquity, he says, was found by Ptolemy to be 23° 51’, “but according to the measurement ordered to be made by Al Mamun of Pious Memory, which was carried out by a number of experts, it is 23° 35’.”  This value is adopted and quoted throughout the book of Aflraganus. (1)

In the development of Arab Astronomy, we may note that the first stage was the collection of astronomical literature from all available sources:  Greek, Hindu, Egyptian, Persian, etc., and their translation into Arabic. 

After the sack of Bagdad in 1258 A.D., the great Astronomical Library of Bagdad is believed to have formed the nucleus of the Mongol library at Maragha in Persia, said to have contained 400,000 books.  (Dr. Martin Johnson, “the Manuscripts of Bagdad Astronomers,” in the Magazine “Observatory” Vol. LIX, No. 746, July 1936, p. 216).

The next stage was the construction of new and improved instruments for astronomical observations, and the checking, by their means, of the results of former times.  The Arab astronomers became noted as good observers, and skilled in instrument making.  They also made important improvements in mathematics, introduced decimal notation, and constructed tables for the facilitation of astronomical calculations.

In Mamun’s Caliphate, the inclination of the Ecliptic was obtained from a Pillar, or Gnomon, surrounded by concentric circles, the vertical and horizontal being secured by a plumb-line and water level. Contact of the Pillar’s shadow with one of the circles at two points, before and after noon, gave an angle whose bisection determined the meridian.  The zenith distances of the Sun were obtained from the radii of the circles and the height of the Pillar, in one case reported as 180 feet.  To obtain the inclination of the Ecliptic, and geographical latitude, the maximum and minimum solar meridian distances were derived by plotting around the time of the solstices.”
(Dr. Martin Johnson, “Manuscripts of Bagdad Astronomers” in the Magazine “Observatory” Vol. LIX, No. 746, July 1936, p. 223)

In general, only the final value of Obliquity determined by the Arab astronomers is given, and the details are often lacking. 

The details of the observations are given, however, for Al Battani and Ibn Junis.  Al Battani (Albategnius), 880 A.D., was a famous astronomer of Syria.  He made astronomical observations at his Observatory at Aracta (the modern Rakka), near the River Euphrates in Syria, in latitude 35° 57’ N., longitude 39° 55’ E.  Ibn Junis, 1000 A.D., noted Arab astronomer and author of the Hakemite Tables, worked at the well-equipped Observatory at Cairo.  Before describing their observations, however, it is desirable to refer to the corrections which must be applied to the Arab observations in general.

Corrections to Arab Observations

(1) Refraction:  The Arabs did not apply any correction for refraction, so that all their observations require this correction.

(2) Semi-diameter of the Sun:  In the time of Al Khujandi (994 A.D.) and Ibn Junis (1000 A.D.), a form of gnomon terminating in a plate at the top with a central hole, to give a circular solar image at the base, had come into use.  The centre of this circular image was observed, and gave the direct altitude of the Sun’s centre.  Ibn Junis is generally given the credit for this improvement in Arab astronomy.  (G. Bigourdan, “Les Cadrans Solaires.”  Annuaire du Bureau des Longitudes, 1918, p. 258.)

Before this time the Arabs were accustomed to use the plain gnomon, and they applied a correction for the semi-diameter of the Sun.  This is clearly the case for the observations of Al Battani, as we find by the latitude of Rakka derived from his observations.  In this investigation I have treated all of the Arab solar observations prior to those of Al Khujandi and Ibn Junis as having been made with the plain gnomon, or other shadow-casting instrument, such as a wall quadrant, with which the shadow-edge, corresponding to the Sun’s upper edge, was observed.  This method necessitated a correction, applied by the Arab observers, for the semi-diameter of the Sun, as we see in the observations of Al Battani. 

The Ptolemaic estimate of the Sun’s semi-diameter was 16’ 9”, and the Arab astronomers do not seem to have altered this very much.  Al Fargani obtained 31 2/5 minutes of arc for the apparent semi-diameter of the Sun at its near distance from the Earth, so that its semi-diameter, according to him, was 15’ 42”.  A value close to the Ptolemaic one is given by other Arab observers.

I have used the Ptolemaic semi-diameter to re-constitute the Arab observations in general, prior to Al Khujandi and Ibn Junis.

(3) Solar Parallax:  the mean horizontal parallax of the Sun (that is, the displacement of the sun at the horizon, as seen by an observer on the Earth’s surface, as compared with its position relative to the Earth’s centre) is 8.”8, according to modern exact measurements.  The Arabs, however, in common with Ptolemy before them, used a much larger value for the Solar Parallax, depending on an erroneous estimate of the Sun’s distance from the Earth.  The following are the Arab estimates of Solar parallax (Dreyer, “Planetary Systems,” 1906, p. 257)

Observer Distance of the Sun in semi-diameters of the Earth Sun’s horizontal parallax
Al Fargani
1220
2’ 49”
Al Battani
1146
3’ 0”
Abu’l Faraj
1260
2’ 44”
MEAN
1209
2’ 51”

Ptolemy had adopted 1210 Earth-radii for the distance of the Sun, corresponding to Solar parallax 2’ 51”.  (The modern measurement of the Sun’s distance is 93 million miles, or 23,491 Earth radii, corresponding to solar parallax 8”.8.)

It is clear, from the varying estimates of the Arab astronomers, that they made measurements to check Ptolemy’s estimate, and the method adopted gave the same mean result.  Ibn Junis (1000 A.D.) however, for some reason not stated, reduced the solar parallax to 1’ 57”, and made use of this value to correct his own observations.

Other Arab astronomers did not accept this value, and, after his time, Ibn Shatir at Damascus, 1363 A.D., used a solar parallax of 2’ 59”, and Ulugh Beigh at Samarkand, in 1437 A.D., also used 2’ 59”. 

In the Elements of Astronomy, written by Al Fargani, 850 A.D., the problem of parallax, as it applies to the observed positions of the various heavenly bodies, is clearly defined and discussed; and it is evident that he and other Arab astronomers clearly understood the nature of this problem, though they did not know the true distance of the sun, and consequently the true amount of solar parallax.  Before their time, authors of commentaries on Ptolemy’s Almagest, such as Proclus, in the Hypotyposes (about 450 A.D.) had explained in detail the principle of correcting observations of the Sun, Moon, and Planets for the parallax of these bodies.

The Arabs, following Ptolemy, generally believed the solar parallax to be an appreciable quantity, nearly 3 minutes of arc, and as they wished to check Ptolemy’s results as accurately as possible, we may reasonably conclude that, as a general rule, they applied a correction the same, or nearly the same, as Ptolemy’s value for solar parallax.

In Berry’s History of Astronomy (1898, p. 78), it is said, in reference to “the Bagdad School,” that “so much importance was attached to correct observations, that we are  told that those of special interest were recorded in formal documents, signed on oath by a mixed body as astronomers and lawyers.”

Ibn Junis states definitely that his altitude of the Sun, which is given for both summer and winter solstices, is “corrected for the effect of parallax, which diminishes it.”

I am unable, however, to find similar direct evidence that all the Arab astronomers applied this correction; and, as it seems possible, and even likely, that some of them gave results for the Obliquity without doing so, I have shown, in the general graph of Arab Obliquity results [at the end of this chapter] the value both with and without a correction (in most cases the Ptolemaic one) for parallax. 

Possibly some of the Arab astronomers were influenced by Hipparchus, who could not find any parallax for the Sun, and left the problem unsolved. (See Dreyer, Planetary Systems, 1906, p. 184)  Others, perhaps feeling uncertain about the exact amount of parallax of the Sun, thought it better to give their results without this correction.  In some cases, where the altitude of the Sun at both solstices is given, the latitude obtained from the observations gives a clue to the question whether the Ptolemaic parallax correction was applied or not.

As seen from the observations of Al Battani, 880 A.D., the latitude of Rakka obtained from his observations is only 2’ 8” higher than the modern latitude, 35° 57’ N., if we assume that he did not apply this correction.  This difference, 2’ 8”, further must be made a little smaller, since the ruins which mark the site of mediaeval Rakka are some distance North of the modern village of Rakka.  On the other hand, if he did use the Ptolemaic parallax correction, then the latitude given by his observations would be 3’ 39” higher than the modern latitude, but subject to a small reduction for the mediaeval site.   These figures leave the question, on the whole, rather indeterminate, but with the probability in favour of non-application of the Ptolemaic parallax correction by Al Battani.

Similar remarks apply to the observations made by Abul Wafa at Bagdad in 987 A.D., and the latitude obtained from Abul Wafa’s observations is only 2’ 2” higher than the modern latitude of Bagdad (33° 21’ N.) if we assume that he did not use the Ptolemaic solar parallax correction; but, if he did use it, the error of latitude would be greater, namely 3’ 28” higher than the modern latitude of Bagdad.  The probability, therefore, seems to be that Abul Wafa did not apply a correction for parallax.

Ibn Junis, at Cairo in 1000 A.D., is the first Arab astronomer who expressly states that he applied a correction for solar parallax, besides giving the details of both summer and winter observations of the Sun’s altitude.  The observations are quoted by Laplace, as follows (extract from Chapter XI of the work of Ibn Junis):

I have measured the greatest declination, and I have found 23°35’, making the parallax of the sun different from that which is reported by Ptolemy, as I will explain in this table.  I have found with the instruments of our Lord Prince of the Faithful, Aliziz-Billah-Nazar-Aboul-Mansour, the altitude of the Sun at mid-day, corrected for the effect of parallax, which diminishes it, 36° 21’ 30”, the sun being then in the first degree of Capricorn.

I have taken this measure with all the precision and all the care possible.  I have found likewise the altitude corrected for the effect of parallax at the commencement of Cancer, when it was at its maximum, 83° 31’ 30”.  Subtracting the smaller of these two altitudes from the greater, we have 47° 10’, of which the half or the greatest declination is 23’ 35”.  It is this which I have adopted in this table.

I have compared also, a great number of times, the meridian altitude at the commencement of Cancer and of Capricorn with the corresponding altitudes before and after mid-day, and I have found that they agree with the greatest declination which I have observed; for this reason I can guarantee its accuracy.  I have chosen these two points of the Ecliptic for this reason, because, if there should be an error of several minutes in the place of the Sun, this would not produce any perceptible difference, the change of declination being then very small.

We are informed that Ibn Junis reduced the Ptolemaic Solar parallax to 1’ 57” (unpublished chapters of Ibn Junis reviewed by Delambre, Histoire de l’Astronomie du Moyen Age, page 101.  See also Dreyer, Planetary Systems, p. 261.)

With regard to the gnomon used by Ibn Junis for these observations, it is stated in the Encyclopaedia of Islam, by Houtsma, (Vol III, p. 537) that “Ibn Junis cut out a groove, in the side of the gnomon, which ended in a hemispherical cavity.  In the groove a thread was hung from the top of the gnomon, with a ball shaped weight.  When the gnomon is perpendicular, this comes to rest in the hollow.”  The leveling, by means of water, of the surface on which the shadow fell is also described.

As mentioned before, in connection with Arab corrections for semi-diameter of the Sun, Ibn Junis used a gnomon with a plate at the top, having a central hole, so as to give a circular image of the Sun, the centre of which could easily be determined.  After re-calculating the observations of Ibn Junis and applying modern corrections for parallax and refraction, we obtain the corrected Obliquity 23° 36’ 11” from his observations, and the latitude of his Observatory 30° 05’ 0”.   The site of the Observatory of Ibn Junis, where the observations were made, is thought to be near the Mosque of the Sultan El Hakem.    This is 1’ 26” north of the centre of Cairo, and it is therefore in latitude 30° 03’ 30”.  The error of latitude from the gnomon observations of Ibn Junis was therefore only 1’ 30”.

Another Arab observation worthy of special mention is that of Al Khujandi, as we have an excellent description of the instrument which he used (See “Manuscripts of Bagdad Astronomers” by Dr. M.C. Johnson, in Observatory vol. LIX, p. 224).  This instrument was a “giant sextant,” having a radius of 60 feet, with the circumference divided into degrees and minutes, and each minute into ten parts, of 6 seconds interval.

A solar image was formed on the circumference, by illumination of a pinhole aperture at the centre, and an artificial solar disc marked with perpendicular axes was fitted to the image to determine the exact coincidence between centre of disc and scale division.  Great care was taken in orientation, leveling and centring the image.  For the Obliiquity he obtained 23° 32’ 21”.

Unfortunately no statement is available about the corrections which Al Khujandi applied to his observations.  But as this is a particularly small value compared with others of the same period, notably Ibn Junis, it is a reasonable inference that Al Khujandi, equally with Ibn Junis, applied a correction for solar parallax, but probably used the Ptolemaic value.  The corrected obliquity then found from his observations, using modern corrections, would be 23° 33’ 55”.

Other Values of Obliquity Determined by Arab and Persian Astronomers Between 830 A.D. and 1019 A.D.

In addition to the foregoing results, the following table gives values of Obliquity recorded by other Arab and Persian astronomers up to 1019 A.D.; and I have shown the results obtained by correcting for parallax, refraction, and the Sun’s semi-diameter, where it is so required, in column 7, on the assumption that the Ptolemaic parallax was used, and in column 8, on the assumption that no parallax was used by the Arab observer.

[Setterfield note:  Dodwell refers to a table here, and evidently that was his original purpose, but what he ended up doing was the graph as shown at the end of this chapter.  Under the graph we have noted how he marked which measurements contained the correction and which did not.]

These are mainly taken from a list obtained by Dr. M.C. Johnson, at Birmingham, from various authoritative sources, together with others found in Houtsma’s Encyclopaedia of Islam, and from a list given by E. Bernard, and published in Philosophical Transactions of the  Royal Society, London, abridged Vol III, p. 75 (1684 A.D.).    I have rejected observations obviously affected with serious error, such as those ascribed to Al Kwarizmi, 23° 51’ (2) (in addition to his former result 23° 35’), Ibn al Alam 23° 40’, and Rustam 23° 51’, (2) also the earliest attempts of the Arab astronomers between 776 A.D. and 786 A.D. 23° 31’.

It is said, in the Encyclopaedia of Islam, vol III, p. 535 describing the gnomon as used by the Arabs, that it was “a perpendicular rod, often with a cone-shaped top.”  If this kind of gnomon with cone-shaped top were used, it would give too small a value of Obliquity, (see Chapter 2)  with a cone of 90° at the top, a correction of +1’.7 is required to the obliquity determined with it; 80° at the top, +2’.4; 70° at the top, +3’.4; and 60° at the top, +4’.6.

The Arab results, however, suggest that, in  general, the flat-topped gnomon was used, after the first short period of observations; but the small value recorded at the earliest stage 23° 31’, corresponds with the use of a cone-shaped gnomon.

The Obliquity for the mean date of the following table, 916 A.D., according to Newcomb’s Formula, is 23° 34’ 49”; and according to the New Curve, including oscillation, it is 23° 36’ 12”.  If we admit that some of the Arab observations were corrected for Ptolemaic parallax, and some were not, and also that, probably in the earliest part of the period, a gnomon with a conical top may sometimes have been used, then the observed mean value of the Obliquity would agree more closely with the New Curve than with Newcomb’s Formula.  As may be seen in the following Figure, the curve of oscillation tends to bring the observations in the Arabian period nearer to the position corresponding with Newcomb’s Formula.  Furthermore, it can be seen at a glance that Newcomb’s Formula does not satisfy the observations, taken as a whole, during this period.

medieval obliquity

The squares are the raw data and the circles the corrected values

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  1. M.A. Orr (Mrs. John Evershed), “Dante and Early Astronomers,” Section VII, Arab Astronomy, p. 185 return to text
  2. Possibly these observations were made at the summer solstice only, and were uncorrected for the Sun’s semi-diameter. return to text

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