ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

42 ASTRONOMY IN ANCIENT NATIONS
He imagines a fixed ecliptic (in the ninth sphere) which intersects
the equator in two points (the mean equinoxes) under an angle of
23° 33' 30", and a movable ecliptic (in the eighth sphere), attached
at two diametrically opposite points to two small circles, the
centres of which are in the mean equinoxes and the radii of which
are = 4° 18' 43". The movable tropical points of Cancer and
Capricorn never leave the fixed ecliptic, but move to and fro to
the extent of 8° 37' 26", while two points on the movable ecliptic
90° from the tropical points move on the circumferences of the
small circles, so that the movable ecliptic rises and falls on the
fixed one, while the points of intersection of the equator and the
movable ecliptic advance and recede to the extent of 10° 45'
either way, This is a motoin of the eighth sphere, common to
all stars, and the Sun will, therefore, sometimes reach its
greatest declination in Cancer, sometimes in Gemini. Tabit
does not say that the obliquity of the ecliptic is variable, and
perhaps it did not occur to him that this would be a necessary
consequence of his theory; he only notices the change in direction
and amount of the motion of the equinoxes, which, he says, has
increased since the days of Ptolemy, when it was only 1° in 100
years, while later observers have found 1° in 66 years. The
erroneous value given by Ptolemy was, therefore, mainly responsi-
ble for the continuance of the imaginary theory. It is to be
observed that Tabit expresses himself with a certain reservation,
and seems to think that further observations are necessary to
decide if the theory is true or not. His younger and greater
contemporary Al Battani was even more cautious, for though he
repeats the account of the trepidation given by Theon (which he
says that Ptolemy manifeste in suo libro declarat¹) he does not
make use of it, but simply adopts 1° in 66 years (or 54".5 a year),
which he finds by a comparison between his own observations and
some made by Menelaus. In rejecting the erroneous value of
Ptolemy, which Al Fargani alone had accepted,² Al Battani was
followed by Ibn Junis, who came still nearer to the truth by
adopting 1° in 70 years or 51".2 a year, and who does not allude
to trepidation. It is greatly to the credit of several other Ara-
bian writers that they were not led astray by this imaginary phe-

1. Cap. 52, (205). Plato's translation gives the period as 84 years, but Nallino's
   ed. has 80 (p. 127).
2. c. 13, p. 49. .
3. Schjellerup, Descr. des etoiles fixes, p. 43,