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

44 ASTRONOMY IN ANCIENT NATIONS
the ninth sphere; the annual precession varies between 26″.45±
28″.96, or from + 55″.41 to −2″.51.¹ It was now necessary to
assume the existence of a tenth sphere, which as primum mobile
communicated the daily rotation to all the others, while the
ninth produced the progressive and the eighth periodical
motion on the small circles, which are situated "in the conca-
vity of the ninth sphere." This was a nice and comfortable
theory on account of the long periods involved and the slow
changes it produced in the amount of annual precession; and
oblivious of the fact that the theory had no foundation except
the circumstance that the obliquity of the ecliptic was now about
20′ less than it had been stated to be by Ptolemy, and that he had
given the amount of precession as 36″ a year instead of about
50″, and often shutting their eyes to several of the necessary
consequences of it, such as the changes in the latitudes of stars
which it ought to produce², astronomers continued to accept the
theory until at last a real observer of the stars arose and wiped
it out by showing that the obliquity of the ecliptic had steadily
diminished, and that the amount of annual precession had never
varied. We have in this place only alluded to it because it in-
volved some rearrangement of the spheres and because it is
eminently characteristic of the period during which no persistent
observations were taken, and hardly an attempt was made to
improve the theories of Ptolemy. The theory of trepidatio or
titubatio, as it was sometimes called, was one attempt and it
would have been better left alone. But it forms a not uninter-
esting chapter in the history of astronomy.
(Continued from previous page)
this development to a Jew of Toledo, Isaac Hassan (see above. p. 38),
adding that Alfonso four years after the completion of the tables became
convinced of the futility of the theory by reading the book on the fixed stars
by Al Sufi. Riccioli, Almag. novum, I. p. 166.

1. In the Alfonsine Tables the maximum took place at the birth of Christ. In
   Essler's Speculum astrologicum, p. 224 (appended to Purbach's Theoricae
   novae, Basle, 1573) the epoch is A.D. 15, diebus 137 completis. Reinhold in
   his commentary to Purbach (Paris, 1558, f. 163b) explains that 26″.45 is
   the space passed over by the Sun in 10 mins. 44 secs., by which amount
   the Alfonsine Tables made the tropical year smaller than 365¼ days.
2. Abraham ben Chija (p. 103, Schrackenfuchs) says that trepidation does
   not change the latitudes. Perhaps he refers to the earliest form of the
   notion, that described by Theon of Alexandria.