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

114 INDIAN LUNI-SOLAR ASTRONOMY
the truth or fallacy of the supposition." We next consider the
second inequality of the Moon.
Moon's Second Inequality or Equation
In ancient times it was Prolemy who first really found a
second inequality of the Moon. According to Godfray (Lunar
Theory, p. 107) "by dint of careful comparison of observations
he (Ptolemy) found that the value of this second inequality in
quadrature was always proportional to that of the first in the
same place, and was additive or subtractive according as the first
was so; and thus, when the first inequality was at its maximum or
5°1′, the second increased it to 7° 40′ which was the case when
the apse line happened to be in syzygy at the same time."
It is well known that though Ptolemy discovered the second
inequality in the Moon's motion he was not able to ascertain its
true nature. His corrections in this case are true when at the
quadrature the Moon's apse line passes through the Sun or it is
at right angles to the line joining the Earth and the Sun.¹ In
the general case his construction does not lead to the elegant
form of the evection term as we know it now, nor does it lead
to the nice form in which it was given by later Indian astrono-
mers from the time of Mañjula (or Muñjāla, 854 Śaka era = 932
A.D.).
As has already been pointed out, the early Indian astrono-
mers from Āryabhaṭa to Brahmagupta aimed at accuracy in
lunar calculation only for the eclipses and syzygies, and did not
interest themselves about the Moon's longitude at the quadra-
tures. Hence this second inequality is absent in the works of
these makers of Indian astronomy, as also in the Pre-Ptolemaic
Greek astronomy. This points to the conclusion that in both
the earlier Indian and Greek systems of astronomy, the modes of
observation of the Moon were copied from an earlier system of
astronomy whether Babylonian or Chaldean. Even in the
Romaka Siddhānta of the Pañcasiddhāntikā, there is no mention
of evection.² Thus inspite of the transmission of a vague system
of Greek astronomy, Indian astronomy as developed by Ārya-
bhaṭa and Brahmagupta must be regarded as independent and

1. Godfray's Lunar Theory. pp. 108-110.
2. Vide the Summary in P.C. Sengupta's paper, "Āryabhata the Father
   of Indian Epicyclic Astronomy." Journal of the Department of letters, vol.
   XVIII, Calcutta University Press.