Page:Hindu astronomy, Brennand (1896).djvu/249

 by 16, will be the measure of the earth's circumference. What reason, then, is there for attributing such (50,000 Yojanas) an immense magnitude to the earth?

"For the position of the moon's cusps, the conjunctions of the planets, eclipses, the times of risings and settings of the planets, the lengths of the shadows of the gnomon, etc., are all consistent with this (estimate of the extent of the) circumference, and not with any other; therefore, it is declared that the correctness of the afore-measurement of the earth is proved, both directly and indirectly (directly by its agreeing with the phenomena, and indirectly by no other estimate agreeing with the phenomena)."

The Siddhantas did not all agree regarding the numerical dimensions of the diameter and circumference.

In the geometry of the sphere, the small circle, or parallel of latitude, of any place on the earth's surface, is referred to in Indian astronomy as the rectified circumference (the Sphuta), and Rule (60) gives the ordinary method by which it is determined, thus: The rectified ) Earth's Circumference ( Sin Colatitude of } = X circumference J Kadius ( place.

The same rule gives a correction to be applied to the mean place of a planet, calculated for midnight on meridian of Lanca, to make it serve for a place that may be East or West of that Meridian, the so-called middle-line, or Madhya-Rekha.

This correction is called the Desantara Correction, and its amount is found from

Distance in Yojanas from mid-line ( Planets daily Desantara = X Rectified Circumference ( motion in minutes

This correction is applied also by some astronomers to the place of a planet computed for sunrise.

Rule (61) directs the Desantara to be subtracted from the mean place of the planet at midnight on the first Meridian, if the given