169 The term vimardärdha means "half the duration of the totality of an eclipse", i.e., the time-interval between the immersion and the apparent conjunction or between the apparent conjunction and the emersion. The time-interval between the immersion and the apparent conjunction is called the sparsa-vimardardha and that between the apparent conjunction and the emersion is called the mokṣa-vimardärdha. AKBA-VALANA The above stanza gives the method for finding the first approxima- tion to the vimardärdha in minutes of arc. The corresponding nadis are obtained by multiplying that by 60 and dividing by the difference between the true daily motions of the Sun and the Moon. The nearest approximations to the sparsa- and mokṣa-vimardärdhas are obtained as in the case of the sthityardhas. A rule for knowing the time of actual visibility of the first contact in the case of a solar eclipse : 41. On account of the brightness of the Sun, the time of (actual visibility of) the first contact (in the case of a solar eclipse) is the (computed) time of the first contact plus the time corresponding to the minutes of arc amounting to one-eighth of the Sun's diameter. Aryabhata I says: "When the moon eclipses the Sun, even though one-eighth part of the Sun is eclipsed this is not perceptible because of the brightness of the Sun and the transparency of the Moon's circumference."¹ A rule for finding the magnitude and direction of the akşa- valana: 42-44. Multiply the Rversed-sine of the asus intervening between midday and the tithi (i.e., the time of the first contact, the middle of the eclipse, or of the last contact) by (the Rsine of) the (local) latitude and divide that (product) by the radius. Reduce the resulting Rsine to the corresponding arc (called akşa-valana) and determine its direction. When the above asus exceed (those corresponding to) a quadrant, add the Rsine of the excess to the radius and operate as before and then find the direction.
1 A, iv. 47.
