पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

on the ecliptic in such a way that its projected position rises and sets at the same time as it itself rises and sets, then the time can be found like lagma, by the method given in Chap. IV for that purpose. In order to effect the said projection two corrections have to be applied to the Moon, one for the inclination of the ecliptic called Ayana-dṛkkarma (we did this for visibility), and the other for the latitude of the observer called Akṣa-dṛkkarma. The Siddhānta gives the correction for latitude alone here, which is got by multiplying the latitude of the Moon by the equinoctial shadow and dividing by 12. The following is its rationals: The latitude is measured on the great circle perpendicular to the ecliptic and directed towards the pole of the ecliptic. If the latitude is projected on secondaries to the pole, and we get the true declination of the Moon by adding this to the mean declination, we can find its time of rising and setting directly, as we find the rising and setting of the Sun, by com- puting its cara etc. and getting its own ascensional differences. But if the latitude is small, it can roughly be taken as the correction for the Moon's mean declination, given by its longitudes. So the correction to the vināḍis of true cara can be found by the latitude taken as part of the declination, by proportion from the cara-vināḍis for the mean declination already used in finding the ascen- sional differences. Therefore, as in getting the cara-vināḍis, here too we have to multiply by the equinoctial shadow and divide by 12. But the division by the diurnal radius is not done, because here we are not finding actually the vināḍis of cara, but an element of the ecliptic corresponding to the cara, for the sake of which we have to multiply again by the radius of the diurnal circle, and the two cancel out. Thus the correction will permit us to consider the Moon to be on the ecliptic. We shall now consider when it is additive, and when subtractive. In the northern hemisphere, the Unmaṇḍala is elevated above the horizon, the elevation increasing towards the north. Therefore if the Moon is a little to the south of the ecliptic on account of its south latitude, it rises later. As successive points on the ecliptic rise later and later, the correction got from the Moon's south latitude is equi- valent to an increase in the Moon's longitude, and so the correction to the longitude is additive. From this we can see why the correction is subtractive if the Moon's latitude is north. As for the time of the setting of the Moon, the further north a body is, the later it sets, and therefore the correction is additive if the latitude is north, from which we see it is subtractive if the latitude is south. The Siddhānta has in view only observers in the northern hemisphere, as we have already said. We have already drawn the attention of the reader to the omission of the correction due to the inclination of the ecliptic (Āyana-dṛkkarma). It may be that the author expects us to make this correction also, taking the hint from the computation of the heliacal rising of the Moon (visibility). The part of the instruction to find the time when the corrected Moon rises is explained thus: The corrected Moon minus Sun is the segment of the ecliptic between them, and the time taken for its rise after sunrise is the time of the rise of the corrected Moon itself. If this segment is less than six rāśis, the Moon must rise in the day-time, because just after the rise of six rāśis from sunrise the sun sets, but this segment is less. Clearly, if it is more than six rāśis the Sun has set, and it is night when the Moon rises. As for moonset, the point of the corrected Moon plus (or minus) six rāśis rises at that time. So, the time of its rise, or which is the same, the time taken by the corrected Moon minus Sun ± six rāśis, after sunrise is the time. Of ±, the author has chosen minus, because the effect of both is the same. By analogy with mid-day Sun, the Moon is on the meridian at the middle of its day-time, provided its motion and change of declination is tolerably uniform. We must add here that it would have been sufficient if the author had said, 'Treat the corrected moon as Lagna, and its time of rise is the time of moonrise. Treat the corrected Moon plus (or minus) six rāśis as Lagna, and its time of rise is the time of moonset'.