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

VI.2 VI. VĀS.-PAUL. SIDDHĀNTA – LUNAR ECLIPSE 155 is on its orbit, at a distance equal to its latitude. Therefore only when the latitude is equal to the sum of the semi-diameters, is there at least a grazing of the rims¹. (See Fig. 1b) Fig. VI. 1-b. As according to the Pauliśa the sum of the semi-diameters is always 55', (this will be shown later), and as this much latitude can be got only if Moon ~ Rāhu is 13°, and not more² there can be no eclipse, if Moon ~ Rāhu is greater than 13°. As for the little darkening from 13° to 15°, it is due to the Moon entering the penumbra alone and getting out, instead of entering the umbra. It is well-known that if the source of light is not a point, there is a region not so dark round the shadow, which is darker and .darker as the shadow is approached, and becomes sufficient to be seen. This Siddhānta has taken this region to be about 8', round the shadow. Therefore, the Moon's orb will touch this region at full moon if the latitude is 63', and for this its distance from Rāhu must be 15', as given here. As for deducting 1° 36' from Rāhu, the author has found this is necessary by observation, and we have to accept it, as agreement with observation is necessary, otherwise people will lose faith in the Śāstra. Or the Pauliśa Siddhānta itself gives this correction for agreement with observation, for, in the phenomena intended to be seen, such correction is the practice of the writers of this Śāstra. But it may be asked how this need for correction arises at all. This implies that either the longitude of Rāhu or that of the Moon is incorrect. We showed in ch.III that at epoch Rāhu-head was 235° 59'

1. What we have said here is a little inexact and taken as such by most of the ancient authors. Actually, since the Moon's orbit is inclined to the ecliptic by about 5°, the minimum distance between the Moon and the Shadow, given by SM', the perpen- dicular on the orbit from S, is a little less than SM, and it is only when SM' is equal to the semi-diameters that the grazing occurs. Therefore even if the latitude at full moon is a little greater, an eclipse can occur, but this has been neglected as being very small, actually less than a quarter of a minute of arc.
2. As explained by us under III.31, taking 380' as the maximum latitude (i.e. for 90° distance), and taking the latitude as proportionate to the Bhuja of Moon-Rāhu, as given by the siddhānta there, we get 380' × 13° ÷ 90° = 55', for Moon ~ Rāhu equal to 13°. This agreement here is the proof of the correctness of what we said above in the explanation that the latitude is proportionate to the degrees of Bhuja. If we take the maximum latitude to be 280', as given by the reading of the text there, or to be 270' as TS have taken there without assigning any reason, neither taking the latitude as proportionate to the degrees of Moon ~ Rāhu, nor correctly as proportionate to sin (Moon ~ Rāhu) will give 55'. This is the reason why TS them- selves have, in this section, in verse 5, abandoned both 280' and 270', and taken 240' as the maximum latitude. (vide their Sanskrit and English explanations under VI.5.). 23