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

70 PAÑCASIDDHĀNTIKĀ III.31 The rule is explained thus: The Moon moves in its own orbit, inclined to the ecliptic at an angle equal to the maximum latitude. Hindu astronomy assumes this motion to be on the ecliptic itself and gives the Moon's longitude, because there is only a maximum difference of 7'. Between the ascending and the descending nodes the orbit is north of the ecliptic and therefore the latitude measured on the great circle perpendicular to the ecliptic and passing through the Moon, is north. Between the descending node and the ascending, the orbit is south and the latitude is south. The distance between the node and the Moon, the latitude and the angle of inclination forming a spherical triangle, we have : sin latitude = sin interval × sin maximum latitude. The maximum being small and the latitude being generally less than this, sin latitude and sin maximum latitude are propor- tional to the latitude and maximum latitude, and we have the formula, lat = max. lat × sin interval. But the Paulīśa takes the latitude proportionate to the interval itself and gives the rule. We have to consider here whether the author intends that the latitude is to be found in propor- tion to the actual degrees of the interval or the sine of the interval in degrees. The triangle being spherical, the correct thing would be to use the sine. But we have reason to think that the degrees themselves are intended to be used in the proportion, for if the sine is to be used it must be men- tioned. Also, this Siddhānta uses only the proportion by degrees in other places also, where propor- tion by sines alone would be correct, as for e.g. in the solar eclipse, in correcting Rāhu and in calculating valana, i.e. transformation of direction (see VI. 2-4, 8). Therefore the original Paulīśa itself has instructed proportion by degrees, as being sufficiently accurate, which the author reiterates here. But in computing the parallax (in time) in the case of the solar eclipse the sine is used either by the Paulīśa itself, to avoid too much inaccuracy, or by the author VM to save the Siddhānta from ridicule. As for TS they say that the author intends here proportion only by sine, that being the proper thing to do. Another thing should be mentioned here. In using proportion by degrees, the maximum error will be in the neighbourhood of the nodes. With the maximum latitude 280', the latitude for 13° interval would be 40½ minutes, which would be incompatible with the formula for eclipses (vide VII. 5-6). Therefore it seems that the Siddhānta, though knowing that proportion by sine is the correct thing for latitudes, gives proportion by degrees for the sake of ease of computation. Or by taking liptāśatatrayeṇāśītim as the correct reading, which would make the maximum 380', the incompatibility can be avoided. It may be argued that the error in the latitude would be great in the neighbourhood of the maximum. But this is only erring one side while some others err on the other. The mean maximum latitude is 309'. If some like Ptolemy give 240', which is less by 70', what is wrong in taking that the Paulīśa gives 380', which is greater by the same amount? Now for the readings: In the fourth foot of verse 30, mu is corrected into su because murāt is meaningless. In the third foot of the 31st verse two syllables are wanting and nā is added for pur- poses of syntax. For the same reason, śī-tama-nupā in the fourth foot is corrected into śī-tyā-nupā. The correction of aśīti into saptati by TS here is unwarranted, because it is not known what it was in the original Paulīśa. If this is done in conformity with the Saura, why not in conformity with the Romaka, which gives 280', (see VIII. 11), and which is nearer to the Paulīśa? Now follow six verses devoted to criticising the views of the Romaka, and an astronomer by name Bhadraviṣṇu, the intention of the author being to create faith in his own work. (This was a custom in those days, vide for instance the Brāhma-Sphuṭa-Siddhānta, Dūṣaṇādhyāya and the Vaṭeśvara Siddhānta, Madhyamā-dhikāra, Chapter X). In several places of the text the readings are not clear and we cannot be sure of what exactly the author intends to say, though the gist is clear, the matter