Epigraphia Indica Vol 14

Author(s): Sten Konow, F W Thomas
Publisher: Archaeological Survey of India

Page 16

No. 1.] THE TRUE LONGITUDE OF THE SUN IN HINDU ASTRONOMY.
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true Mesha-sar krinti, the value of s is practically the same by the two authorities; about Day 150 the Arya s is about 3' 36" ahead of the Strya s. The difference increases and diminishes regularly throughout the year.
The principal reasons for this difference are that by the Sürya-Siddhanta the position of the sun's perigee-point is different from that assumed by the Arya-Siddhānta, and that there is a difference in the two year-lengths.
239. I have stated above that this difference has only & very slight effect as regards the value of the tithi-index; its effect on the ordinary calculation of the nakshatra and lagna must now be noticed. In so doing we take first the nakshatra and note the process by which those who have used the Indian Calendar have hitherto calculated its index.
Our method of computing the sun's true longitude, s, by the system of the Indian Calendar has been to take the c found for the desired moment, that is to say the value, in thousandths of the circle, of the sun's mean anomaly according to the Sürya-Siddhānta, making this serve for both Siddhantas; to multiply this c by 10 to get its approximate value in ten-thousandths ; to add to it a figure, 7207, representing the longitude of the son's perigee-point (taken as 7146-3 by the Sürya-Siddhānta) in A.D. 1100 plus a small addition (60-4) rendered necessary by the construction of the Tables in order to avoid the necessity for sometimes adding and sometimes subtracting the equation of the centrel; to deduct from the result the figure representing this equation, and so to obtain the sun's true longitude, 8. The tithi-index, ??, having been already found, we add s to t, and find the nakshatra-index n, or the longitude of the true moon; this index shews in which nakshatra she stands at the moment. The result is an approximation, but it is not close enough. If we are working for an Arya-Siddhānta date, we have used Sürya-Siddhānta values (which differ slightly), and we have arrived at the value of , in part by multiplying - by 10 a value obtained in thousandths so as to be able to apply it to the other value, that of the moon, which has been obtained in ton-thousandths of the circle. This multiplication by ten creates a possibility of error not inconsiderable. Thus, if we have, in thousandths, the figure c = 623, this may stand for any value in ten-thousandths between 6225 and 6235, and may lead to a miscalculation amounting to anything under 10 units in our estimate of the nakshatra index *; and 10 units represent in time-valuation 39 minutes.
240. All these possibilities of error are entirely removed by the present Tables. The exact value of s by either Siddhanta is easily found--a value which we know to be absolutely correct, and when we add this to the already found t we know that the result gives the correct nakshatra-index; or at least that the only possibility of error lies in the value found for the tithi. As for this last we must for the present trust to the correctness of Prof. Jacobi's calculations for the moon's place relative to the sun (a) and for the moon's equation (6), correcting the sun's equation by my new Tables.
241. These Tables will also be found very useful for calculating the lagna accurately. Hitherto our process for finding, in working for the lagna, the value of the sun's true longitude, s, at mean sunrise of the day concerned has been the same as the process for finding the nakshatra. We have found the value of s by both Siddhantas from a calculation really correct only by one Siddhanta, and even that after a rather clumsy multiplication by 10, which itself may cause an error of 39 minutes of time. The present Tables give the accurate by either Siddhanta, and they give it in degrees, etc., thereby simplifying the calculation.
1 See Indian Calendar, &$ 107, 108 ; pp. 60, 61.
* The tithi-index, "+", gives the distance of true moon from true sun, i.e. shews the moon's true place with reference to the true son. When this is added to the true sun's longitude, we have the trae moon's place in the heavens, "*", or the required nakshatra-index,