Epigraphia Indica Vol 16

SR No.: 032570
Original Sutra Author: N/A
Author: F W Thomas, H Krishna Sastri
Publisher: Archaeological Survey of India
Publication Year: 1921
Total Pages: 474
Language: English
Classification: Book_English
File Size: 22 MB

Page 140

No. 14.]
THE FIRST ARYA-SIDDHANTA: "TRUE" SYSTEM.
105
equations with four decimal places for a large number of anomaly angles. For an explanation as to the construction of these Tables see my paper on the Siddhanta-siromani (abore, Vol. XV, $ 275).
294. It is advisable to explain clearly my reason for differing from Prof. Jacobi as to the amount of the greatest equation of the moon, which he values, in ten-thousandths of the circle, at 139.0 as against my 1394.
"Egn. 6." The general formula ($ 290, ix) for the equation of the moon's centre is, a being the angle of mean anom., sin. eqn. = sin. a. To obtain the equation from the sine of the equation-angle the proportion eqn.: sin. eqn.. diff. in angle : diff. in sine is used. The Hindu astronomers always worked by sections of anomaly-arc, each mensuring 3° 45', or 225'. Reference to the Equation-Table LXXV will shew that in the case of the first group anom. 0° to 3° 45' the diff. in anom. is 225' and the diff. in sine is also 225'. Hence, in the case of all anom. angles between 0° and 3° 45' eqn.=sin. eqn. But in the case of all anom. angles between 3° 45' and 7° 30-and no equation angle of the moon's anom. exceeds the latter quantity the diff. in angle is 225' and the diff. in sine is 224'; so that the formula to be used for all angles
coming into this second group is eqn.=550 sin. eqn. This applies only to the excess in the angle over 3° 45'. The working rule, therefore, for finding the equation of angles lying between 3° 45' and 7° 30' is as follows:
With the formulasin. a, find the sin. eqn. From the sin. eqn. deduct 225'. Multiply the remainder by 225' and divide the product by 224'. Add 225' to the result.
Or, a little more simply,-From the sin. eqn. deduct 225'. Divide the remainder by 224 Add the result + 225' to the sin. eqn.
For an example let us suppose that it is required to find the moon's eqn. for anom. 67° 30'. Sin. 67° 30'=(Table LXXV) 3177'.
7x 3177'.
-=277-9875, or 4° 37' 59"-25, an angle
between 3° 45' and 7° 30'. 277.9875 - 225'=529875, and this divided by 224'=0236551. 52.9875 +0.236551 +225'=278-224051, or 4° 38' 13.44306. This is the correct equation b for the given anom. It is stated by Prof. Jacobi (aboce, Vol. 1, Table XXIV A) shortly as 4° 38' 13".
Turning now to the equation of 90°, the greatest equation (, and working in the same
way, sin. 90°=3438'. **0438 = 300 -825. This less 225'=75%-825, and this divided by 224'=
80 0-338504464. 75-825 +0338504464 +225' =301'.163504464, or 5° 1' 9*.810268, which is the exact equation required. In ten-thousandths of circle thig=139:427548361.
295. "Eqn. c." [Working similarly for the greatest equation or the equation of sun's anom. 90°.] The formula for finding sin. eqn. in this case is ($ 290, viii) a sin. a. Sin. 90=
3438'. Sin. eqn. =**80 =128"-925, or 2° 8° 555, or, in ten-thousandths of circle, 59-6875; and, because this angle is one in the first group, being less than 3° 45', the eqn.= sin. eqn. Hence