________________
228
THE INDIAN ANTIQUARY.
[JUNE, 1891.
“No, my supreme lord ! you are wrong. Can you prevent the sun from going to Punganûr by all your vigilance ? It must go and return every day : is it not so ? Even so Ekadasi travels with the sun, and appears once on every fifteenth day at Punganûr as the sun appears there every day."
This simple illustration at last convinced the king, that I his efforts to catch the Ekadasi were a mad-man's project after all! He returned to his kingdom, and, appointing Êkadabi, the Brahman, as his minister, reigned for a long time. Owing to the intelligence of this minister, the kingdom improved a little, but they say that it took several generations for it to reach the level of the intelligence of its neighbours !
10
18
:10
MISCELLANEA. THE SINES OF ARCS IN THE
Siddhanta it is made equal to 120' (or perhaps PANCHA-SIDDHANTIKA.
degrees). Now we find Ptolemy, in his table of I have just seen Prof. Thibaut's Panchasid- right-lines' or chords, divides the radius into 60 dhuintiku, and would call attention to ch. IV., parts (or degrees') and subdivides them sexagesi. translation, pp. 23, 24. In éll. 6-11 we are told that mally for the values of the chords of each arc. the 'sines' of the twenty-four aros are -'7 The Paulida Siddhanta had followed the same minutes 51 seconds, 15 minutes 40 seconds,'&c. system, if it did not derive the actual values Comparing these values with those given in the from Ptolemy, by the shortest and best way, Sarya-Siddhanta, we remark that, if wo read dividing the area by 2, while retaining the values degrees and minutes instead of minutes' and of the chords as the simplest method of presery.
seconds,' we have rather more than double the ing the exact values of these ratios without fracvalues giren for these sines in later astronomical tional parts of a minute. The agreement is shown works: in fact we find that the radiusor sine of 90° in the following table, where the arcs' are multiis in the Sarya.Siddhanta made 'equal to 3638' or ples of 3° 45' in the Hindu table of sines, and of -7° 18' or the chord of 60°; but in the Pauliba. 7° 30' in Ptolemy's table of Chords: No. of Pao-Siddh. Ptolemy's No. of Pa-Siddh. Ptolemy's No. of Pao-Siddho Ptolemy's arc. sines. chords. aro. Bines. chords. aro. sines.
chorde. 17° 51' 7° 50'54"
91
66° 40 66° 40'. 711 17 107° 38' 107° 37' 30 15° 40' 15° 39' 47"
73° 3 | 73° 3' 5" | 110° 53' 110° 51' 52 23° 23° 23° 24' 39" 79° 7 790 7" 18"
113° 33' 113° 37' 54" 41 31° 3' 30" 84° 51' 84° 51' 10"
115° 56' 115° 54' 40" 38° 34' 22" 90° 13' 90° 13' 15"
117° 43' 117° 41' 40 45° 56' 45° 55' 19" 14 95° 13' 95° 1291 22 119° 0 118° 58' 25"
53' 5' 5,3° 4' 29" | 15 99° 46' 99° 46' 35" 23 119° 45' 1190 44' 36" 8 60° 0' 60° 0
16 103° 56' 103° 55' 23" || 24 120° 1' 120° 0 0 From this it will be seen that most of them irregular they are, especially towards the end of agree to the nearest minute, and only a very few the series, - a proof of slight errors in the sines differ by a full minute; and in the case of the themselves. 4th we must suppose an error in the text, as it
From sl. 1 of this chapter IV., we find = V10 differs from the radius. The others may have
or 3-1623, and the circumference being 360° this arisen from errors of computation when fractions
gives the radius equal to the arc of 56° 55': are rejected, or from inaccuracies in the MS.
the Surya-Siddhanta makes this 57°18' or 3438', Whether the values are to be expressed in minutes
and employs this as the sine of 90°, which is a and seconds, as Prof. Thibaut has rendered his
distinct and important advance on the method of text, or in degrees and minutes, must depend on
the older Siddhanta. the manuscripts; all that is meant by these in Ptolemy and this Siddhanta is equal parts of the
Lastly, the ratio of 57° 18' to 120° being nearly radius or diameter, and nothing of the nature of
as 21 to 44, or, better, as 191 to 400, the Paulisa
Siddhanta values of the sines may be compared arcs. The differences too of these sines, given in áll.
with those of the Sarya-Siddhanta, by multiply.
ing the former by 21 and dividing by 44; or 12-15, are also included in Ptolemy's table, and he explains their nse for interpolation. No use more accurately, by multiplying by 191 and divid
J. BURGE98. is assigned to them in the Siddhanta: but if the icg by 400. second differences are noted it will be seen how Edinburgh, 24th March 1891.
001C"
