284 
G. Tliibaiit —Yardlia Mihira s Fanchasvldhdntlhd. 
[No. 2, 
We now proceed to consider some verses whicli teacli how to employ 
the general principles stated above for the purpose of calculating the 
mean places of snn and moon. They are found in the 8th adhyaya 
whose general subject is the calculation of solar eclipses according to the 
Romaka : 
(Without entering on the discussion of a few necessary emendations 
of the above text I at once proceed to render its undoubted sense.) 
“ Multiply the ahargana by 150, subtract from it 65 and divide by 54,787 ; 
the result is the mean place of the sun according to the Romaka." 
(From one of the following verses we see that the mean places of the 
Romaka are calculated for the time of sunset at Avanti.) I wish, with 
regard to the above verse as well as those verses which will be trans¬ 
lated later on, to confine myself to the general jDart of the rule and not 
to enter for the present on a discussion of the additive quantity—the 
kshepa—which as we have seen when considering the corresponding rules 
of the Surya Siddhanta is introduced for the purpose of enabling us to 
start in our calculations from the epoch of the karana. The additive— 
or in this case subtractive—quantity (—65) being left aside the remain¬ 
der of the rule presents no difficulties. As we have seen above the 
a calculation, independent from the former one, of the length of the sidereal month 
and the sidereal year. Ptolemy when determining the mean motions of the moon ex¬ 
clusively avails himself of the first mentioned equation between 126,007 days plus one 
hour and 4,267 synodical months and—employing the mean tropical motion of the snn 
settled independently—derives therefrom the mean tropical motion of the moon. 
From the latter it is easy to calculate the length of the periodical (tropical) month, 
with the result 27<1 7^ 43' 7'27", and from that again, if we avail ourselves of the 
value of the yearly precession which Ptolemy had accepted, viz., 36", the value of 
the sidereal month, for which we find 27^ 7^ 43' 12‘1". (Thus also in the Compara¬ 
tive Table of the sidereal revolutions of the planets, Burgess—Whitney’s translation 
of the Surya Siddhanta, p. 168.) Hipparchus on the other hand who had not 
settled a definite value of the annual jjrecession would, in order to ascertain the 
duration of the sidereal month, most probably have made use of the second of the 
above-mentioned equations. The resulting length of the sidereal month is 27d 7h 
43' 13‘57" (thus also Biot etudes sur 1’ astronomie Indienne, p. 44). A certain rate 
of the precession may be derived from comparing this sidereal month with the 
tropical month mentioned above (regarding whose length Ptolemy and Hipparchus 
agree if we set aside aside the insignificant difference resulting from the inadvertence 
of Ptolemy remarked on in the preceding note). Or again the rate of the preces¬ 
sion may bo calculated by comparing the length of the sidereal year which results 
from the third of the stated equations (vide 365d 6'^ 14' 11‘79") with the duration 
of the tropical year ; we thus obtain for the annual rate 46'8". 
