1884.] G. Thibaiit —VardJta MtJnras FancJiasiddhdntiJid. 
288 
periods containing integral numbers of all the different constituent 
elements, as otherwise the already laborious calculations would have 
become vastly more troublesome. For this reason the author of the 
Romaka Siddhanta formed his yuga of 2,850 years which is not only a 
multiple of 19 years, from which circumstance it follows that it com¬ 
prises an integral number of intercalary months ; but which in addition 
comprises as we have seen an integral number of civil days. That 150 
is the smallest multiplier by which the desired purpose can be effected 
it is easy to see. The Romaka period has the additional advantage of 
being based on the exact tropical year of Hipparchus while the period 
of 304 years demands a lengthening of the year by 3 seconds. 
From the verse translated above we moreover derive the length of 
the month according to the Romaka Siddhanta. Dividing the savana 
days of the yuga by the number of its synodical months we obtain for 
the length of one synodical month 29‘^ 12^^ 44' 2‘25". Further, adding to 
the number of the synodical months of the ynga the number of solar 
revolutions and dividing by the sum the number of savana days, we 
arrive at a periodical month of 27^^ 7^^ 43' 6'3''. (It need not be men¬ 
tioned that the periodical month of the Romaka is, like its year, a 
tropical one.) A comjDarison of these values with those assigned to the 
same periods by the Greek astronomers offers, owing to the particular 
nature of the case, no special interest. Hipparchus had found for the 
length of the synodical month 29*^ 12^ 44' 3’262"^ and this estimation 
might not improbably have been known to the author of the Romaka 
Siddhanta; but since, as we have seen above, the absolute equality of 
19 solar years and 235 synodical months was insisted on, the length of 
the month had to be modified slightly.f 
* This is the value resulting from Hipparchus’s lunisolar period (about which see 
the following note). Ptolemy, as pointed out by Biot, Resume de Chronologie 
Astronomique, p. 401, derives his value of the synodical month from the same 
period, arrives, however, from unknown reasons at a result differing in the decimal 
places of the seconds (29*1 12li 44' 3'333") and employs this value in all his subse¬ 
quent investigations. 
•f The above remark on the synodical month of course api)lies to the periodical 
month likewise. Although, however, I do not wish to enter in this place into a 
detailed comparison of the Greek and Indian determinations of the length of the 
month the following hints as to the course of procedure of the chief Greek astro¬ 
nomers may find a place. The lunisolar period employed by HijDparchus and de¬ 
scribed by Ptolemy in the 2nd chapter of the 4th book of the Syntaxis sets 126,007 
days plus one hour equal on one side to 4,267 synodical months and on the other side 
to 4,612 sidereal revolutions of the moon minus 7 ^°; the same period is said to com¬ 
prise 345 sidereal revolutions of the sun oninus 7i°. On these equalities may be based 
in the first place a calculation of the length of the synodical month, in the second place 
