Skyscript Astrology Forum

Dieter,

I must admire both your thorough investigation and your thoughtful reconsideration of the matter. After reading it carefully, I think there is one point on which I may be able to contribute:

Now, verse 34 about the solar year length at the beginning of the "theory of the planets":
sapa?ca?a??i? tri?ata? din?n?? / dy?na? dvibhinna? tu din???ak?n?m
try?na? ?at?rdha? dinak?tsam? sy?t / yay? bhavarga? savit? bhunakti
var. (b) yug?dibhinna?
Shukla: yug?dvibhinna?
Pingree translates:
?A year of the Sun consists of 365 days and 14;47 sixtieths (a??as) of a day, in which the Sun traverses the signs.?
[...]
Or could the same verse be interpreted in different way that would support a sidereal year? (Is dy?nam correct?)

No, I don't think it is. Again, I haven't the Sanskrit text in front of me, but I know it is in Pingree's handwriting (!). Are you sure it doesn't read dvy?nam 'less by two', to match try?nam 'less by three' in the next line? The only meaning I can find for dy?nam is 'sorrowful', which is clearly out of place.

If we accept the reading dvy?nam, a very literal (and considerably less reader-friendly) translation of the verse would be: Three hundreds of days with sixty-five [added] / then a fraction of two, less by two, of the parts of a day / [and] half a hundred less by three would be a year of the sun / within which the Vivifier (Savit?) traverses the zodiac.

Now, if a day and night are divided into 60 parts in all, then the day has 30 parts. Half of that would be 15, and 15 less by 2 is 13. What we get, then, is 365 days + 13/60 days + 47/60/60 days, which comes very near to 365.23 days. This is neither the tropical nor the sidereal year as we know it today, but it has the virtue of agreeing very closely with the value 365.2303 that you get from verse 7. In other words, there is internal consistency.

To come up with 14 rather than 13, Pingree would have to do the maths of the second quarter-verse the other way around, first subtracting 2 from 30 and then dividing the result by 2. That would break the syntactic pattern of the first and third quarter-verses, in addition to creating mathematical inconsistencies in the text. This illustrates the importance of close reading.

Good morning,

May i enquire if astronomers living during the period in which the cited text was written were able to calculate and record astronomical data with a degree of precision required to accurately differentiate, based on observations, amongst the durations of a year quoted?

Best regards,

lihin

Martin,

thanks a lot for your precious time and contribution.

Martin Gansten wrote:

Now, verse 34 about the solar year length at the beginning of the "theory of the planets":
sapa?ca?a??i? tri?ata? din?n?? / dy?na? dvibhinna? tu din???ak?n?m
try?na? ?at?rdha? dinak?tsam? sy?t / yay? bhavarga? savit? bhunakti
var. (b) yug?dibhinna?
Shukla: yug?dvibhinna?
Pingree translates:
?A year of the Sun consists of 365 days and 14;47 sixtieths (a??as) of a day, in which the Sun traverses the signs.?
[...]
Or could the same verse be interpreted in different way that would support a sidereal year? (Is dy?nam correct?)

No, I don't think it is. Again, I haven't the Sanskrit text in front of me, but I know it is in Pingree's handwriting (!). Are you sure it doesn't read dvy?nam 'less by two', to match try?nam 'less by three' in the next line? The only meaning I can find for dy?nam is 'sorrowful', which is clearly out of place.

Pingree?s handwriting is quite clear, he wrote dy?nam, and as I did not dare to assume a mistake, I concluded that he understood dy?nam ("sorrowful, lamenting") as meaning "just under" (just under 15 = 14). But I haven?t ever seen this meaning of the word, it is not found in dictionaries, and I don?t know if it appears in other places of this text or in other texts. Could a 99 be considered a "lamenting 100"?

But I agree with you that dvy?nam is a very likely reading and makes the text clearer.

If we accept the reading dvy?nam, a very literal (and considerably less reader-friendly) translation of the verse would be: Three hundreds of days with sixty-five [added] / then a fraction of two, less by two, of the parts of a day / [and] half a hundred less by three would be a year of the sun / within which the Vivifier (Savit?) traverses the zodiac.

Now, if a day and night are divided into 60 parts in all, then the day has 30 parts. Half of that would be 15, and 15 less by 2 is 13. What we get, then, is 365 days + 13/60 days + 47/60/60 days, which comes very near to 365.23 days. This is neither the tropical nor the sidereal year as we know it today, but it has the virtue of agreeing very closely with the value 365.2303 that you get from verse 7. In other words, there is internal consistency.

I think you are making an interesting point. And there is another verse (11), which will add to this internal consistency:
tri??addin?? s?vanam?sa ?rkas / tryagrairvi?i??? da?abhirmuh?rtai?
kal?catu?ke?a ca pa?ca?a?kais / tryagry???akai?ca dvigu?ai?caturbhi?
Pingree translates: ?A civil month equals 30 days, a solar month equals (a civil month) plus 13 muh?rtas and 4 kal?s and 56 thirds and 2 fourths.?
This results in a month length of 30.436074 days and, multiplied by 12, a year length of 365.232893, which again is close to 365.23. Pingree notes about this verse (p. 407) that "the year is apparently tropical", although one could consider it too short for that. (And as I said before I don?t think that the text understand the tropical-sidereal difference.)

Again, I think, there are some minor problems with Pingree?s translation: The text uses the expression pa?ca?a?ka- again, as it did in vs. 6, which Pingree interprets as 65, but most probably means 5 x 6 = 30. (In the following verse 12, which gives the length of the synodic month, he himself interprets ?a?pa?cakam ekah?nam as "6x5-1" = 29 days.)
The last quarter of the verse also raises some questions. Pingree apparently understands tryagry???ak?? as "thirds", but it could also be equivalent to tryagr?? (cf. first half of verse) and mean that 3 have to be added to the 5 x 6. Besides, I think that dvigu?ai?caturbhi? must be read as "2x4" rather than as "2 fourths". But for the month and year lengths these changes do not make a major difference.
Now, if the month consists of "30 days, 13 muh?rtas, 4 kal?s, 33 (thirds), 8 (forths)", then the month length is 30.435862 days, which, multiplied by 12, gives a year length of 365.230348 days, again consistent with the results from verses 7 and 34.

Dieter

lihin wrote:Good morning,

May i enquire if astronomers living during the period in which the cited text was written were able to calculate and record astronomical data with a degree of precision required to accurately differentiate, based on observations, amongst the durations of a year quoted?

lihin

Good morning, Lihin,

yes, this was possible if the period of astronomical observations was long enough. The length of the tropical year was quite accurately determined by Hipparchus in the 2nd cty BC. The sidereal year was quite accurately determined in ancient India (e.g. Suryasiddhanta). A year length of 365.29 days in Yavanajataka would be rather strange, in my opinion.

Dieter

dieterkoch wrote:Again, I think, there are some minor problems with Pingree?s translation: The text uses the expression pa?ca?a?ka- again, as it did in vs. 6, which Pingree interprets as 65, but most probably means 5 x 6 = 30. (In the following verse 12, which gives the length of the synodic month, he himself interprets ?a?pa?cakam ekah?nam as "6x5-1" = 29 days.)
The last quarter of the verse also raises some questions. Pingree apparently understands tryagry???ak?? as "thirds", but it could also be equivalent to tryagr?? (cf. first half of verse) and mean that 3 have to be added to the 5 x 6. Besides, I think that dvigu?ai?caturbhi? must be read as "2x4" rather than as "2 fourths". But for the month and year lengths these changes do not make a major difference.

The difference is small, but I agree with your arguments. While I have immense respect for the scope and breadth of Pingree's scholarship as a whole, his abilities as a Sanskritist were not of the highest order.