पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

XVIII.28 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 333
An examination of the rate shows that the perigee is situated at the end of the Makara (Capricorn)
and the apogee at the end of Kaṭaka (Cancer), which both fairly agree with the actual.
TS say that they do not understand this verse, and no translation is given; its place being taken
by a question mark. NP translate thus: “In the first gati 240 plus 28 minus 1/2 (= 267 1/2) (days). One
should calculate days for every two signs from Pisces.” It is clear that they do not see that this verse
gives the detailed rate of motion of the Type I gati in the diads of rāśis from Pisces, as affected by
the equation of the centre. They think that the first motion given in verse 25, which 186° according
to them, takes 267 1/2 days, as given by them here. If so, what use is the instruction to calculate for
“every two signs from Pisces”?
'विषय-[रस-] खर-(रस-)र्तु-पञ्चका[न्] 'दशगुणान् द्वि[ती]यगतौ |
सहितान् 'स्वरैकपक्षर्तु-चन्द्र-शीतांशुभिः' क्रमशः || २८ ||
28. The II type motion, in the same order, (i.e. for each month of the diads,
Pisces–Aries, etc.) for the 18° take 5 × 10 + 7, 6 × 10 + 1, 7 × 10 + 2, 6 × 10

• 6, 6 × 10 + 1, and 5 × 10 + 1 days.
  This gives 57 days each to move in the signs Pisces–Aries, 61 days for each of Taurus-Gemini,
  75 days for each of Cancer-Leo, 66 days for each of Virgo-Libra, 61 days for each of Scorpio-Sagit-
  tarius, and 51 days for each of Capricorn-Aquarius. From the days given, it can be seen that there
  is a slight tilt in the apogee towards Leo, and in the perigee towards Aquarius. This small difference
  from the findings in verse 27 shows that the values are empirical.
  As for the readings, rasa has been inserted because we want six numbers for the six diads, and one
  is wanting. Symmetry requires that it must be rasa (= 6) there. Also two mātrās are wanting. sapta is
  emended into rasa because, 76 for Virgo-Libra, with 72 on one side, and 61 on the other side, will
  take the apogee to the end of Virgo, 60° off from its place.
  The average for II type motion is 18° for 81 days which is about the average of the mean rate and
  0 (stationary). Thus I type motion is faster than the mean, and the II type slower, as we have sur-
  mised.
  TS have expressed inability to interpret this verse also, and not translated it. Yet they have made
  an emendation which need not be taken seriously, since it has been done without understanding.
  NP have interpreted the verse as giving 57, 71, 72, 66, 61 and 51 by inserting ṛtu as the fourth.
  But symmetry shows that the second number 71 is wrong, and it must be 61, to avoid the jump from
  57 to 72. At any rate, read with their interpretation of verse 27, we can see that they do not under-
  stand the use of this series of numbers. They do not even say these are days.
  28a. A.B.C.D.विषयस्वरसप्तर्तु (D.र्त्तु)
  b. A.B.पंचकदशगुणाद्विग्गतौ (B. ०द्विद्यगतौ)
  C. पञ्चैकदशगुणान् द्विगगतौ; D. पञ्चकम्
  दशगुणान् द्वि[वी] यगतौ
  c. A.B. सहिता; C.D. सहिताः;

334 PAÑCASIDDHĀNTIKĀ XVIII.32
झषवृश्चिकाज(चा)पेषु (वक्रं) षट्सप्तकेन (नव) भा(गान्) ।
‘(द्वि)कृतेन’ (तैर्नवा)ऽतिवक्री दिनषष्ट्या षोडशानुगतिः ॥ २९ ॥
गोमिथुनतौलिकन्या(ख'त्रिसागरैः स्व)रा'नंशान् ।
‘(त्रि)कृतैर्दश त्रिष(ष्ट्या)' सप्तदश यथाक्रमं वक्राशा[त्] ॥ ३० ॥
कर्कटसिंहयो'र्वेदसागरैः 'सप्त ‘(रसार्णवैः ‘शिवा'नंशान्' ।
षट्(ष)ष्ट्याष्टादश क्रमात्कुजो वक्रपूर्वासु ॥ ३१ ॥
घटमृगयो' (र्नग) दहनैः' षड्भागा' (नवहु)ताश(नं)'(च) ।
‘मुनिविषयैः' पञ्चदशांशकांश्च तद्व(त् त्र)येऽप्यारः ॥ ३२ ॥
29. In the signs, Pisces, Scorpio, Aries and Sagittarius, Mars moves 7° in 42
[L11

XVIII.33 XVIII. VĀSIṢṬHA-PAULIŚA — RISING AND SETTING 335
Types III, IV and V, called, respectively, retrograde (vakra), extra-retrograde (ativakra) and
follow-up after retrograde (anuvakra) are given in these verses. The first two are actual retrograde
motion, and the third is the slow direct motion following. They are shown hereunder in a tabular
form.

336 PAÑCASIDDHĀNTIKĀ XVIII.34
Aquarius, there is a small excess of days for ativakra, but even this is far too small. The sum of vakra
and ativakra is 18° and a maximum at Cancer-Leo, and minimum 15°, at Capricorn-Aquarius, and
fairly evenly distributed in between. But actually, at Capricorn-Aquarius, the sum is near 9°, as a
comparison with the motion of Mars given in the Vākyakaraṇa will show (vide App. III, Kujavakra,
where retrograde occurs in the signs Capricorn-Aquarius).
TS have translated verses 29-32, omitting verse 33 as obscure. But they think that all three types
are retrograde motion, (while actually only III and IV are retrograde, and V is direct motion). This
would make the range of the retrograde motion from 36° in Cancer-Leo to 30° in Capricorn-
Aquarius, while the range given is 18° to 15°, actually the latter is even as small as 9°. Also, they do
not see that the IV type should be greater than the III. So they give the numbers as they got from
the words, instead of emending them appropriately. So, in verse 29, navabhāgam as emended by
them should be navabhāgān. nagān vakrī should be navātivakrī. In verse 30, their emendation
abdhisamudraiḥ should be agnisāgaraiḥ Khakṛtaiḥ should be trikṛtaiḥ. In verse 31, their khārṇavair
divasaiḥ giving no degrees at all for the days, and defective in mātrās should have been emended into
rasārṇavaiḥ śivānamśān. In verse 32, symmetry requires our emendation of yamadahanaiḥ into
nagadahanaiḥ, while TS have kept it.
As for NP, they have understood that type III gives retrograde and type IV, extreme retrograde,
though the numbers they give for degrees and days are untenable in many cases. Seeing that the
degrees of V are the sums of those of III and IV, they think that V is the total of the retrograde
motions, while actually V is direct motion. They do not see that if the degrees of V are the total of
III and IV, the days too must be the sum of the days, and therefore V is not the total retrograde.
They have translated verse 33, but this does not give any sense.
'एकेन्द्रियवसुशिवमनु [मनु] भव त्रिवर्गतुं (पञ्च ) 'संयुक्तम् ।
शीघ्रगतौ पञ्चाष्टकमूनं च 'शशाङ्ककृतवेदैः' || ३४ ||
34. In the quick motion following śīghragati (= type VI), there are the days,
40 + 1, 40 + 5, 40 + 8, 40 + 11, 40 + 14, 40 + 14, 40 + 11, 40 + 9, 40 + 5,
40 – 1, 40 – 4 and 40 – 4 for every 30 degrees.
Obviously, these days are given for each one of the signs beginning from Pisces. The numbers
are almost perfectly symmetrical on both sides of the inter-section of Cancer-Leo, and Capricorn-
Aquarius, re-inforcing the conclusion that the former intersection in apogee, and the latter
perigee.
manu for Leo is a glaring omission and is inserted. Symmetry requires 45 for Scorpio, and so pakṣa
is emended into pañca. The number-words forming a 'dvandva' compound, trivargam is wrong for
trivarga, and so has been emended. — tu is removed being an extra mātrā and purposeless. This verse
is of the same kind as verses 27, 28 combined, giving types I and II.
TS have not understood what is given here, and its purpose, as they have not understood the
corresponding verses 27-28. But they have translated this verse as the words go, and wrongly too,
the numbers given by them forming a mere jumble, without any instruction, 2 + 1, 2 + 5, 2 + 8, 2

• 14, 2 + 11, 2 + 9, 40 – 1, 40 – 4, 40 – 4. No wonder, they append this with a question mark.
  34a. A.B.C.D. Hapl om. of one मनु A.B.C. पक्षसंयुक्तम्; D. पञ्च संयुक्तं
  b. A.B.C.D. भवत्रिव (B. om व) र्गं (B2. ग्रं) c. D. पञ्च षष्टिं
  तु (A2.B1.2. नु: D. वर्गर्तु d. A. ०मूनं व B1.3. ततवेदैः; B2. ततवेदै

• का - र्क: it has ङ्क!
  Wait, what about D. ह्यनिलाङ्कार्क?
  ह्य - नि - ला - ङ् - का - र्क. It has नि and ला!
  Wait, in line 20: "TS have emended dvikālāhvārkā into dvyanalāṅkārka".
  And D is NP, they had hyanilāṅkārka?
  Wait, in line 43:
  C. ह्यनलङ्कार्क; D. ह्यनिलाङ्कार्क
  Wait, look at C in line 43:
  Is it ह्यनलङ्कार्क or ह्यनलइका्र्क?
  There is ह्य, न, ल, then ङ्क with ा? No, ह्यनलङ्कार्क has ङ्का!
  Wait, is there an ा on ल?
  Let's look at ल: no ा on ल. It's ह्यनलङ्कार्क.
  Wait, look at the ङ्क: is it इ with a dot?
  Look at line 8:
  ('ह्यनलाइ्‌कार्क) or ('ह्यनलाङ्कार्क)?
  Wait, look at line 8:
  ह्य न `ला

338 PAÑCASIDDHĀNTIKĀ XVIII.35
Example: Find true Mars at 800 days from Epoch.
Days from Epoch 800 — 0 — 0
Subtract days at first rising 256 — 40 — 0
543 — 20 — 0
No. of revolutions gone (543-20) / 700 = 0
Remainder 543 — 20 — 0
Correction for revolutions gone 0 — 0 — 0
Days after rising 543 — 20 — 0
Mars at rising = (18 × 0 + 85) / 133 revolutions = 230°, i.e. 20° in Scorpio.
Starting from this point, i.e. 20° in Scorpio at rising, true Mars moves in 543-20 days, as per the
scheme given in verses 24-35, to 29° 47′ in Cancer as per details given below:
Type I: 146° Total days = 543-20
Balance 10° in Scorpio 14 days (10/30 × 42)
30° in Sagittarius 42 ”
30° in Capricorn 38 ”
30° in Aquarius 38 ”
30° in Pisces 41 ”
16° in Aries 21 + 52 (16/30 × 41)
Total 194 + 52
Balance No. of days .......... 348.28
II: 18°
14° in Aries 44-20 (14/18 × 57)
4° in Taurus 13-33 (4/18 × 61)
57-53
Balance No. of days .......... 290-35
III: 7° (Retrograde)
— 4 in Taurus 24-34 (4/7 × 43)
— 3 in Aries 18-00 (3/7 × 42)
42-34
Balance No. of days 248-1

XVIII.36 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 339
IV: 9° (Fast Retrograde)
– 9 in Aries 42-00
Balance No. of days 206-1
V: 16° 12° in Aries 45-00 (12/16 × 60)
4° in Taurus 14-49 (4/17 × 63)
——————
59-49
VI: 85° 47' 26° in Taurus 41-36 (26/30 × 48)
30° in Gemini 51-00
29° 47' in Cancer 53-36 (53-36/54 × 30)
——————
146-12
Therefore, True motion in 543-20 days from 20° to 29° 47' Cancer = 249° 47
Mean motion in 543-20 days: 408 – 43 × 543 1/3 /780 = 284° 42'
——————————
Therefore days to be added = 34-55
True motion for 34-55 to be added
In Cancer 0-13' for 0-23, and for the balance 34-32 days,
In Leo 30 × (34-32 / 54) = 19° 11'
Therefore True Mars: 19° 11' in Leo.
Motion of Mercury¹
As in the case of other planets, the epoch date is so selected that Mercury rises heliacally in the
west on that date. Since, for Mercury, the elongation required for heliacal rising is given as twelve
degrees, on the epoch day its longitude is 12 degrees ahead of the Sun. Then, the number of days
elapsed from the epoch is obtained and divided by the sidereal period of Mercury, so that the
resulting quotient represents the number of risings that had taken place since the epoch, and the
remainder the number of days elapsed in the current sidereal cycle.
The movement of Mercury in one synodic period being known, (given by the text), the total
longitude moved during the elapsed number of risings is also known and adding to this the epoch
constant, that is, the position of Mercury on the epoch day, its longitude on the day of the current
rising is obtained. However, these figures are on the assumption that the motion of Mercury is
uniform, which is not the case. So, what we have got is only the mean position of Mercury and not
its true position. Here, as also in the text, 'mean position' does not mean the mean heliocentric
position as we now understand, but the mean geocentric position on the assumption of uniform
motion. The true position varies from the mean by quite a few degrees. The date of rising also is
only a mean date and the true date may be several dates behind or ahead.

1. Mercury : Translation and Notes by S. Hariharan, Bangalore.

340 PAÑCASIDDHĀNTIKĀ XVIII.37
The text then gives a table from which for a given mean longitude the true position on the true date can
be obtained. Since the Sun's position has to be 12 degrees behind the true position of Mercury, the
same correction applied to Mercury has to be applied to the Sun. That means, keeping in mind that
the Sun moves one degree in one day approximately, the true date is ahead of the mean date by as
many days as the number of degrees in the correction, if the correction is positive, and vice versa.
Consequently, the number of days elapsed since the (true) rising is also modified by the same
number of days, reduced, if the correction is positive, and vice versa.
Having got the true Mercury as on the true date of rising and the number of days elapsed since
rising, we have now to get the degrees moved by Mercury during these remaining days in the
synodic cycle. For this purpose the synodic period is divided into several sections just as in the case
of other planets. In the case of Mercury the division is made into four sections or gati-s. The first is
from rising to starting of retrogression, the second is the period of retrogression, the third is from
end of retrogression or anuvakra to setting, while the fourth is from setting in the east to rising in
the west. The number of days for each section and the movement are not constant but vary
depending upon the position of Mercury in the zodiac. Accordingly, tables giving these values for
each of the twelve signs are given in the text. With the help of these tables we can trace the move-
ment of Mercury during the remaining days and finally arrive at its position.
What is new in the case of Mercury is the method of interpolation within these tables. For other
planets no specific method of interpolation is suggested, with the result we assume linear interpo-
lation. But here a second degree interpolation is suggested for certain sections.
TS and NP do not appear to have understood the procedure nor the rationale expounded by
these verses, as could be gauged from the emendations they make and explanations they give to the
verses.
[बुधमध्यम्] [बुधचारः]
(दद्यात् सप्तचतुष्कान्) द्युगणे त्र्यंशं च 'वसु'गुणो भागः |
'मुनियमनवके'रपि (रौहिणस्य) वेद्या, दिनाष्टांशाः || ३६ ||
[हत्वा] चतुर्भिरुदयान् नाड्यः शोध्या बुधस्य दिवसेभ्यः |
'त्रिरसयम'घ्नानुदयान् 'रामार्णव' वर्जितान् छिन्द्यात् || ३७ ||
'नवयमवसु [भि] र्मध्यमथो सक्रमानुदयांशैः क्रमाद् |
Mean Mercury
36-38a Add to the ahargaṇa seven times four, i.e., 28, and a third. Multiply by
eight and divide by 927. The quotient is the risings of Mercury. Take the
eighth part of the remainder and deduct therefrom, in nāḍikās, one fourth of
the risings, and the result is the (remaining) days of Mercury. Multiply the ris-
36a. A. दद्या B. सप्तनुक्कान् D. दिनाष्टांशः
b. B. द्यगणो A. त्र्यंशः; B. त्र्यंश 37a. A.B. कृत्वा
B. गुणभागः D. भाव्यः b. A. दुधस्य; B. बुछस्या
c. A. नवकै c. A.B. त्रिदशयमध्नान्; D. [अद्रिदशयम्] यमध्नान्
d. A.B. रोचितस्यः C. रोहिणस्य; D. रोचिताः स्युः B. ॰नुदयां
A. मेद्या; B. मेधा; D. शोध्यो d. B. रामणववर्जितान्; D. पाण्डववर्जिते श्छिन्द्यात्

XVIII.37 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 341
ings by 263, deduct 43 and divide by 829 and the result is the mean Mercury
(in revolutions).
These will lead to the following:
i. 28 1/3 days before the epoch, Mercury rises in the west, after which the countings of the risings
begin.
ii. One synodic revolution takes (927/8 + 1/240) days. The deduction of 1/4th nāḍīs or 1/240th
day per rising is for taking the synodic period as approximately 927/8 days. The balance remaining
after division by 927 is the number of eighth parts of a day elapsed since the last rising. So, dividing
this by eight, the number of full days are obtained. During a synodic period the motion of mean
Mercury is equal to 263/829 revolutions (which is the same for Sun). Hence for one full revolution
Sun will take,
(927/8 + 1/240) × 829/263 days, or, 365.261708 days, i.e., 365-15-42.
iii. At the epoch date, that is 28 1/3 days before 20-3-505 AD., Sun’s longitude is 357-37 minus 27-55
or 329-42.
iv. On this date, Mercury’s longitude is given by:
(No. of risings (zero) × 263 – 43)/829 or – 43/829 revolutions. This reduces to – (18-40), or 341-
20, which is ahead of Sun by 11-38 as against 12 needed, and therefore acceptable.
In verse, 36c, we, also others, have emended the ms. reading muniva.nanaca as muniyamanava to
get the correct figure 927. In 37a kṛtvā has been made as hṛtvā.
The meaning and rationale of these verses is clear. But NP have made medhā in 36d as śodhyo and
have translated it as “Subtract an eighth part of a day (for every synodic period)” etc. and comment,
“We find in XVII, 36 a subtraction of 1/8 of a day and a division of the number of risings by 4. We
cannot explain these steps which seem in excess of the normal procedure.”
It is rather surprising that NP missed the elementary step of dividing the remainder by 8 to get
the number of days, particularly when TS have correctly interpreted it. Without the correct
number of days (elapsed since the last rising) the further processing does not make sense. Hence
we feel that NP have not understood the process at all.
In the next step of finding the longitude of Mercury at the time of the last rising, the figures in
the verses have been badly corrupted. In 37b tridaśayama has been emended as tridivasapa by TS,
and in 38a navavasuyama as navavasurāma, so as to give them a multiplier of 123 and divisor of 389.
But this would give the Sun’s period as 366.479641 days which cannot be.
NP have made tridaśayama as adridaśayama; rāmārṇava as pāṇḍava and navavasuyama as
navavasurasa. They have also changed the meaning so as to subtract pāṇḍava (5) from the divisor
689 rather than to make the deduction from the product. All these they have done just to make
these constants agree with those of Babylonian and then claim that “Table 24 reveals exact numeri-
cal agreement for the outer planets and Mercury” (!). They forgot that in this process they have
obliterated the initial epoch constant of the longitude of Mercury and comment “For Mercury we
have no epoch constant giving us directly a longitude.”
We have emended tridaśayama as trirasayama, and navavasuyama as navayamavasu. As shown
above, these numbers give the sidereal period of Sun as 365-15-42, which is within limits. Of

342 PAÑCASIDDHĀNTIKĀ XVIII.40
course, the constants as emended by NP also will give the correct sidereal period, namely, 365-15-
35, as it should be, but the emendments made are too violent.
[बुधस्फुटः]
पञ्चयुतैस्त्रिंशद्भिस्त्रिंशद् [भुङ्क्ते] स्फुटानंशान् ॥ ३८ ॥
‘नव(षष्ट्या)षष्टिः [स्यात्] ‘वसु’युताशीत्या शतं (वितीक्ष्णांशुः) ।
सर्वैस्त्रिभिरभ्यधिकैस्त्रिंशद्भिस्त्रिं(शद्युताश्वांशाः) ॥ ३९ ॥
चतुरधिकेन शतेना[र्कयुतं] शत, मतोऽर्थ’संयुतया ।
षड्‌विंशत्या त्र्यधिका त्रिंशतिरेवं स्फुटः सौम्यः ॥ ४० ॥
True Mercury
38c-40. For the rising degrees in order, we have
for 30 + 5 35 degrees 30 degrees
9 + 60 69 60
8 + 80 88 100 - 12 88
3 + 30 33 30 + 7 37
4 + 100 104 100 + 12 112
5 + 26 31 3 + 30 33
Total 360 360
Thus true Mercury.
We have made some minor emendations like navakṛtyā ṣaṣṭim to navasaṣṭyā ṣaṣṭiḥ, ca tīkṣṇāṁśum
to vitīkṣṇāṁśuḥ, triṁśadbhuṅkte for triṁśadbhakta, to get the total as 360 for both sides as they should
be. With this table corresponding to the mean mercury obtained as per the previous verse the true
mercury can be got. This is for the true date of rising. Now, the true date has to be obtained or, what
is the same as getting the true remaining days passed after the true rising date. This is dealt with
in the next verse.
38a. A.B. नववसुयममध्य (B. rep. यममध्य) मध्योः
C.D. नववसु रामै मध्यं D. [मध्यमो]
b. A. सा क्रमांनुदशैशः B. शक्रमाह दर्शैश
D. [बुधोऽष्टांशान् क्रमादहर्दसैश्च]
38c. B3. Hapl. om. युतै [स्त्रिंशद्भि] त्रिं०
d. A.B. त्रिंशद्भक्तस्फुटानंशान्
39a. A.B. नवकृत्यात् षष्टिः; C.D. नवकृत्यात् षष्टिं
b. A.B. युतयावशीत्या. A.B. शतं सतीक्ष्णांशोः;
C.D. शतं सतीक्ष्णांगुम्
c. C.D. शर्वे. A. रभ्युधिकै
d. A.B. त्रिंशदेवाकांन्; C.D. त्रिंशदेवांशान्
40a. A1. चतुरधिकेन्. A.B.C.D. शतेन त्रिभिरूनं
c. A.B.C.D. त्र्यधिकां
d. A.B.C.D. विंशतिमेवं

XVIII.40 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 343
These verses actually give the true longitudes at the time of rising corresponding to mean lon-
gitudes. The mean longitude is obtained as per the previous verse.
TS and NP think that, in verses 38b-40, the true motion of Mercury is given, for certain days cer-
tain degrees, and so on. They have made some emendments of their own and both of them get the
total degrees moved as 360 but as for the number of days TS get 389 while NP get 388. The 389 of
TS is the same as the divisor of the previous verse and so they think that corresponding to the
remaining days which will be upto 389 these verses give the true śīghra-sphuṭa. But their idea is
vague and they are not able to expand it properly.
NP think that what is given is an eightfold division of the ecliptic but they are not able to explain
anything further. They comment, "The text calls n1 'days' which, in any case, is meaningless". In
fact there seems to be no reference to days at all in these verses.
अनयोर्विश्लेषांशान् दिवसेभ्यः शोधयेत् स्फुटाभ्यधिके ।
अधिके.तु (मध्यमेऽंशान्) दद्याच्चारः स्फुटबुधाच्च ॥ ४१ ॥
41. Deduct from the days the degrees of difference of these two, (i.e., of the
mean and true places of Mercury), in case the true place is in excess of the
mean place, and add if the mean is in excess of the true. Then the course of
true Mercury is as follows.
TS and NP have not been able to appreciate the rationale for this operation. TS have not given
any rationale. NP think that the correction applied to the days is a mistake and it should be applied
to the longitude; and the correction to the days should be applied by dividing the correction (in
degrees) by the synodic motion per day. This however is not the correct position.
Since this relates to the rising position of Mercury on the true date the Sun will be 12 degrees less
than the true Mercury. So the Sun also will have to be corrected by the difference between the true
and mean positions of Mercury. Since the motion of the Sun can be taken as one degree per day
for small durations, to that extent of the difference the rising date will shift. If the true Sun is in
excess, the date will get advanced, and, consequently, the remaining days will get reduced, and vice
versa. Obviously the number of days will be equal to the number of degrees.
Note on Verses 42-53
These verses give the gati-s of Mercury relating to the twelve signs, Aries to Pisces. In each verse,
the first quarter gives the degrees (days) of motion from the rising of the planet to the commence-
ment of retrogression, the second quarter for the period of retrogression, the third for the period
from the end of retrogression to the setting of the planet and the fourth from setting to its rising.
In order to check the accuracy of the figures, they have been calculated by modern methods. The
variants, as: चतुरधिके पञ्चशतेन तिरूनं and
41a. A.B. ॰पांशा धिशातिरवं.
b. A. शोधये स्फु. C. धिके च. c. A.B. मध्यमे स्या
c. A.B. repeat after b, verse 40, with a few d. A.B. दद्याच्चार (B1.2. चारः)

344 PAÑCASIDDHĀNTIKĀ XVIII.43
textual figures might be seen to agree with the calculated figures in several cases with minor differ-
ences, of course on account of the constants used in Pauliśa and Vāsiṣṭha, and due to observational
errors. Where they differed widely, it has been examined whether there could be due to defective
readings and suitable emendations have been suggested in consonance with the reading of the manus-
cripts, as far as possible. Neither TS nor NP appear to have understood the purport of these verses
and have suggested all sorts of emendations. TS do not translated at all verse 54.
[मेषः]
मेषे 'दिन'षट्कृत्या' 'शिव'-'भव'-'ख'-'द्विसप्त' हीन्या (भागाः) ।
'पञ्चविंशत्'-'त्रिः''कृत'-'षट्सप्तक'-'त्रिवर्गौरिषु'गुणितम् ॥ ४२ ॥
Mercury’s gatis for Aries
42. The gati-s in Aries are:

43. In Taurus, the gati-s are:
    | | Degrees | Minutes | Textual | Calculated |
    | :--- | :--- | :--- | :--- | :--- |
    | | | | ° ′ | ° ′ |
    | 1. Rise to Retro. | 4 × 8 + 0 = 32 | 44 − 11 = 33 | 32 33 | 31 34 |
    | 2. Retro. | 2 × 8 + 8 = 24 | 44 − 33 = 11 | 24 11 | 24 9 |
    | 3. Retro. to Set. | 4 × 8 + 3 = 35 | 44 − 7 = 37 | 35 37 | 33 36 |
    | 4. Set. to Rise | 2 × 8 + 3 = 19 | 44 − 1 = 43 | 19 43 | 20 43 |
    | | |
    | :--- | :--- |
    | 42a. A.B.2.3. कृत्यां; B1. षट्कसा | 43a. A. गाव; B. माव. A1. वेदे; A2- दे. |
    | b. A.B. शंमव; C.D. समुवा (D. समव) सप्त. | A. कृतो; B. ततो; |
    | A.B. भागः; C.D. भागान् | C.D. वेदयमद्विकृतैः |
    | c. A.B. विकृति; C. त्रिकृति; | b. A.B. द्विम्रैः; C.D. दिग्घ्नैः. |
    | D. द्विकृति | A.B.C.D. विषयाग्रिगणनवाभ्यधिकैः; |
    | d. A.B.C.D. त्रिसप्तकं. A.B. षड्वगौव (B. षट्दव) | c. A.B. शतार्धममलो; C.D. शतार्धममरैः |
    | गणितं (B. गणित); C. षट्कमिरिषुगुणितम्; | d. A.B. रुद्रावथ; C. रुद्रैरथ; D. रुद्रूनं च. |
    | D. षडङ्गगुणितम्. | C. सप्तभिर्हीनम्; D. सप्तर्ति व्येकाम् । |

XVIII.46 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 345
[मिथुनम्]
द्विदशं सपञ्चवर्गं [त्रि-रस-गुणा] न्वितं च मिथु(ने) च |
भागार्धशत (द्व्यूनं) 'मुनय' - 'स्त्रिघनं च [पञ्चवेदाश्च] || ४४ ||
44. In Gemini, the gati-s are:
| Degrees | Minutes | Textual ° ' | Calculated ° ' |
| 1. Rise to Retro. | 20 + 25=45 | 50 - 7=43 | 45 43 | 38 42 |
| 2. Retro. | 20 + 3=23 | 3 | 23 3 | 23 8 |
| 3. Retro. to Set. | 20 + 6=26 | 3³ =27 | 26 27 | 27 29 |
| 4. Set. to Rise | 20 + 3=23 | 45 | 23 45 | 21 45 |
[कर्कः]
(कर्किकणि 'दिग्घ्नै:') ['कृता'-'श्वि'-'गुण'-'पक्षै:'] स ('दि'-'ग्')-'ष्ट'-'शून्य'-'रसैः' |
('सेभान्') 'दलितान्' ('सेन्दून्') 'पञ्चकवर्गान्विता' नंशान् || ४५ ||
45. In Cancer, the gati-s are:
| Degrees | Minutes | Textual ° ' | Calculated ° ' |
| 1. Rise to Retro. | 8 × 4+8=40 | 40 + 7=47 | 40 47 | 42 48 |
| 2. Retro. | 8 × 2+8=24 | 24 × 1/2=12 | 24 12 | 24 10 |
| 3. Retro. to Set. | 8 × 3+0=24 | 24 + 1=25 | 24 25 | 22 24 |
| 4. Set. to Rise | 8 × 2+6=22 | 22 + 25=47 | 22 47 | 23 47 |
[सिंहः]
सिंहे ('बाण'-'गुणा'-'क्षि'-'रामै:' 'दिग्'घ्नैः 'सार्णवे'-'न्दु'-'यम'-'विषयै:' |
(सप्ताधिकां) दलितां स('कृता')मधिकां 'विषय'कृत्या || ४६ ||
44b. A.B.C.D. स्वरसघनान्वितं A.B. मिथुनं च
c. B. शत; C.D. शतं. A.B. द्यून; C.D. द्व्यूनं
d. A. पवसुतश्च; B. त्रिघनपवसु and indicated omission upto सप्ताष्ट of verse 47c below; C. पञ्चवस्; D. पञ्चसप्त
45a. A. कर्किनि. A.B. दिग्घैः
b. A.C.D. कृतशशिगुणवेदैः सद्द्रिकाष्टशून्यरसैः
c. A.C.D. सैकान्. A. सेन्दु
d. A.C.D. पञ्चकवर्गान्वितांश्चांशान्

346 PAÑCASIDDHĀNTIKĀ XVIII.48
46. In Leo, the gati-s are:

47. In Virgo, the gati-s are:
    | Degrees | Minutes | Textual (° ′) | Calculated (° ′) |
    | :--- | :--- | :--- | :--- |
    | 1. Rise to Retro. | 46 | 3³ × 2=54 | 46 54 | 44 52 |
    | 2. Retro. | 24 | 9 × 5=45 | 24 45 | 23 14 |
    | 3. Retro. to Set. | 20 | 3 × 8=24 | 20 24 | 19 23 |
    | 4. Set. to Rise | 35 | 50 + 9=59 | 35 59 | 35 59 |
    [तुला]
    ‘विंशतिरेकेन युता’ [हीना] ‘खा’-‘शा’-‘ष्ट’-‘खा’दिभिर्द्विसंगुणाश्च ।
    अंशास्त्रि [युता] ‘वसु’विहीना ह्योक-त्रयोविंशद्युता चैव ॥ ४८ ॥
    46a. A.C.D. गुणेन्दुग्मार्णवदिग्ग्रहैः (D. र्णवैर्दिग्ग्रहैः)
    b. A.C.D. सार्णवर्तुयम. A. विषयाः
    c. A.C.D. तुल्यां (A.B. तुल्या) at the commencement of the line. A.C.D. सप्तविहीनां
    d. A.C.D. सदृशां० (A. सदृशां)
    47a. A.C.D. कन्यायामृतुकृत्या
    b. A. ष्टत्रिंशत्तया तया न भूत:; C. ष्टत्रिंशता तया तयात्र भूयः; D. ष्ट[दशत्रि] त्रिंशं त्रिकृतैर्न भूयः
    c. B1.2.3. commerce again with सप्ताष्टकं शतार्धं, after the indicated gap. A.B. सप्ताष्टकदशशतार्धं च रवियुक्तम्, C.D. सप्ताष्टकं शतार्धं (D. ष्टकमष्टशतार्धं) च रवियुक्तम् | for ०कत्र्यष्टकं etc.

XVIII.50 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 347
48. In Libra, the gati-s are:

49. In Scorpio, the gati-s are:
    | Degrees | Minutes | Textual (° ') | Calculated (° ') |
    | :--- | :--- | :---: | :---: |
    | 1. Rise to Retro. | 10×3+ 6=36 | 36 + 2=38 | 36 38 | 35 39 |
    | 2. Retro. | 10×1+11=21 | 21 − 7=14 | 21 14 | 21 16 |
    | 3. Retro. to Set. | 10×3+ 4=34 | 34 + 3=37 | 34 37 | 33 38 |
    | 4. Set. to Rise | 10×4+ 2=42 | 42 + 26=68 | 43 8 | 43 6 |
    [धनु:]
    धन्वनि द्विदशावष्टौ, [विंशं], षट्सप्तकं, 'कृतोनं' च ।
    ते ('इषु'युत) 'विषयोनाः' ('शैला' : त्रिंशा) न्विता भागाः ॥ ५० ॥
    48a. A.B. रेकेण
    b. A.B. व्यनखांसां तिथिद्विसंगुणैश्च; C. हीना खाशाग्रिभिर्द्विसंगुणाश्च; D. युता जूके सशून्यतिथिर्द्विसंगुणाश्च |
    d. A.B.C.D. ह्येक (A. ध्येक) त्रिंशद्युताश्चैव |
    49a. A. दशघ्नी; B. दशघ्ना
    b. A.B.C.D. शशिकृत (B. om. त, D. शशिद्विकृत) for त्रिशशि. A.B. दहनाः षड्खरावर्णवाष्टयुताः; C. दहनयुगा वसु-शराणंवाष्टयुताः; D. दहनाः शरार्णवाष्टयुताः |
    c. A. तेशा; B1.3. तेषां. A.B.D. यममुनीशोना; C. यममुनीशेन
    d. A.B. समेना व (B. च)

348 PAÑCASIDDHĀNTIKĀ XVIII.52
50. In Sagittarius, the gati-s are:

51. In Capricorn, the gati-s are:
    | | Degrees | Minutes | Textual | Calculated |
    | :--- | :--- | :--- | :---: | :---: |
    | | | | ° ′ | ° ′ |
    | 1. Rise to Retro. | 20+ 3=23 | 23 + 4=27 | 23 27 | 23 28 |
    | 2. Retro. | 20+ 0=20 | 20 − 4=16 | 20 16 | 20 16 |
    | 3. Retro. to Set. | 20 + 7+18=45 | 45 + 7=52 | 45 52 | 46 54 |
    | 4. Set. to Rise | 20+12=32 | 32 +26=58 | 32 58 | 33 56 |
    [कुम्भः]
    कुम्भे (ऽह्नां) विंशत्या [रूप] युतया 'हुतभुग्वेद'-'द्विदिननाथैः ।
    द्वाविंशतिरंशा पञ्च (दशा-ऽर्थार्थका) षष्टिः ॥ ५२ ॥
    50a. A. धन्वि; B. धन्वनि. A.B. दिच साधाष्टौ (B. याष्टौ); | 51a. A.B. द्युदशं.
    C. दिवसाधार्ष्टौ; D. दिवसानाष्ट्रि षट्कृति षट् | b. A.B.C. मुनिहीनं; D. [मुनियुक्तं]
    b. A.B.C.D. षोडश (A. षोडस) for विंशं | c. A.B.C.D. अंशा रूपेणोनाः
    A.B.C.D. दशोने. A. व for च | d. A.B.C.D. सैकैकाश्रोत्कृति
    c. A1. ते स्फुः; A2.B. ते स्युः. A.B.C.D. शशिविषयोनाः |
    (A.B. नौः) |
    d. A.B.C.D. सैकास्त्रिं (A. त्र्यं) शान्विता. |

XVIII.53 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 349
52. In Aquarius, the gati-s are:

53. In Pisces, the gati-s are:
    | | Degrees | Minutes | Textual (° ') | Calculated (° ') |
    | :--- | :---: | :---: | :---: | :---: |
    | 1. Rise to Retro. | 18 + 1=19 | 20 | 19 20 | 19 19 |
    | 2. Retro. | 18 + 5=23 | 13 | 23 13 | 23 14 |
    | 3. Retro. to Set. | 43=43 | 50 | 43 50 | 43 52 |
    | 4. Set. to Rise | 3 × 8=24 | 49 | 24 49 | 24 47 |
    [बुधगतीनां निर्णयः]
    (अस्तो)दयान्तरांशा बुधस्य दिवसाश्चतुर्थ [या] गत्या ।
    उदयाद् वक्रं प्रथमा तृतीयगत्याऽऽनुवक्र(मस्तमयान्तम्) ॥ ५४ ॥
    52a. A.कुंभेह्ना. A1.त्रिंशत्या; D.त्रिकृत्या
    b. A.B.दगतभुग्विदेवदिननाथैः; C.D.हुतभुग् द्विवेद (D.दिनेश) दिननाथैः
    d. A.B.C.पञ्चवर्गमथाब्ध्रिका षष्टिः (C.र्गमर्थाब्ध्रिका)ः D.पञ्चवर्गं सुराधिपाः षष्टिः
    53b. A.B.C.D.मीने त्र्यष्टकमह्नां
    b. for सागरका;, A1.संशरं; B1.शशीष्टं, B2.शासशिष्टं; B3.शशीरं; C.D.संयुक्तम्
    c. A.B.C.D.त्र्यष्टककृतिर्विंशत्या (D.विंशत्याः)
    d. B2.शनार्थ. A.B. मष्टां स्युः

350 PAÑCASIDDHĀNTIKĀ XVIII.56
Specifications of the gati-s of Mercury
54. From setting to rising the degrees and days are given by the fourth gati.
From rising to vakra (beginning) is (given by) the first gati. The third gati is
(from) anuvakra (i.e., end of retrogression) to setting.
It will be seen that this verse explains what the four gati-s indicate a fact which has not been men-
tioned earlier. Actually, there is no direct reference to the second gati. But it can be inferred that
this gives the retrogression period and the degrees.
TS have made some emendations but have not translated them but say that they are not able to
comprehend the meaning of these verses. NP have adopted the emendations of TS and have just
translated them as they are and that does not make any sense. They comment: "We cannot connect
any rational procedure with the verses XVII, 54-56".
गतिविश्लेषकृतिघ्नैरंशैर्गतिवर्गभाजितैर्लब्धम् |
हित्वा राशिभ्यो भुक्तं प्रथमगतौ वक्रपश्चाच्च || ५५ ||
वक्रगतौ पूर्वार्धे तृतीयगत्यां च यत्कृति गुणितैः |
भागैर्गतिकृतिभक्तैः फलमनुपाताच्चतुर्थगतौ || ५६ ||
55. By the square of the difference in gati-s (days) multiply the degrees and
divide by the square of the gati-s. The result is to be subtracted from the
degrees and that gives the degrees gone in the first gati and in the second half
of vakra-gati.
56. In the first half of vakra-gati and in the third gati multiply the square (of
the days passed) by the degrees and divide by the square of the gati-s (days).
For the fourth gati the result is obtained by (direct) proportion [since the
motion in this section is practically uniform.]
54a. A. अष्टो; C. अर्कौ; D. अथो. A.B.C. न्तरांशान् 55a. B. ॰रंसैगत॰
b. A.B.C.D. दिवसाथतुर्थगत्या occurs as c. They c. B. भुक्तं
have as b, बुधस्य कालांश (A.B. कालांश) d. A. गातौ. A. वक्रपश्वाद्वा; B. वक्रपश्चाच्च;.
कांस्त्रिगत्यूनान् (A.B. गत्यूनात्, D. गतीनाम्) D. वक्रपश्चात्
d. A.B.C.D. अनुवक्रमजमीनयोर्मन्दम् (A. योन्दम्,
B. योर्मदम्). 56a. A. वर्गाक्रगतौ; B. चक्रगतौ
b. A.C. गत्या च; D. गत्याश्च
A. यात्कृतं; B. तक्षत. C. गुणितम्; D. [यात्कृति गुणितैः]
c. A.B. गतिकृति (B. क्रति). B1. भत्यै; B2.3. भृत्यै
d. D. ॰मनुपाञ्च च. A.B. ॰र्थभागगतौ (B2.3. गतौ)

XVIII.58 XVIII. VĀSIṢṬHA-PAULIŚA – RISING AND SETTING 351
[दृकर्म—आक्षम्]
ज्याविधिविक्षेपघ्ना (च्च) रकाला‘म्बराष्टवेदां’शम् |
जह्यात् क्षिपेच्च याम्योत्त(रे) ग्रहे खं यथा(काष्ठम्) || ५७ ||
एवं कृते [ग्रहान्त]रांशकैरस्तदर्शनं तेषाम् |
Correction for mean elongation in heliacal rising
57. Find the R sine of the latitude of the body. Multiply the (maximum) half-
cara (i.e. the half difference between the half day-time or night-time from 15
(nāḍis.) in vināḍis, by this R sine, and divide by 480. Add this or subtract this
(to or from the Moon or star-planet) if the latitude is north or south, according
to the proper direction, (i.e. according as the phenomenon of setting or rising,
takes place in the west or east, respectively).
58a-b. When this is done, their setting or rising happens according to the
interval in degrees (between the Sun, and the planet given in XVII.12, or the
Moon).
Note 1. There is a lot of lacunae in verse 57. The half-cara-vināḍīs meant is the maximum for the
place. yathākakṣam is meaningless here and is corrected into yathākāṣṭham, i.e. according to the direc-
tion, but the direction is not mentioned. If north latitude, the addition is for the Moon or planet in
the west. Also if north latitude, the subtraction from the Moon or star planet is to be done for the
east. If south latitude, the subtraction is for the west, and the addition for the east. These things can
be got by a little reflection.
Note 2. The amount of degrees to be applied can simply be got by multiplying the degrees of
latitude of the body by the tangent of the latitude of the place. (The equinoctial mid-day shadow
of the 12" gnomon ÷ 12, is tan. latitude of a place). The amount got is very rough.
The degrees wanted = Sin. half cara (i.e., tan latitude of place x tan. declination of the Sun) ×
sin (90° – angle for heliacal rising), nearly. The last term is neglected here, tan declination is
roughly taken as 48', half-cara is converted into degrees by division by 10, and the conversion into
sine-function is applied to the latitude of the planet instead of the half-cara, as roughly equal.
Note 3. This application is what is technically called Ākṣa-dṛkkarma. The Āyana-dṛkkarma is
neglected.
Note 4. The heliacal rising of the Moon, and of Venus and Mercury when retrograde, takes place
in the west. The heliacal setting of the Moon and retrograde Venus and retrograde Mercury takes
place in the east. Otherwise, all star-planets set in the west and rise in the east. (This Siddhānta does
not envisage the setting or rising of Venus and Mercury when retrograde, no separate degree for
that being given).
57a. B1.3. ज्याविधिविधि d. A. ०्तरं; B. ०तंर०. C. स्वे. D. [कक्ष्यम्]
b. A.B. च for च्च A. ०दंबराष्ट; B. चरकादि 58a-b. A.B.C.D. ग्रहार्कन्तरांशकैः
(B2. कालादि) चराष्टवेदांशं B. ०तिष्ठतितिथ०
c. A. जह्याक्षि. A. यान्मो
26

352 PAÑCASIDDHĀNTIKĀ XVIII.60
चन्द्रादीनां 'द्वादश मनुरवितिथ्यष्टतिथि'संज्ञैः ॥ ५८ ॥
58c-d. The setting and rising (mentioned above in verse 58a) is by 12°, 14°,
12°, 15°, 8° and 15° for the Moon etc.
Note 1. This has to be taken with verse 58a. The degrees given here separately are according to
the Vāsiṣṭha-Pauliśa, which do not instruct the correction due to the latitude of the planet or for
even the latitude of place (ākṣa-valana). The result will therefore be very rough.
Note 2. These degrees are necessarily arbitrary as mentioned already, and the correctness of the
numbers cannot be verified in the absence of the original siddhāntas which are now lost. But we can
guess the probable values as we are sure of the relative luminosities of the planets. The numbers
seem to have been misplaced. They should be dvādaśa, tithi, manu, ravi, aṣṭa, tithi (12°, 15°, 14°, 12°,
8°, 15° for Moon etc.) All siddhāntas give 17° for Mars instead of 15°. The rest are nearly correctly
given, according to one siddhānta or other.
[कालभागानां क्षेत्रभागकरणम्]
(त्रि) शतविनाडीगुणितै (रू) द (य) [वि] नाडीप्रमाणहृतैः ।
लब्धांशकप्रमाणादुदयोऽस्तं वा स्फुटं वाच्यम् ॥ ५९ ॥
Conversion of time-degrees into distance-degrees
59. Multiply the degrees by 300 and divide by the vināḍīs of oblique ascen-
sional difference of the sign, rising at that moment, (near sunset or sunrise,
as the case may be), and get the respective degrees. When the distance bet-
ween the sun and planet is that much, the respective setting or rising takes
place.
Note 1. This work is what is known as the conversion of time-degrees (kālabhāga) into degrees of
distance on the ecliptic (kṣetrabhāga). Since the rule has to apply commonly to Saura on the one hand
and the Vāsiṣṭha-Pauliśa on the other, it has been placed last.
Note 2. Since the positions of the Sun, Moon and planets are given only on the ecliptic, this con-
version is necessary to measure distances.
ज्ञसिताऽऽरेज्या (र्व्यू) नाः शशिनः प्रत्युत्तरं खरां (शुश्च) ।
ज्ञात्वैवं विक्षेपादादेशमनागतं कुर्यात् ॥ ६० ॥
60. (The rising takes place in the east when) Mercury, Venus, Mars, Jupiter
and Saturn are less in longitude than the Sun, and the Sun is less than the
Moon in the opposite direction, (i.e., west). Making the computation according
to the instruction given above using the latitude etc, the phenomenon should
be predicted.
60a. A.B.C. र्ज्यकोर्नाः
59a. A. त्रिंशत; B. त्रिशति. B. विनाडी b. A.B. खरांशोना; C. खगांशेन; D. [खंशाश्च]
b. A. घदशनाडी; B. श्रदशनाडीं d. B. मनागमतत्