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Indian Chronology (Solar, Lunar and Planetary): A Practical Guide to the Interpretation and Verification of Tithis, Nakshatras, Horoscopes and other Indian Time-records, B.C. 1 to A.D. 2000 c38: Part IV.—Planets and Planetary Chronology

Indian Chronology (Solar, Lunar and Planetary): A Practical Guide to the Interpretation and Verification of Tithis, Nakshatras, Horoscopes and other Indian Time-records, B.C. 1 to A.D. 2000 c38

Language
English

Contents

Part IV.—Planets and Planetary Chronology

c38.1

281. Indian astronomy reckons nine planets, spoken of collectively as navagrahas, namely the Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn, Rahu and Ketu. It will be seen that the first seven are named in the order of the days of the week, and this is always the order in which they are referred to in Indian astronomy. Rahu is another name for the moon's ascending node, one of the points at which the moon's orbit cuts that of the Sun (the ecliptic), the other point, or the descending node, being called Ketu. An eclipse cannot happen except when the moon is at either node and the sun is at the same or the opposite node; hence the popular legend which depicts Rahu as a dragon swallowing up the moon or the sun at the time of an eclipse. All the planets, except Rahu and Ketu, move like the Sun, from West to East in their apparent path round the earth. Rahu moves in the opposite direction, and Ketu is always assigned a position 180° from that of Rahu.

c38.2

282. All the data necessary for calculating the geocentric longitude and latitude of the five planets, Mars, Mercury, Jupiter, Venus and Saturn, are given at pages 200 to 206 of the Tables (Table XVII).

c38.3

283. The longitude of any planet is its distance, measured in degrees, from an arbitrary point in the ecliptic, which point may perhaps best be defined as the 0 point of the Sun's mean longitude. The Sun's mean longitude is always 0 at a certain part of the Indian Solar Year, namely, at 2·1707 days from the commencement of each Indian Solar Year: while at the moment of commencement of the Indian Solar Year, the Sun's actual longitude is 0. The difference between the Sun's mean and actual longitude at any time is his equation of the centre, and this difference is due to his varying pace at different times of the year as he journeys round the earth. The Sun's mean longitude and equation for every complete day of the Solar Year are given in Table XVII-A (pp. 207, 208), and these are most important data in Indian astronomy. Table XVII-C (p. 209) gives the increase of the Sun's mean longitude for hundredth parts of a day.

c38.4

284. The Sun's mean longitude at any moment is ascertained by deducting 2·1707 from the number of days and fraction of day elapsed since the commencement of the Indian Solar Year, and applying to the result the Table of Sun's longitude (Table VII-B, p. 8). The difference between the Sun's longitude thus calculated and the longitude for the same moment given in any European Nautical Almanac, is the true Indian precession, and this difference should always be added to the longitude of a planet given in this work in order to ascertain the corresponding longitude according to the Nautical Almanac. The following table gives the precession to be added to Indian celestial longitudes at various epochs since A.D. 520 (when the European and Indian longitudes coincided), in order to arrive at the European celestial longitude. The rate of precession adopted for this table is 1 degree for every 61¼ years, or 59″ per annum, the rate arrived at in Sec. 277 supra.

c38.5

(The European longitude is called the tropical longitude of a planet from its being regulated by the tropical year, whereas the Indian longitude is generally called a sidereal longitude from its being regulated by the sidereal year.)

c38.6

| A.D. | Kaliyuga. | Indian Precession in Degrees. | A.D. | Kaliyuga. | Indian Precession in Degrees. | A.D. | Kaliyuga. | Indian Precession in Degrees. |
| **520** | 3621 | 0·0 | **1040** | 4141 | 8·5 | **1561** | 4662 | 17·0 |
| **551** | 3652 | 0·5 | **1071** | 4172 | 9·0 | **1591** | 4692 | 17·5 |
| **581** | 3682 | 1·0 | **1102** | 4203 | 9·5 | **1622** | 4723 | 18·0 |
| **611** | 3712 | 1·5 | **1132** | 4233 | 10·0 | **1653** | 4754 | 18·5 |
| **642** | 3743 | 2·0 | **1163** | 4264 | 10·5 | **1684** | 4785 | 19·0 |
| **673** | 3774 | 2·5 | **1194** | 4295 | 11·0 | **1715** | 4816 | 19·5 |
| **704** | 3805 | 3·0 | **1225** | 4326 | 11·5 | **1745** | 4846 | 20·0 |
| **735** | 3836 | 3·5 | **1255** | 4356 | 12·0 | **1775** | 4876 | 20·5 |
| **765** | 3866 | 4·0 | **1285** | 4386 | 12·5 | **1806** | 4907 | 21·0 |
| **796** | 3897 | 4·5 | **1316** | 4417 | 13·0 | **1837** | 4938 | 21·5 |
| **826** | 3927 | 5·0 | **1347** | 4448 | 13·5 | **1867** | 4968 | 22·0 |
| **856** | 3957 | 5·5 | **1377** | 4478 | 14·0 | **1898** | 4999 | 22·5 |
| **887** | 3988 | 6·0 | **1408** | 4509 | 14·5 | **1929** | 5030 | 23·0 |
| **918** | 4019 | 6·5 | **1439** | 4540 | 15·0 | **1960** | 5061 | 23·5 |
| **949** | 4050 | 7·0 | **1469** | 4570 | 15·5 | **1990** | 5091 | 24·0 |
| **980** | 4081 | 7·5 | **1500** | 4601 | 16·0 | **2020** | 5121 | 24·5 |
| **1010** | 4111 | 8·0 | **1531** | 4632 | 16·5 | **2051** | 5152 | 25·0 |

c38.7

285. We will now explain briefly how the planetary tables at pages 200 to 206 are to be used in practice.

c38.8

The mean longitude of a planet at any moment is obtained by adding together its mean longitude at the commencement of the century, the mean motion for the given odd year, and the mean motion for the given day. Thus for 202·54 days of the Indian Solar Year, A.D. 961 (Kaliyuga 4062) we have —

c38.9

| | Degrees. |
| Mars' mean longitude at commencement of K.Y. 4001, | 79·4873 |
| Mar's mean longitude for 61 years, | 155·72 |
| ,, ,, ,, 202 days, | 105·85 |
| ,, ,, ,, 54 day, | ·2830 |
| *Answer* | 341·34° |

c38.10

**286.** This is the mean longitude of the planet in his path round the Sun, though not his longitude, as he appears to us from the earth. To obtain this, which is called the geocentric longitude, and which is the longitude usually cited in Indian chronology, we have to perform a fairly tedious sum. So far as the geocentric longitudes of the planets from A.D. 1840 to A.D. 1919 are concerned, the reader is saved the trouble of doing any such sum, because the geocentric longitudes, as finally determined for Lankâ Sunrise on every tenth day in each solar year from A.D. 1840 to A.D. 1919, are given in a handy form at pages 210 to 225 (Table XVIII), so that all he has to do to ascertain the position of the planets in a horoscope, say, for April 13, A.D. 1911, is to look up the particular day of the Solar Year (in this instance 0 day against A.D. 1911 on p. 224) and set down the positions of the planets as follows:—

c38.11

Sun, 357° + ·4 + 2·7 = 360·1 or 0·1° in Mesha; Mars, 298·4°, *i.e.*, 28·4° in Makara; Mercury, 16·3° in Mesha; Jupiter, 198·8°, *i.e.*, 18·8° in Tulâ; Venus, 31·8°, *i.e.*, 1·8° in Vrishabha; Saturn, 14·3° in Mesha; Rahu (Table XVII-B), A.D. 1911 : 21·90° in Mesha. (*N.B.*—Only mean places, and not actuals, are calculated for Rahu and Ketu).

c38.12

Ketu (*vide* Sec. **281**) 21·90° + or - 180° = 201·90°, *i.e.*, 21·90° in Kanyâ. The result for Ketu is the same, whether 180° are added to, or deducted from, the longitude of Rahu.

c38.13

**287.** The place of the moon, the only remaining planet, can be deduced either from the tithi or from the Nakshatra. The latter method is illustrated in Sec. **292** *infra*. The former, which is easier, is shown below:—

c38.14

We first of all calculate the ending moment of the tithi, as usual.

c38.15

| | | ☉'s Anom. | ☾'s Anom |
| | d. gh. | d. gh. | d. gh. |
| (Tab. XII, p. 151) New Moon, March 1911 | Mar. 29 57½ | 350 45 | 22 16¼ |
| (Eye-Table) Collective duration of 15 tithis ... | 14 46 | 14 46 | 14 46 |
| | Mar. 44 43½ | 365 31 | 37 2¼ |
| Deduct 1 anomalistic year and month respectively | | 365 15 | 27 33½ |
| | | 0 16 | 9 29 |
| (Eye-table) ☉'s Eqn. = + 10½ gh; ☾'s Eqn. = - 21 gh. | | | ☉'s Eqn. + 10½ |
| Sum of ☉'s and ☾'s Eqns. ... ... | | - 10½ | 9 39¼ |
| | | Mar. 44 33 = 33 gh. on Ap. 13. |

c38.16

This was the ending moment of the tithi, when the moon's elongation or distance from the sun was 15° × 12° = 180°. For the moon's longitude at any moment = moon's elongation plus Sun's Longitude. (Secs. 36, 254.)

c38.17

Therefore, if we find the Sun's longitude at ending moment of tithi and add it to the moon's elongation, 180°, we shall obtain the moon's longitude, or which is the same thing, the Nakshatra current at ending moment of tithi.

c38.18

⊙'s Longitude at Sunrise = 0·1° (see above).

c38.19

Do. at ending moment of tithi = 0·1° plus increase of longitude for 33 ghat. or ·55 of a day (Eye-Table.) This increase, by Table XVII-C is ·54°.

c38.20

∴ ⊙'s Longitude at ending moment of tithi = 0·1° + ·54° = 0·64°.

c38.21

∴ Moon's do. do. do. = 180° + 0·64° = 180·64°.

c38.22

The corresponding Nakshatra (by Eye-Table) was Chitrâ, and the Râśi Tulâ.

c38.23

We want however the moon's longitude for sunrise on the same day which was 33 ghaṭikas or ·55 day (Eye-Table) earlier.

c38.24

The increase of ☾'s Long. for ·55 day is roughly (Tab. XVII-D) 7·33°.

c38.25

∴ ☾'s Long. at Sunrise 13 Ap. A.D. 1911 will be roughly 180·64° - 7·33° = 173·31° which will be 23·3° in Kanyâ. The Nakshatra is Hasta. (Eye-Table.)

c38.26

N.B.—In strictness we should have ascertained the total duration of the Nakshatra and the unexpired part of the Nakshatra at sunrise. If this was ·50, Table XVII-D would give us 6·6° which we should deduct from 180·64°. Result 174·0° which is Chitrâ Nakshatra.

c38.27

288. For years before A.D. 1840 the true geocentric longitudes of planets will have to be calculated in the following manner :—

c38.28

The planets are divided into two classes: *Inferior* (Mercury and Venus) and *Superior* (Mars, Jupiter and Saturn.) Three quantities, which we may call *a, b, v*, in the case of the inferior planets, Mercury and Venus, and *A, B, N*, in the case of the superior planets, Mars, Jupiter and Saturn, have to be determined first of all, before working out the actual geocentric longitude of any planet. Having determined these three quantities, the further procedure is the same, whether the planet is superior or inferior. We give below the calculations (1) for an inferior planet, Mercury, and (2) for a superior planet, Mars, for 202·54 days of the Solar Year A.D. 961 (i.e., 9 ghaṭikas after sunrise on 11th October A.D. 961.)

c38.29

I. *True Geocentric Longitude of Mercury for 202·54 days of the Indian Solar Year A.D. 961-62.*

c38.30

*Time and English date.* 9 ghaṭikas after sunrise on 11th October A.D. 961.

Mercury (Inferior Planet)

c38.s1.1

(1)—*a*. Mean Long. of Mercury minus Mean Long. of Sun.

c38.s1.2

| | Mean Long. of Mercury. | Mean Long. of Sun. |
| For A.D. 900 (p. 201) | 173·55° | 202 days (XVII-A) 196·95° |
| 61 years ” | 100·87° | 54 day (XVII-C) ·53° |
| 202 days (p. 202) | 106·65° | |
| ·54 day | 2·21° | 197·48° |
| | 382·78° | |
| *Deduct* 360° | | |
| | 22·78° | |

c38.s1.3

| | | 382·78° |
| | | - 197·48° |
| | | 185·30° *a* |

c38.s1.4

(2)—*b*. Long. of Mercury's Apsis minus Sun's mean Long. Long. of Mercury's Apsis for A.D. 900 (p. 201)* | ... | 220·44° | Sun's mean Long. (as above) : | | - 197·48° |

c38.s1.5

| | | 22·96 *b* |

c38.s1.6

(3)—*v*. Mean Long. of Sun | ... | 197·48° *v* |
(4) Mercury's annual equation for *a* (p. 202) : | | - 3·0° (4) |
(5) Take half of (4) with reversed sign, and add to *b* | ... | 22·96 |

c38.s1.7

| | | + 1·5 |
| | | 24·5 (5) |

c38.s1.8

(6) Mercury's anomalistic equation for (5) (p. 242) : | + | 1·9° (6) |
(7) Take half of (6), with reversed sign, and add to (5) | ... | 24·5 |

c38.s1.9

| | | - 0·9 |
| | | 23·6 (7) |

c38.s1.10

(8) Anomalistic equation of (7) (p. 202) : | + | 1·8 (8) |
(9) Take (8), with reversed sign, and add to *a* | ... | 185·3 |

c38.s1.11

| | | - 1·8 |
| | | 183·5 (9) |

c38.s1.12

(10) Annual equation of (9) (p. 202) : | - | 2·0 (10) |
(11) Add (8) and (10) : + 1·8° - 2·0° = | - | 0·2 (11) |
(12) Add *v* and (11) : 197·48° - 0·2° = | | 197·3° (12) |

c38.s1.13

This last result 197·3° is the true geocentric place of Mercury for the moment in question.

c38.s1.14

∗ The apses and nodes of planets, except the moon, have such slow motions that their places need not be calculated for odd years and days.

c38.s1.15

289. II. To find the latitude of Mercury (i.e., his distance above or below the ecliptic for the same moment.)

c38.s1.16

(13) Mercury's mean longitude ... 22·78° minus Longitude of Mercury's node (p. 201): - 20·72 2·06° (13)
(14) Take (8) above, with sign reversed, and add to (13) : - 1·8 0·3° (14)
(15) Sine of (14) according to Table XVII-F (p. 209) ... 18 (15)
(16) Equation corresponding to (9) supra, by Table XVII-E. Equation for 183·75° = 2173. " " 2° = 05 × 5 = 25. ∴ Equation for 183·5° = 2173 minus 25 = 2172·75 ... 2173 (16)
(17) Multiply (15) by 120, as a constant for Mercury, and divide the product by (16) 120 × 18 / 2173 = 2160 / 2173 = 9. Now by Table XVII-F, 225 is the sine of 3·75° ∴ 9 is the sine of (3·75° × 9) / 225 = 3·375 / 225 = 015°.

c38.s1.17

N.B.—The corresponding constants for the other planets are the sines of their greatest apparent latitudes, given at foot of Table XVII-E.

c38.s1.18

The latitude of Mercury is 015° and inasmuch as (14) is less than 180°, i.e., above the ecliptic, the latitude 015° is North.

Mars (Superior Planet)

c38.s2.1

290. I. To find the Geocentric Longitude of Mars (Superior Planet) for 202·54 days in Solar Year A.D. 961-62.

c38.s2.2

Time and English date. 9 ghatikas after sunrise on 11th October A.D. 961.

c38.s2.3

(1) A. Mean longitude of Sun minus Mars' mean longitude.

c38.s2.4

Mean longitude of Sun (already found) 197·48° or 197·48° + 360° = 557·48°

c38.s2.5

Mean longitude of Mars For A.D. 900, 79·49° " 61 years, 155·72° (Table XVII, p. 200.) " 202 days, 105·85° See also p. (104) supra. " 54 day, ·28° 341·34° - 341·34° 216·14° A (2) B. Long. of Mars' Apsis *minus* mean long. of Mars. Long. of Mars' Apsis [*vide* foot-note on p. (106)] (p. 200) 130·04° or 490·04° Mean longitude of Mars ... ... ... - 341·34° 148·70° B

c38.s2.6

(3) N. Mean longitude of Mars ... ... ... 341·34° N
(4) Mars' annual equation for A (p. 200) ... ... - 39·0° (4)
(5) Take half of (4) with reversed sign, and add to B ... 148·70° + 19·5 168·2° (5)

c38.s2.7

(6) Mars' anomalistic equation for (5) (p. 201) ... ... + 2·4° (6)
(7) Take half of (6), with reversed sign, and add to (5) ... 168·2°
- 1·2° 167·0° (7)

c38.s2.8

(8) Anomalistic equation of (7) (p. 201) ... ... + 2·7 (8)
(9) Take (8) with reversed sign, and add to A ... ... 216·14°
- 2·7 213·4° (9)

c38.s2.9

(10) Annual equation of (9) (p. 200) ... ... - 38·0° (10)
(11) Add (8) and (10) : + 2·7° - 38·0° ... ... - 35·3° (11)
(12) Add N and (11) : 341·34° - 35·3° ... ... 306·0° (12)

c38.s2.10

The true **Geocentric Longitude** of Mars at the moment in question was 306·0°.

c38.s2.11

291. II. To find the latitude of Mars, *i.e.*, his distance above or below the Ecliptic for the same moment.

c38.s2.12

(13) Mars' true geocentric longitude ... ... 306·0° *minus* Longitude of Mars' node for A.D. 900, (Tab. XVII, p. 200) - 40·07 [*vide* foot-note on p. (106).] 265·93° (13)

c38.s2.13

(14) Take (10) above for Mars, with sign reversed, and add to (13): + 38·0 308·9° (14)

c38.s2.14

(15) Sine of (14) according to Table XVII-F ... ... 2267 (15)
(16) Equation for (9) above, by Table XVII-E ... ... 2011 (16)
(17) Multiply (15) by 90, as a constant for Mars, and divide by (16) 90 × 2267 = 2040·30 = 101. 2011 2011

c38.s2.15

*N.B.*—The corresponding constants for the other planets are the sines of their greatest apparent latitudes, given at foot of Table XVII-E.

c38.s2.16

Now by Table XVII-F the sine 101 belongs to an angle between 0° and 3·75° 225 is the sine of 3·75°

c38.s2.17

∴ The latitude of Mars sought is 1·7 which is South since (14) is above 180°.

c38.s2.18

292. *To find the longitude and latitude of the moon for the above moment.*

c38.s2.19

We should first of all find the moon's true longitude which we may calculate either from the tithi direct, with the aid of Table XVII-A and XVII-C (as we did in Sec. 287), or from the Nakshatra. We shall follow the latter method, although the former is easier.

c38.s2.20

The last New moon before our date (11 Oct. A.D. 961) was that on September 12·74 (Table X, p. 73). This was Āśvina New moon. The tithi for our date is that corresponding to the interval between Oct. 11·02 and Sep. 12·74, or between 41·02 and 12·74, *i.e.*, 28·28 days. This, by Eye-Table, is less than the interval for 29 tithis, which is 28·55 days.

c38.s2.21

As our Nakshatra must fall on the same day as the Tithi, we must take a Nakshatra in the lunar month of Āśvina, whose interval, after correction, shall be near 28·55 days.

c38.s2.22

The Nakshatra correction for A.D. 961 is (by Tab. XI) that for 26·47 days, *i.e.*, 1·95 (correction for 26 days) + ·03 (correction for 47 day) = 1·98, and 28·55 + 1·98 = 30·53. This is 1 day more than a lunar month and an interval of 30·53 days from Āśvina New moon takes us to 1 day from Kārttika New moon. The nearest interval to this in Table XI is 1·0757 days under Kārttika (col. VII), for which the Nakshatra is No. 14 *Chitrā*.

c38.s2.23

The interval for No. 14 *Chitrā* is 1·0757 days from Kārttika New moon, *i.e.*, 1·08 + 2953 or 30·61 days from Āśvina New moon. Deduct correction for A.D. 961 — 1·98

c38.s2.24

Actual interval of No. 14 Nakshatra is 28·63 days from Āśvina New moon. ∴ Time of mean ending moment of No. 14 Nakshatra was Sep. 12·74 + 28·63 = Sep. 41·37 = Oct. 11·37.

c38.s2.25

The ☾'s anomaly for the ending moment of the Nakshatra : 7·09 (Anomaly of First New moon in solar year A.D. 961, vide Tab. X, p. 72) + 9·88 (addition for ☾'s Anom. at Āśvina New moon : Table X, head line) + 28·63 (actual interval from Āśvina New moon to No. 14 Nakshatra) = 45·60 days, from which deduct 1 anom. month, 27·55. Remainder, 18·05 days.

c38.s2.26

The Nakshatra eqn. for 18·05 days is + ·333 (Table IX-*k*). Nak. No. 14 *Chitrā* ended therefore on Oct. 11·37 + ·33 = Oct. 11·70 or 42 ghaṭikas after sunrise (Eye-Table). The moment for which we want the moon's true place is earlier than this by ·55 day, which (by Table XVII-D) corresponds to 7·33 degrees of moon's longitude. (See, however, *N.B.* to Section 287.)

c38.s2.27

At the ending moment of No. 14 Nak. the moon's longitude is 186·7° (Eye-Table); the true place of moon at the moment now in question (9 ghaṭikas after sunrise on 11 Oct. A.D. 169) was, therefore, 186·7° - 7·3° = 179·4°.

c38.s2.28

293. *Now to find the Moon's latitude at the moment sought.*

c38.s2.29

(1) Find the place of Moon's node, *i.e.*, Rahu. By Table XVII-B place of Rahu for A.D. 900 is ... 147·65 By same table Rahu's motion for 61 years, 100·52° N.B.—Remember that Rahu's mean motion for 200 days, 10·60° odd years and days should be subtracted from the '54 day, ·03 mean place for century—*vide* Sec. 295 (4). 61 yrs. 200·54 days = 111·13 ... —111·13° 36·52° (1)
(2) Moon's true place *minus* place of her node ... ... 179·4° —36·5 142·9 (2)
(3) Sine of (2) by Table XVII-F ... ... 2094 (3)
(4) Multiply (3) by 270/3438, as a constant for the moon: (2094 × 270)/3438 = 164. By Table XVII-F, 225 is the sine of 3·75° ∴ 164 " (164 × 3·75)/225 = 2·73°

c38.s2.30

Inasmuch as (2) is less than 180°, the latitude sought is 2·73° North.

c38.s2.31

294. The reader should note—

c38.s2.32

(*a*) that for Venus the procedure is the same as for Mercury;

c38.s2.33

(*b*) that for Jupiter and Saturn, the procedure is the same as for Mars;

c38.s2.34

(*c*) that for Mercury and Venus, the geocentric longitude has for its basis the Sun's mean longitude and not that of the planet; whereas the geocentric places of Mars, Jupiter and Saturn are based on their respective mean longitudes;

c38.s2.35

(*d*) that we may always subtract a larger number of degrees from a smaller by adding 360° to the smaller number, as we did for (1) *a* on p. (106), for (1) A on p. (107) and for (2) B on p. (108);

c38.s2.36

(*e*) that the apsis of any planet except the moon does not change materially in position during a century, and that therefore we need not calculate the change of apsis for odd years or odd days; [*vide* foot note on p. (106)].

c38.s2.37

(*f*) that after calculating *a, b* and *v*, and A, B and N, respectively, the procedure is the same for all planets, whether inferior or superior;

c38.s2.38

(*g*) that the mean longitudes of planets for decimals of a day may be obtained from the longitude for odd days by prefixing decimals to the latter. Only we should remember that a mean revolution of Mercury is completed in 87 days and a mean revolution of Venus in 225 days, [*vide* Sec. 276] and the increase of Mercury's longitude for ·89 day is not 0·422°, but 3·6422°. Similarly, the increase of Venus' longitude for ·231 day is not 01009°, but ·37009°;

c38.s2.39

(h) that the latitudes of planets are not referred to in Indian usage except in what is known as a planetary fight in astrology;

c38.s2.40

(i) that the greatest apparent latitudes of the several planets and their corresponding Hindu sines are given at foot of Table XVII-E.

c38.s2.41

295. In using Table XVIII, Geocentric (Indian) Longitudes of Sun and Major planets at Ujjain Sunrise for every ten days from A. D. 1840 to A. D. 1920, the reader will do well to bear in mind the following instructions:—

c38.s2.42

(1) Table XVIII is intended to be of use in constructing or verifying the horoscopes of persons now living or to be born in the next nine years.

c38.s2.43

(2) The elements of a horoscope are the rāsi positions of laghna, Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn, Rahu and Ketu.

c38.s2.44

(3) Of these, the positions of Sun,* Mars, Mercury, Jupiter, Venus and Saturn are given in Table XVIII.

c38.s2.45

(4) The laghna may be ascertained with the aid of the rules given in sections 71 to 76 supra. The position of Rahu for any day of the solar year may be ascertained from Table XVII-B. In using this table remember that the signs of Rahu are counted backwards and therefore the longitude of Rahu for odd years and days should be deducted from its longitude for centuries in order to arrive at its position at any moment. Ketu is always 180° from Rahu. It does not matter whether for Ketu we add or subtract 180° from Rahu's place: the result will always be the same.

c38.s2.46

(5) The position of the moon should be determined from her Nakshatra. It would have been no use to have given the position of the moon for every ten days of the year in Table XVIII, since her position shifts by 13° every day and is liable to considerable perturbations on account of her anomaly. Numerous examples are given in the text, showing how the moon's longitude may be ascertained either from the Tithi direct or from the ending momemt of the Nakshatra. [See especially Sections 287 and 292.]

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(6) For planets other than Moon, Rahu and Ketu, Table XVIII gives precise information for every ten days, beginning each year with what is called 0 day of the solar year. The 0 day of the solar year is the day on which the solar year commences, as shown in Table X, not as shown in Table XII (Ephemeris). The English date shown in Table X in the 4th column headed "Month and day A.D.", is the 0 day of each solar year. For example, the 0 day of the solar year A.D. 1911-12 is April 13.

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(7) English dates corresponding to days of the solar year are given most exactly in Table XVIII and not merely by approximation. The Tamil dates shown in the headlines of Table XVIII are approximate: the exact Tamil date corresponding to any English date can be easily ascertained from Table XII.

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∗ To the mean longitude of the Sun given in the second head-line of Table XVIII should be added the equation given in the third head-line, and the correction for ☉'s long. given under each particular year. See example in Sec. 286.

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(8) For dates between every 10th day which is shown in Table XVIII, take proportional parts. Thus, position of Mercury on 23 May 1910 is 44·1° Do. do. do. 2 June 1910 is 36·6° Difference for 10 days=7·5° ∴ Difference for 6 days= 6/10 × 7·5 = 4·55° ∴ Position of Mercury at Ujjain sunrise on 29 May 1910 is 44·1° - 4·5° = 39·6°. *N.B.*—Except in A.D. 1905, A.D. 1909 and A.D. 1913, the actual places of Mercury from A.D. 1886 to A.D. 1919 are practically identical with those for A.D. 1840 to 1873. In other words, Mercury's actual places follow in general a cycle of 46 years. Compare Sec. 228 regarding the moon's cycle of 46 years.

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(9) The interval between the 360th day of each solar year and the 0 day of next solar year is either 5 or 6 days according as the former Indian solar year is one of 365 or 366 days. To ascertain this point, refer to Table X: if the fraction of day at which a year commences increases beyond unity in the next year, the year with the former fraction is one of 366 days; where there is no increase of fraction, the length of the year in integral days is 365. Thus, fraction of day for commencement of A.D. 1909-10 is ·9492 Do. do. do. 1910-11 is ·2080 Do. do. do. 1911-12 is ·4667 We infer that A.D. 1909-10 (Indian Solar Year) is a year of 366 days and that A.D. 1910-11 and A.D. 1911-12 are years of 365 days each. Of course an Indian Solar Year with 366 days will not, except by chance, correspond with an English leap year.

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The difference in the longitude of any planet between the 360th day of one solar year and 0 day of the next solar year should be divided by 5 or 6 (according as the year is one of 365 or 366 days) in order to get the difference of longitude for *one day* during that interval, and the difference for one day should be multiplied by as many days as we want.

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(10) Two English dates are marked in Table XVIII (just as in Table VIII, vide Sec. 215), when there is a possibility of a year with Feb. 29 alternating with a year in which February has only 28 days. Thus under 330th day on p. 225, "March 6, 7" is entered, which means that if before reaching either of these dates we have passed "February 29", March 6 is the equivalent of the 330th day of the Solar Year, otherwise March 7 is the 330th day.

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(11) The positions marked in Table XVIII are all for Ujjain sunrise and any given moment for which we wish to verify or construct a horoscope should first be reduced to Ujjain time by adding or deducting the total correction for the place, day of the solar year and latitude shown in Table XIII or Table XIII-A. Of course the reader will remember that corrections shown in Table XIII are intended to enable him to obtain local time from Ujjain time, and that to obtain Ujjain time from local time, the signs of the corrections must be reversed.

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(12) It is assumed that the reader knows the ordinary facts about the apparent motions of planets, *i.e.*, they are occasionally stationary or nearly so, and often in retrogression; that any planet is in conjunction with another whose longitude is the same; and in opposition when the distance between the longitudes or the two planets is 180°.

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(13) The houses or signs in which the planets are situated according to Table XVII show only occupation (in the language of astrology). Ownership or lordship of houses by planets is purely an astrological convention and has nothing to do with astronomy.

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(14) The entries at foot of Table XVIII show the limits or ending points of signs or rāśis and nakshatras, while the Eye-Table gives the longitude at commencement of each Rāśi or Nakshatra. Both sets of entries will be found very useful, and examples of their use are given throughout this work: see for example Sections 49, 186, 266, 287; foot-note to p. (45) of the text, etc.

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(15) In order to keep the present work within its proper limits, it has been considered essential that the information furnished by it shall be such as will be directly useful for chronological investigation. That it may serve indirectly the purposes of Indian astrology is from the nature of the case, inevitable, but judicial astrology, or the interpretation of planetary phenomena for astrological purposes, is entirely beyond the author's scope: and it has been finally decided not to include in this book any criticism of judicial astrology.

Construction of Indian Horoscopes.—Navamsas

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296. Indian usage has, for a long time past, adopted a well-known method of exhibiting the places of planets at particular moments. This is the familiar horoscope, which, relieved of its astrological excrescence, has a scientific value as a chronological record; since a genuine horoscope may, by the exercise of a little ingenuity, be always referred to its date, however remote that date may be, and even though there may not be a single figure indicative of an era or a year. It is for this chronological reason that horoscopes are introduced into this work.

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Having ascertained the longitudes of planets and the lagna, which is merely a device for indicating the time of day without the use of figures (see Sections 71 to 76), we may exhibit them in the form of a horoscope, as shown on the next page. This is a horoscope for the moment already examined, viz., sunrise on 13 April 1911, being 0 day of the Indian Solar Year A.D. 1911-12, Kaliyuga 5012.

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297. It might seem at first sight that the first of these tables, which distributes the planets among 12 signs of 30 degrees each, cannot serve the purposes of an accurate chronological record. It is a fact, however, that no other horoscope within perhaps 5000 years will be exactly like this one: and given such a horoscope as this, one may, without further indications, though after some trouble, discover the year; and once the year is discovered, the month, day and hour can be identified in a few minutes.

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298. In practice, it is usual for the astrologer or chronologer to frame a more detailed record, and as Indian tradition demands that figures should, as far as practicable, be dispensed with in chronological records, the details of degrees in a horoscope are given by means of a Navāṁśa scheme such as that shown on the next page. In the Navāṁśa scheme, each sign of 30° is sub-divided into 9 Navāṁśas, whence their name, and 12 such Navāṁśas constitute a full horoscope. Table XXI compares the Rāśis and Navāṁśas, and shows clearly how, given a Rāśi and the corresponding Navāṁśa, the exact position of a planet can be indicated within three degrees. For instance, if we know that Śukra is in Rāśi Vrishabha (II) and Navāṁśa Makara (X) we can, from the Navāṁśa Table XXI, find that Śukra must be between 30° and 33°3°; this is a fairly close approximation to the exact longitude.

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Other divisions of the Rāśis into dvādaśāṁśas (12 divisions of 2½ degrees each), triṁśāṁśas (30 divisions of a degree each) and shashthiāṁśas (60 divisions of half a degree each), will be self-evident.

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| XII | I | II | III |
| Mina OR Pisces. | Mesha OR Aries Lagna Sun or Ravi Mercury or Budha Saturn or Sani Rahu. | Vrishabha OR Taurus Venus or Sukra. | Mithuna OR Gemini. |
| XI Kumbha OR Aquarius. | | | IV Kataka OR Cancer. |
| X Makara OR Capricornus Mars or Kuja. | | RASI. | V Simha OR Leo. |
| IX Dhanus OR Sagittarius. | VIII Vrischika OR Scorpio. | VII Tula OR Libra Jupiter or Guru Ketu. | VI Kanya OR Virgo Moon or Chandra. |

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| XII | I | II | III |
| Mina Guru. | Mesha Lagna Ravi. | Vrishabha. | Mithuna. |
| XI Kumbha. | | | IV Kataka Chandra. |
| X Makara Sukra. | | NAVAMSA. | V Simha Budha Sani. |
| IX Dhanus. | VIII Vrischika. | VII Tula Rahu. | VI Kanya Kuja. |