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.s2: Mars (Superior Planet)
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.s2
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Mars (Superior Planet)
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290. I. To find the Geocentric Longitude of Mars (Superior Planet) for 202·54 days in Solar Year A.D. 961-62.
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Time and English date. 9 ghatikas after sunrise on 11th October A.D. 961.
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(1) A. Mean longitude of Sun minus Mars' mean longitude.
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Mean longitude of Sun (already found) 197·48° or 197·48° + 360° = 557·48°
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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
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(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)
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(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)
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(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)
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(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)
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The true **Geocentric Longitude** of Mars at the moment in question was 306·0°.
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291. II. To find the latitude of Mars, *i.e.*, his distance above or below the Ecliptic for the same moment.
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(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)
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(14) Take (10) above for Mars, with sign reversed, and add to (13): + 38·0 308·9° (14)
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(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
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*N.B.*—The corresponding constants for the other planets are the sines of their greatest apparent latitudes, given at foot of Table XVII-E.
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Now by Table XVII-F the sine 101 belongs to an angle between 0° and 3·75° 225 is the sine of 3·75°
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∴ The latitude of Mars sought is 1·7 which is South since (14) is above 180°.
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292. *To find the longitude and latitude of the moon for the above moment.*
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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.
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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.
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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.
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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*.
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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
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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.
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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.
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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.)
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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°.
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293. *Now to find the Moon's latitude at the moment sought.*
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(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°
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Inasmuch as (2) is less than 180°, the latitude sought is 2·73° North.
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294. The reader should note—
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(*a*) that for Venus the procedure is the same as for Mercury;
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(*b*) that for Jupiter and Saturn, the procedure is the same as for Mars;
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(*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;
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(*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);
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(*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)].
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(*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;
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(*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°;
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(h) that the latitudes of planets are not referred to in Indian usage except in what is known as a planetary fight in astrology;
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(i) that the greatest apparent latitudes of the several planets and their corresponding Hindu sines are given at foot of Table XVII-E.
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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:—
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(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.
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(2) The elements of a horoscope are the rāsi positions of laghna, Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn, Rahu and Ketu.
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(3) Of these, the positions of Sun,* Mars, Mercury, Jupiter, Venus and Saturn are given in Table XVIII.
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(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.
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(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.