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 c14: Chapter IX. Sunrise
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 c14
- Language
- English
Chapter IX. Sunrise
c14.2
62. As explained in sections 130, 131, Part II "Use of the Tables", all Indian time is reckoned, in the first instance, from Laṅkā sunrise, and corrections are then applied so as to arrive at the time reckoned from local sunrise. These corrections are three in number :—
c14.3
(1) A correction for terrestrial longitude ;
c14.4
(2) A correction for equation of time ;
c14.5
(3) A correction for the sun's tropical longitude.
c14.6
63. To understand the nature of these corrections, we shall give in popular language the astronomical theory of local time, as applied by Indian Astronomers.
c14.7
(1) CORRECTION FOR TERRESTRIAL LONGITUDE.—If the sun moved uniformly along the celestial equator, all places on earth would have sunrise at exactly 6 a.m., local time. On this supposition local time for any moment of the day could be deduced from Laṅkā time by adding or subtracting four times as many minutes of time as there are degrees of longitude between Laṅkā (or Ujjain) and the given place. The longitude of Ujjain being 76° East of Greenwich, any place whose longitude is more than 76° from Greenwich has a positive correction, and any place whose longitude is less than 76° has a negative correction for terrestrial longitude. For example: the longitude of Madras being 80¼° East of Greenwich, *i.e.*, 4¼° more than Ujjain, local time at Madras is obtained from Laṅkā time by adding 4¼° × 4' = 18 minutes of time.
c14.8
*N.B.*—A meridian of terrestrial longitude makes a revolution of 360° in 24 hours, that is, it revolves 1° in 24 × 60 ÷ 360 = 4 minutes. This interval of 4 minutes may be called the *time-difference* corresponding to a degree of terrestrial longitude.
c14.9
The TIME-DIFFERENCE or correction for terrestrial longitude for nearly 200 important places in India (their importance being gauged by their population according to the Census Report of 1901) is given in Table XIII-A, pages 189, 190. The correction is given in seconds of time which can be converted into *palas* or *vināḍis* by simply dividing the correction by 24.
c14.10
(2) CORRECTION FOR EQUATION OF TIME.—The sun does not move uniformly throughout the year, as we know from Table IX-c and Table XVII-A. Hence, for each day of the solar year, we have to apply a correction which depends on the day's equation of the centre. The correction for each day of the solar year on account of the equation of time is given in Table XIII and it is expressed, like the first correction, in seconds of time.
c14.11
(3) CORRECTION FOR THE SUN'S TROPICAL LONGITUDE.—The sun does not move along the equator, as in our first supposition, but along the ecliptic; and therefore it is only at the points where the ecliptic cuts the equator, *i.e.*, at the moments of vernal and autumnal equinox that the first supposition holds good. At other times of the year, a correction has to be applied, depending on the sun's tropical longitude, *i.e.*, on his distance from either equinox measured along the ecliptic.
c14.12
64. Now, how are we to determine the sun's tropical longitude? The longitude that is given by the day of the Indian solar year is a sidereal longitude, *i.e.*, the longitude of the sun measured from a fixed point of the ecliptic, which fixed point was the true vernal equinox about A.D. 500 or Kaliyuga 3600. Every year since then, the vernal equinox has been moving further and further away from that fixed point, and the sun's tropical longitude for any year subsequent to 3600 Kaliyuga must be found by adding to his sidereal longitude 3 degrees for every subsequent period of 200 years.* In this portion of our treatise degrees are always converted into days, and for the purpose of Sūrya Siddhānta tithis, the tropical longitude for any day in any year is determined by adding to the day of the solar year 1 day for every 64 years expired since 3740 Kaliyuga (A.D. 639). Other Siddhāntas give the precession as 1 day for every 60 years, which is more correct than 1 day for every 64 years (see Sec. 277).
c14.13
[65. By reckoning 3740 Kaliyuga and not 3600 Kaliyuga as the date of coincidence of the sidereal and tropical longitude, we eliminate the Sodhya of 21707 days (Sūrya Siddhānta); otherwise we would have to deduct the Sodhya from the day of the solar year in order to arrive at the sidereal longitude and then add to the sidereal longitude so arrived at as many days as there were periods of 64 years since 3600 Kaliyuga. (21707 × 64 = 1399248, which is nearly 140.)]
c14.14
∗ This is the correction for precession of equinoxes. The addition to be made to Indian sidereal longitudes on account of the precession of equinoxes is given in degrees in sec. 284 under "Planetary Chronology" for various epochs from A.D. 520 to A.D. 2051.
c14.15
66. The present is perhaps the best occasion in a popular work of this description for explaining what is meant exactly by the *Sodhya* when applied to the sun's sidereal longitude. The sun's equation of the centre, according to Table XVII-A on 0 day of the solar year, is + 2·1378 degrees, which, by Table VII (b) is the sun's motion for 2·17 days.
c14.16
In other words, when the mean sun is at 0 day of the solar year, the actual sun has already done 2·17 days journey of his annual course. Therefore, whenever we wish to express in days the sidereal longitude of the true or actual sun, i.e., his distance from the position he occupied on 0 day of the mean solar year, we deduct the *Sodhya* of 2·1707 days from the day of the solar year we are at.
c14.17
67. For the year A.D. 1919 the tropical longitude is found by adding to the day of the Solar Year (1919-639)/64 = 1280/64, i.e., exactly 20 days, and this addition holds good for 64 years, i.e., for 32 years before and 32 years after A.D. 1919 or from A.D. 1887 to A.D. 1951. In Table XIII the correction for Tropical longitude which applies to the year A.D. 1919 is assumed to apply to the whole period of 80 years from A.D. 1840 instead of only to the period of 32 years from A.D. 1887. There is no great error in this assumption.
c14.18
68. For 30 important places in India, including one for every degree of N. Latitude between 8° and 35°, and also Calcutta and Bombay which are dealt with separately at pp. 183 to 188, the total of all the three corrections is given in Table XIII for each day of the solar year. Further, the same table gives the equivalence of English and Indian solar dates for all solar years which commence on the 13th April; for other years we must make a deduction or addition according as the Indian solar year in question commenced after or before 13th April.
c14.19
69. With these elementary notions on Time, we are ready to work out quite accurately (according to the Siddhântas) any problem in local time. We shall work out, by way of illustrations, the somewhat formidable array of problems which are presented in Professor Jacobi's learned article in Vol. II of the *Epigraphia Indica*.
c14.20
(i) Kaliyuga 4128 ; 4 Bhâdrapada (Bengal solar month); place RATNAGIRI, 17° N. Lat.) Correction (1) for terrestrial longitude; - 34 vinadis. (We do not use this correction.)
c14.21
Correction (2), equation of time: for 4 Bhâdrapada, i.e., the 129th day of solar year, in 17° lat. + 425 seconds.
c14.22
Correction (3), tropical longitude for Kaliyuga 4128, 4 Bhâdrapada: the number of days to be added to 129 is (4128-3740)/64 = 388/64 = 6. Now, 129 + 6 being 135, it follows that correction (3) is that for the 135th day, 17° N. Lat., i.e., + 746 seconds. Total of the corrections (2) and (3) is + 425 + 746 = + 1171 seconds = 1171/24 or 49 vinadis.
c14.23
*N.B.*—Corrections (2)+(3) are sufficient for determining local sunrise: in this case the result "+ 49 vinadis" means that on the day in question the sun rose at Ratnagiri 49 vinadis or 20 minutes before 6 a.m. [Result arrived at by Professor Jacobi, 50 vinadis which is also 20 minutes of time.]
c14.24
(ii) Kaliyuga 4325, 4 Mârgaśira (Bengal solar month), SRINAGAR, latitude 34°. Correction (1) : - 8 vinadis. (We do not use this correction.) Correction (2) : + 437 seconds (220th day.)
c14.25
Correction (3): For 220 + (4325-3740)/64 = 220 + 585/64 = 220 + 9 = 229 days, the correction is - 2248 seconds.
c14.26
Total of corrections (2) and (3): + 437 - 2248 sec. = - 1811 seconds = - 75 vinadis. [Professor Jacobi arrives at the result - 74 vinadis.]
c14.27
(iii) Kaliyuga 4128; 7 Jyeshtha (Bengal solar month); Aligarh, latitude 28°.
c14.28
Correction (1), + 14 vinadis. (We do not use this correction.)
c14.29
Correction (2), - 291 seconds (37th day). Correction (3), + 2576 seconds (43rd day). . Total of corrections (2) + (3): + 2285" / = 95 vinadis (94 vinadis according / to Professor Jacobi).
c14.30
(iv) Kaliyuga 3585; Āshādha sukla 12 (lunar month), Eran, 24° N. Lat. See Part III, sec. 261, p. (92) of the text.
c14.31
70. The reader should note carefully when the total of all three corrections should be used and when the total of corrections (2) and (3) will suffice. When we merely want to know by how many seconds local sunrise preceded or followed 6 a.m., we should simply add up the second and third corrections, for here there is no need to consider the effect of terrestrial longitude. If the total correction is positive, sunrise precedes 6 a.m.; if the total correction is negative, sunrise is later than 6 a.m. The first three examples above illustrate this aspect of the problem.
c14.32
When we want to know how many seconds should be added to or deducted from the ending moment of a tithi or nakshatra, of which we already know the Lankā time, i.e., the time relatively to Lankā sunrise, we should sum up all three corrections, and if the sum is positive we should add it to Lankā time, while if the sum is negative it should be subtracted from Lankā time.
c14.33
For examples, see the tables for determining the local Madras time of the ending moments of 30 tithis and 27 nakshatras in sections 167 and 175, Part II infra.