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 c15: Chapter X. Lagna
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 c15
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Chapter X. Lagna
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LAGHNA.
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71. Closely analogous to the calculation of sunrise is that of the laghna, i.e., the portion of the ecliptic which appears at the eastern horizon at a particular moment of the day. At other times we might require to know the moment of the day when a particular portion of the ecliptic will be laghna. An example of the first kind of problem is:—
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"What is the laghna at the moment of a person's birth"?
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N.B.—The portion of the ecliptic which is laghna or "out" at the horizon at any given moment is ordinarily referred to as "the laghna".
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An example of the second problem is:—
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"At what moment of a day, suitable for marriage, will a particular sign of the zodiac be laghna, so that the hour as well as the day most suitable for marriage may be determined"?
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The best exposition of the Laghna is that given by Professor Jacobi at pp. 189, 190 of the Indian Antiquary for 1900, Vol. XXIX. A slight adaptation of Professor Jacobi's rules will be necessary to suit our Sunrise Table XIII.
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72. The Rules are :—
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(1) Calculate the time-difference for the interval of space between the sun and the portion of the ecliptic which is laghna.
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(2) Apply the necessary corrections for tropical longitude.
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73. Problem I.—At how many ghatikas and palas after sunrise was the 165th degree of the ecliptic (i.e., the 15th degree of the sign Kanya vide Eye-table—) laghna on the 6th Jyeshtha (Bengal solar month) in Kaliyuga 4000, Latitude 20° North? By Table VIII, the end of 6th solar Jyeshtha was 60+30·93+6=37·53 days from the first day of the solar year.
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(N.B.—We add 60 on account of the commencement of the solar year according to Table X—Surya Siddhanta).
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Now, the sidereal longitude corresponding to any day of the solar year is found from Tables XVII-A and XVII-C (Tables, p. 207 208) thus :—
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⊙'s Long. for 37 days of the solar year (Table XVII-A). 34·32° ⊙'s Long. for ·53 day (Table XVII-C) ... ... ·52 34·84°
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For the present purpose we take the nearest whole degree, i.e., 35 degrees.
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The interval in space between 35° and 165°=130°.
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Now 360° of the ecliptic rise above the horizon in 1 day or 60 ghatikas.
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∴ 180° . . . . . (130 × 60)/360 = 21 ⅔ ghatikas = 21 ghatikas 40 palas.
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In other words, the 165th degree of the ecliptic was laghna about 21 ghatikas 40 palas after sunrise on the day in question.
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74. Next, we proceed to apply the corrections for tropical longitude.
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The difference between the tropical and sidereal longitude of the sun for the year 4000 Kaliyuga = (4000-3740)/64 = 4 days. Now 37·53 days + 4 days = 41·53 days.
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The correction for the tropical longitude of the sun is that pertaining to the 41st day in Table XIII, p. 165, under latitude 20°, i.e., + 1865 seconds.
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For the correction for tropical longitude of the laghna, i.e., sidereal 165° of the ecliptic in Kaliyuga 4000 we have to determine the day when the sun accomplishes 165° of the ecliptic, which is determined as follows from Tables XVII-A and XVII-C :—
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(Table XVII-A) 169 days = 164·43° (Table XVII-C) ·58 day = ·57° 169·58 days = 165°
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We add 4 days to 169·58 days for tropical longitude in the year 4000 Kaliyuga. Total 173·58 or 174 days.
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The correction for tropical longitude corresponding (in Kaliyuga 4000) to sidereal 165°, or tropical 174 days, is, + 151 seconds.
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We add this correction *with the sign reversed* to the first:— + 1865 - 151 = 1714 seconds = + 72 palas. Adding this correction to the approximation first arrived at, we have 21 ghaṭikas 40 palas. + 1 ghaṭika 12 palas. 22 ghaṭikas 52 palas.
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This was the moment (according to Professor Jacobi, *loc. cit.*) when the 165th degree of the ecliptic was *laghna* on the day in question.
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*N.B.*—Firstly, we had to convert 165° of the ecliptic into days in order to apply Table XIII, which expresses the various portions of the ecliptic as days of the solar year.
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Secondly, we reversed the sign of the correction in the case of the *laghna* because what we wanted was the difference between the corrections on account of the tropical longitude of the sun and of the *laghna* respectively.
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75. *Second Problem.*—"What portion of the ecliptic was *laghna* on the same day at 20 ghaṭikas after sunrise"?
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We have seen that the Solar 6th Jyeshṭha corresponds to 35° sidereal longitude.
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Now, a time-difference of 20 ghaṭikas answers to an interval in space of 20 × 360/60 = 120 degrees.
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∴ The portion of the ecliptic which was *laghna* at 20 ghaṭikas after sunrise was (*roughly*) 120° + 35° = 155° or the 5th degree of the 6th sign *Kanya* (*vide* Eye-table for the longitude corresponding to the different Rāśes).
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This is enough for all ordinary calculations of *laghna*.
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If we wish to be quite accurate, we proceed as follows. The correction for tropical longitude of the sun on the day in question was, as we have seen, + 1865 seconds.
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The correction for the tropical longitude of the *laghna*, i.e., 155° of the ecliptic must be found by applying Tables XVII-A and XVII-C.
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(Table XVII-A) 159 days = 154·57° (Table XVII-C) 44 day = ·43° 159·44 days = 155·00° Add for tropical longitude 4 days 163·44 days.
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The correction for tropical longitude pertaining to the 20th degree of latitude and the 163rd day (in Kaliyuga 4000) is (by Table XIII) + 333 seconds.
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We add this *with sign reversed* to the first correction: + 1865 - 333 = + 1532 = + 64 palas.
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In other words, on the day in question, the 155th degree of the ecliptic was *laghna* at 20 ghaṭikas *plus* 64 palas.
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We want, however, the degree of the ecliptic which was *laghna* at exactly 20 ghaṭikas after sunrise.
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76. The annexed small table adapted from Prof. Jacobi's Table of udayāsus in Vol. 1, Ep. Ind., enables us to accomplish this stage of the problem.
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We learn from this table that in the 20th degree of latitude the 6th sign of the zodiac (Kanyā, with which we are concerned) takes 257 seconds to rise one degree above the horizon.
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∴ 64 palas or 1532 seconds are taken to rise 1532/257 = 5.9611°
or (by Table XX) 5 degrees 57 minutes 40 seconds,
or nearly 5 degrees 58 minutes.
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In other words, we should deduct 5 degrees 58 minutes from 155° in order to know which portion of the ecliptic was laghna at exactly 20 ghaṭikas after sunrise on the day in question.
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The portion in question was 155° minus 5 degrees 58 minutes = 149 degrees 2 minutes, which is exactly the result arrived at by Professor Jacobi.
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TABLE.
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Time (in seconds) taken by a Degree of the Ecliptic to rise above the Horizon. DEGREES OF TERRESTRIAL LATITUDE FROM 8° TO 35°.
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| Signs of the Zodiac. | Degrees of Ecliptic. | | | 8° | 9° | 10° | 11° | 12° | 13° | 14° | 15° | 16° | 17° | 18° | 19° | 20° | 21° |
| I | 0°—30° | XII | 330°—360° | 210 | 208 | 206 | 204 | 202 | 201 | 199 | 197 | 195 | 194 | 192 | 190 | 188 | 186 |
| II | 30—60 | XI | 300—330 | 229 | 227 | 226 | 224 | 223 | 221 | 220 | 218 | 217 | 215 | 214 | 212 | 211 | 206 |
| III | 60—90 | X | 270—300 | 253 | 253 | 252 | 252 | 251 | 251 | 250 | 250 | 249 | 248 | 248 | 247 | 246 | 249 |
| IV | 90—120 | IX | 240—270 | 263 | 263 | 264 | 264 | 265 | 266 | 266 | 267 | 267 | 268 | 269 | 269 | 270 | 270 |
| V | 120—150 | VIII | 210—240 | 250 | 251 | 253 | 254 | 256 | 257 | 259 | 260 | 262 | 263 | 265 | 266 | 268 | 269 |
| VI | 150—180 | VII | 180—210 | ... | ... | 239 | 241 | 243 | 244 | 246 | 248 | 250 | 252 | 254 | 255 | 257 | 259 |
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| Signs of the Zodiac. | Degrees of Ecliptic. | | | 22° | 23° | 24° | 25° | 26° | 27° | 28° | 29° | 30° | 31° | 32° | 33° | 34° | 35° |
| I | 0°—30° | XII | 330°—360° | 184 | 182 | 180 | 178 | 176 | 174 | 172 | 170 | 168 | 165 | 163 | 161 | 159 | 157 |
| II | 30—60 | XI | 300—330 | 208 | 206 | 204 | 203 | 201 | 199 | 197 | 196 | 194 | 192 | 190 | 188 | 186 | 184 |
| III | 60—90 | X | 270—300 | 245 | 244 | 244 | 243 | 242 | 242 | 241 | 240 | 239 | 238 | 238 | 237 | 237 | 236 |
| IV | 90—120 | IX | 240—270 | 271 | 273 | 273 | 274 | 274 | 275 | 275 | 276 | 277 | 277 | 278 | 278 | 279 | 280 |
| V | 120—150 | VIII | 210—240 | 270 | 272 | 274 | 276 | 278 | 279 | 281 | 283 | 285 | 287 | 289 | 291 | 293 | 295 |
| VI | 150—180 | VII | 180—210 | 261 | 263 | 265 | 267 | 269 | 271 | 273 | 275 | 278 | 280 | 282 | 284 | 286 | 288 |