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 c17: Chapter XII. Eclipses
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 c17
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Chapter XII. Eclipses
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82. Eclipses are a most valuable and unerring historical record, and eclipses are freely cited in Indian historical documents. Accordingly, the date of occurrence of solar and lunar eclipses has been indicated in Tables X and XII by means of the symbol ● for solar eclipses and ʘ for lunar eclipses. A solar eclipse can occur only at new moon and a lunar eclipse can occur only at full moon, and as full moons are not specially indicated in Tables X and XII, every lunar eclipse is shown merely as occurring in a particular lunar month. The actual date of a lunar eclipse can be found by working out the exact ending moment of the full-moon tithi, i.e., *panchadasi* or *paurṇamī*. For this, of course, it will be necessary to add the collective duration of 15 tithis, i.e., 14·76 days (Eye-table), to the mean moment of new moon and also to the moon's and sun's anomaly at that moment and add to, or subtract from, the mean moment of full moon the sum of the sun's and moon's equations. (See examples worked out in sections 93 and 94.)
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83. We may preface our observations on eclipses by the following passages from a well-known French work, first published in the 18th century, and still regarded as a standard authority on chronology, "*L'Art de vérifier les Dates*;—
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"The magnitude of an eclipse is indicated in digits. A digit is the twelfth part of the diameter of a heavenly body: accordingly, an eclipse of four digits is one where the third part of the diameter of a heavenly body is in shadow; if one half of the diameter is in shadow, the eclipse is said to be of six digits; and if the whole of the diameter is in shadow, the eclipse is said to be of twelve digits. Further, in a total eclipse, if the part which is least in shadow is removed from the edge of the shadow by as much as two digits, these two digits are added to the twelve, and the eclipse is said to be one of fourteen digits . . . . . "
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84. "The duration of an eclipse of the moon is proportional to its magnitude; but it does not depend on this factor alone. We may say, in general, that a total eclipse of the moon will last at least 3½ hours, and at most 4 hours and a few minutes. A partial eclipse above 6 digits may last as much as 3½ hours or as little as 2½ hours; it seldom goes beyond those limits. An eclipse of between three and six digits lasts between two and three hours. The duration corresponding to 2 digits is 1½ hours; to 1 digit, 1 hour; to half a digit, ¾ of an hour. The duration of total obscurity in a total eclipse is from 1½ to 2 hours........."
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85. "The Moon has no light of her own, but reflects that received by her from the Sun. Consequently, when in an eclipse the Earth passes between the Moon and the Sun, and cuts off the rays of the Sun from the Moon, the latter can shed no more light on Paris than on Pekin or on Constantinople. An eclipse of the Moon, therefore, commences at all points of the Earth at the same instant and lasts everywhere for the same length of time. All that we need see is whether the time of a lunar eclipse falls between local sunset and sunrise, as otherwise the eclipse will not be visible.
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86. "On the other hand, the Sun is a self-luminous body: the Moon is very much smaller than the Earth: she is, in fact, a mere point in comparison with the Sun. From these well-known facts it follows that in a solar eclipse, the Moon passing between the Earth and the Sun, cannot cut off the rays of the Sun from all parts of the Earth, at the same instant. She casts her shadow in succession on different parts of the Earth, and even the successive passage of the Moon's shadow covers during a single eclipse only a small total extent of the Earth's surface. Thus, journeying from West to East, a solar eclipse may first strike Spain, then France, then Germany, and then in succession the eastern countries as far as the farthest East of Asia, but the whole time Africa may remain untouched by the Moon's shadow".
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87. The extent of the earth's surface, affected by a solar eclipse, is therefore a matter of calculation: and an exact calculation is by no means easy to introduce into a popular work of this kind.
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The book entitled *L'Art de vérifier les Dates* gives (1) all lunar eclipses and (2) all solar eclipses visible anywhere in the civilized world known to history, marking, by a series of ingenious conventions, the path of each solar eclipse, the regions where it is visible and the latitudes where it is central (*a*) under the fifth meridian, *i.e.*, the meridian of Paris, (*b*) under the meridian where it is noon at the moment of true conjunction, and (*c*) under the 155th meridian. Other useful details, given under each eclipse, in the same valuable work, need not be reproduced here, as nothing short of a translation of the whole Chapter on Eclipses would give the reader an adequate idea of its contents.
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88. We have given in Tables X and XII *all* lunar eclipses, and it is easy for the reader to calculate the ending moment of the full moon tithi, which will enable him to know whether the eclipse could have been seen in India at the place under consideration. We have given all solar eclipses, as given in the French work, from A.D. 1 to A.D. 300, and after the latter date we have, as a rule, not mentioned eclipses which, according to the same authority, could not have been visible in India. From A.D. 1900 to A.D. 2000 all solar eclipses are marked.
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89. The points where the moon's orbit crosses the ecliptic are called the *nodes* and in order that an eclipse may occur, the opposition at the time of a lunar eclipse, or the conjunction at the time of a solar eclipse, must happen at or near a node. The sun's distance from either node is therefore an important factor in determining whether an eclipse is or is not possible at a particular New or Full Moon. Eclipse-Table X-A (pp. 130, 131) for Centuries and Odd Years will enable the reader to calculate the Sun's distance from either node at any moment from B.C. 1 to A.D. 2000, and by applying the following canons (adapted from Professor Jacobi's article in Vol. 1 of *Epigraphia Indica*) he may determine whether a solar or a lunar eclipse is certain, doubtful, or impossible at a particular New or Full Moon respectively.
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Solar and Lunar Eclipses as determined by Sun's distance from node at New and Full Moon.
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IF SUN'S DISTANCE FROM NODE AT NEW MOON IS
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Between 0 and 15·598 days, or between 157·714 and 173·312 days, Between 15·771 and 18·198 days or between 157·541 and 155·114 days, Between 18·371 and 154·939 days,
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| A SOLAR ECLIPSE IS | Certain. |
| | Doubtful. |
| | Impossible. |
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IF SUN'S DISTANCE FROM NODE AT FULL MOON IS Between 0 and 10·052 days, or between 163·260 and 173·312 days, Between 10·225 and 13·345 days, or between 163·087 and 159·967 days, Between 13·518 and 159·794 days,
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A LUNAR ECLIPSE IS Certain. Doubtful. Impossible.
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90. We shall now apply the canons to some actual cases, and see how far they will be of use to us in practice.
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Opening the first page of Table X, we see a succession of solar eclipses at the Jyeshtha new moon in the years A.D. 12, A.D. 13, and A.D. 14, and we see a similar succession of lunar eclipses in the same lunar month in the years A.D. 20, A.D. 21, and A.D. 22. We also see that in Lunar Jyeshtha, A.D. 12, as well as in Lunar Jyeshtha A.D. 22, there was a lunar as well as a solar eclipse. We shall see if our canons will help us in verifying these eclipses. The reader should note how an eclipse may be located with the help of the secular distance of the sun from the node (i.e., Distance from node for Centuries and Odd Years) as given in Table X-A and the head line entries of Table X.
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| | (1) A.D. 12 days | (2) A.D. 13 days | (3) A.D. 14 days | (4) A.D. 20 days | (5) A.D. 21 days | (6) A.D. 22 days |
| O's Distance from Node Table X-A | | | | | | |
| For century 1 B.C. ... | 62·91 | 62·91 | 62·91 | 62·91 | 62·91 | 62·91 |
| For odd year ... ... | 50·30 | 68·93 | 87·56 | 26·06 | 44·69 | 63·33 |
| Up to first New Moon in Solar Year ... ... | 26·95 | 16·06 | 5·17 | 28·41 | 17·52 | 6·62 |
| Up to Jyeshtha New Moon | 29·53 | 29·53 | 29·53 | 29·53 | 29·53 | 29·53 |
| Up to Jyeshtha Full Moon ... | ... | ... | ... | 14·76 | 14·76 | ... |
| | 169·69 | 177·43 | 185·17 | 161·67 | 169·41 | 162·39 |
| Deduct 173·31 days ... | (7) | * 173·31 | * 173·31 | ... | ... | (8) |
| | | 4·12 | 11·86 | | | |
| Up to Jyeshtha Full Moon. | 14·76 | ... | ... | ... | ... | 14·76 |
| | 184·45 | | | | | 177·15 |
| Deduct ... ... | * 173·31 | ... | ... | ... | ... | * 173·31 |
| | 11·14 | | | | | 3·84 |
| | (1) | | | | | (6) |
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We can now classify these results.
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SOLAR ECLIPSE: Certain, Results at foot of columns (2), (3), and also those in columns (1) and (6) marked (7) and (8) respectively.
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LUNAR ECLIPSE: Certain, Results at foot of columns (5) and (6). Doubtful, Results at foot of columns (1) and (4).
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∗ The period of conjoint revolution of the sun's and moon's nodes is 346·6246 days and the half revolution is 173·3128167 days. This period should therefore be deducted whenever the sun's distance from a node exceeds 173·31 days.
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91. We shall next see to what extent the canons will be of use to us in predicting eclipses. We may take as an example the solar year A.D. 1910. *
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We first of all find out the distance of the sun from the node at the first new moon in the solar year.
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| ☉'s distance from node for century beginning A.D. 1900 | ... | 120·62 |
| " " " for odd year 10 | ... | 18·03 |
| " " " at first new moon in solar year A.D. 1910 | ... | 25·91 |
| | | 159·56 |
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92. As regards solar eclipses, we have to see whether 159·56 by itself, or the same increased by 29·53, or any multiple of 29·53 entered in the head lines of Table X, will bring us within the limits of certain or even doubtful solar eclipses.
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We see at once that the figure 159·56 is itself within the limits of a certain solar eclipse. The date is the first new moon in the solar year, *i.e.*, 9th May, 1910. This eclipse was invisible in India.
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The addition to 159·56 of 29·53 gives us 189·09, which by deduction of 173·31 is equivalent to 15·78, which is beyond the limits of certainty. There was in fact no solar eclipse on the corresponding date, Jyeshṭha new moon, 7th June, 1910.
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The addition to 159·56 of 177·18 (Kārttika new moon) will give us 336·74, which by deduction of 173·31 leaves 168·43, which is within the limits of certainty. In fact, there was a solar eclipse (invisible in India) on Kārttika New Moon, *i.e.* (according to Table X or XII) 2nd November, 1910.
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The addition of no other multiple of 29·53 to 159·56 will give us a figure within "certain" or even "doubtful" limits for solar eclipses.
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93. As regards lunar eclipses, our starting figure 159·56 should be increased by the day equivalent of the full moon tithi, 14·76 days. 159·56 + 14·76 = 174·32 days. Deduct 173·31 ————— 1·01 days.
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We see that in the first lunar month of the solar year A.D. 1910 there must be a lunar eclipse.
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The actual ending moment of the full moon tithi works out as follows :—
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| | Days. | Anomaly of first new moon. |
| First new moon in solar year | 25·9134 | 0·535 |
| | 14·7653 | 14·765 |
| ☉'s Equation for 40·67 + 1140 | 40·6787 | 15·300 |
| ☾'s Equation for 15·414 + 1650 | | + 114 (☉'s Eqn.) |
| | + 2790 | + 2790 | 15·414 |
| Commencement of Solar Year, Ap. | 13·2080 | |
| | 54·1657 | |
| Add total correction for latitude 13° N. on | | |
| 40th day of Solar Year (Table XIII) | ·0286 | |
| | 54·1943 | |
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∗ This portion of the text was written before the eclipse in question happened. The force of the illustration is of course not lessened by its referring to an event now past and it has therefore been retained.
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It thus appears that the centre of the eclipse occurred at Madras at ·1943 of a day, i.e., at 11 ghaṭikas 39 palas after sunrise. It is evident that a lunar eclipse at such an hour would be invisible in India.
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94. The ☉'s distance from node at the first full moon of the solar year A.D. 1910 being 1·01, it is evident that an addition of 177·18 days, which will take us to the Kārttika Full Moon, will give us 178·19, which by deduction of 173·31 gives us 4·88 days, which is within the limits of a "certain" lunar eclipse. Let us calculate the actual ending moment of this Full Moon tithi.
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| | Days of Solar year. | ☾'s Anomaly. Days. |
| First Full Moon in Solar Year A.D. 1910 (sec. 93) | ... 40·6787 | 15·300 |
| Add for Kārttika Full Moon | ... 177·1835 | 11·856 |
| | 217·8622 | 27·156 |
| ☉'s Equation for 217·86 days = − ·1263 | | − ·1263 (☉'s Eqn.) |
| ☾'s Equation for 27·029 days = + ·0453 | − ·0810 | |
| | | 27·0297 |
| | − ·0810 | 217·7812 |
| Commencement of Solar Year 1910, Ap. 13 | ·2080 | |
| | 217·9892 | |
| Total correction (by Table XIII) for 217th day, + ·0111 | | |
| | 218·0003 | |
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∴ the centre of the eclipse at Madras was on the 218th day, reckoned from April 13, i.e., (by Table VIII) 17th November, 1910, at ·0003 of the day, i.e., 1 pala or half a minute after sunrise on 17th November, 1910.
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This very nearly agrees with the prediction in the Nautical Almanac reduced to the longitude of Madras. The eclipse was visible at Madras.
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No other multiple of 29·53, added to 1·01, will give us a lunar eclipse in the Solar Year A.D. 1910 within the limits of certainty.
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95. A third use of the canons is to enable us to detect omissions from or incorrect entries in lists of eclipses.
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The book entitled *L'Art de vérifier les Dates* states that there was no eclipse in the year A.D. 555.
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But seeing that the ☉'s distance * from node at the first new moon in the solar year A.D. 554–55 was 168·66 days, and that the year was one with an adhika month, it is plain from the head-lines of Table X that the addition to 163·66 of 354·37 gives us 518·03 days, which, deducting 346·62 leaves 171·41 days, which indicates that certainly there was a solar eclipse at the corresponding New Moon, i.e., on Chaitra New-Moon day, 8th March A.D. 555. As a matter of fact, it appears from Oppolzer's *Canon der Finsternisse*, that there was a solar eclipse on 8th March, A.D. 555.
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23·76 139·68
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96. Let us take a case in which the canons will show us that the *Art de vérifier* is right and other lists wrong. The French book mentions a Lunar Eclipse (penumbral) on 6th May A.D. 692, while other lists do not mention it.
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We find that the ☉'s distance* from node at the full moon following Jyeshtha New Moon (21 Ap. A.D. 692) was, as shown in the margin, 10·28 days, which makes it almost certain that there was then a Lunar Eclipse. The French chronological work is, therefore, right.