Part 12

All these calculations, even admitting that the division marks the solstice, would still be susceptible of many modifications; and, at first, it appears that their authors have supposed the constellations all of thirty degrees like the signs, and have not reflected that it is far from being the case that they are thus equal, at least as they are represented at the present day, and as the Greeks have transmitted them to us. In reality, the solstice, which is at present on this side of the first stars of the constellation of Gemini, could only have left the first stars of the constellation of Cancer forty-five years before Christ, and had left the constellation of Leo only 1260 years before the same era.

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My distinguished and learned colleague, M. Delambre, has favoured me with the following table and remarks, which illustrate what has been above said.

_TABLE of the Extent of the Zodiacal Constellations, as they are designed upon our Globes, and of the Times required by the Colures to traverse them._

+------------------------------------------------------+ | | | ARIES. | | | +----------+-------------------+-----------+-----------+ | Stars. |Longitudes in 1800.|Year of the|Year of the| | | | Equinox. | Solstice. | +----------+-------------------+-----------+-----------+ | γ | 1^s 0° 23′ 40″ | -389 | 6869 | | β | 1 1 10 40 | -441 | 6921 | | α | 1 4 52 0 | -710 | 7190 | | η | 1 5 18 50 | -742 | 7222 | | 2 θ | 1 6 14 16 | -810 | 7290 | | ζ | 1 19 8 50 | -1739 | 8219 | | τ tail. | 1 20 51 0 | -1862 | 8342 | +----------+-------------------+-----------+-----------+ | Dur. | 20 27 20 | 1473 | 1473 | +----------+-------------------+-----------+-----------+ | | | TAURUS. | | | +----------+-------------------+-----------+-----------+ | ξ | 1^s 19° 6′ 0″ | -1735 | -8215 | | η | 1 27 12 0 | -2318 | -8798 | | α | 2 6 59 40 | -3024 | -9504 | | β | 2 19 47 0 | -3944 | -10424 | | ζ | 2 22 0 0 | -4104 | -10584 | | a Coch. | 2 24 42 40 | -4300 | -10780 | +----------+-------------------+-----------+-----------+ | Dur. | 35 36 40 | 2565 | 2565 | +----------+-------------------+-----------+-----------+ | | | GEMINI. | | | +----------+-------------------+-----------+-----------+ | Propus. | 2^s 28° 9′ 20″ | -4547 | -11027 | | η | 3 0 39 0 | -4727 | -11207 | | γ | 3 6 18 40 | -5134 | -11614 | | δ | 3 15 44 0 | -5813 | -12293 | | Castor. | 3 17 27 30 | -5937 | -12417 | | Pollux. | 3 20 28 9 | -6154 | -12634 | | φ | 3 22 27 10 | -6926 | -12776 | +----------+-------------------+-----------+-----------+ | Dur. | 24 17 40 | 1749 | 1749 | +----------+-------------------+-----------+-----------+

+------------------------------------------------------+ | | | CANCER. | | | +----------+-------------------+-----------+-----------+ | Stars. |Longitudes in 1800.|Year of the|Year of the| | | | Equinox. | Solstice. | +----------+-------------------+-----------+-----------+ | 1 ω | 3^s 24° 21′ 55″ | 6475 | +45 | | ζ | 3 28 32 0 | 6734 | -254 | | β | 4 1 28 20 | 6906 | -426 | | γ | 4 4 45 0 | 7182 | -702 | | 1 α | 4 10 18 50 | 7583 | -1103 | | 2 α | 4 10 50 36 | 7621 | -1141 | | χ | 4 13 23 0 | 7804 | -1324 | +----------+-------------------+-----------+-----------+ | Dur. | 19 1 5 | 1369 | 1369 | +----------+-------------------+-----------+-----------+ | | | LEO. | | | +----------+-------------------+-----------+-----------+ | χ | 4^s 12° 30′ 0″ | -7740 | -1260 | | α | 4 27 3 10 | -8788 | -1908 | | δ | 5 8 30 0 | -9612 | -3132 | | β | 5 18 50 55 | -10357 | -3877 | | ... | .. ... ... ... | ..... | ..... | | ... | .. ... ... ... | ..... | ..... | +----------+-------------------+-----------+-----------+ | Dur. | 36 20 55 | 2617 | 2617 | +----------+-------------------+-----------+-----------+ | | | VIRGO. | | | +----------+-------------------+-----------+-----------+ | ω | 5^s 19° 2′ 22″ | -10371 | -3891 | | β | 5 24 19 0 | -10750 | -4271 | | η | 6 2 2 40 | -11307 | -4827 | | δ | 6 8 41 40 | -11786 | -5306 | | α | 6 21 3 15 | -12676 | -6196 | | λ | 7 4 9 50 | -13620 | -7140 | | μ | 7 7 17 40 | -13845 | -7365 | +----------+-------------------+-----------+-----------+ | Dur. | 48 15 18 | 3474 | 3474 | +----------+-------------------+-----------+-----------+ | Mean | | | | | Dur. | 30 0 0 | 2160 | | +----------+-------------------+-----------+-----------+

+------------------------------------------------------+ | | | LIBRA. | | | +----------+-------------------+-----------+-----------+ | Stars. |Longitudes in 1800.|Year of the|Year of the| | | | Equinox. | Solstice. | +----------+-------------------+-----------+-----------+ | 1 α | 7^s 11° 0′ 44″ | -14113 | -7633 | | 2 α | 7 12 18 0 | -14246 | -7926 | | β | 7 16 35 0 | -14514 | -8034 | | γ | 7 22 20 34 | -14929 | -8449 | | γ Scorp. | 7 27 41 0 | -15312 | -8832 | | ξ | 7 28 30 15 | -15372 | -8892 | | ... | .. ... ... ... | ..... | ..... | +----------+-------------------+-----------+-----------+ | Dur. | 17 29 31 | 1259 | 1259 | +----------+-------------------+-----------+-----------+ | | | SCORPIO. | | | +----------+-------------------+-----------+-----------+ | 1 Α | 7^s 28° 50′ 6″ | -15396 | -8916 | | β | 8 0 23 48 | -15508 | -9028 | | α | 8 6 57 38 | -15980 | -9500 | | ζ | 8 12 35 30 | -16387 | -9907 | | λ | 8 21 47 27 | -17049 | -105569 | | ... | .. ... ... ... | ..... | ..... | +----------+-------------------+-----------+-----------+ | Dur. | 22 57 21 | 1653 | 1653 | +----------+-------------------+-----------+-----------+ | | | SAGITTARIUS. | | | +----------+-------------------+-----------+-----------+ | γ | 7^s 28° 28′ 20″ | -17530 | -11050 | | λ | 9 3 32 56 | -17895 | -11415 | | ζ | 9 10 50 28 | -18421 | -11941 | | ψ | 9 14 15 15 | -18667 | -12187 | | ω | 9 23 2 19 | -19299 | -12819 | | g | 9 25 39 25 | -19487 | -13007 | | ... | .. ... ... ... | ..... | ..... | +----------+-------------------+-----------+-----------+ | Dur. | 27 11 50 | 1957 | 1957 | +----------+-------------------+-----------+-----------+

+----------+-------------------+-----------+-----------+ | | | CAPRICORN. | | | +----------+-------------------+-----------+-----------+ | Stars. |Longitudes in 1800.|Year of the|Year of the| | | | Equinox. | Solstice. | +----------+-------------------+-----------+-----------+ | 1^{er} | 9^s 29° 39′ 15″ | -19775 | -13295 | | 2 α | 10 1 3 58 | -19877 | -13397 | | β | 10 1 15 30 | -19891 | -13411 | | ι | 10 14 53 30 | -20872 | -14392 | | γ | 10 18 59 28 | -21166 | -14586 | | μ | 10 23 1 12 | -21458 | -14978 | | ν | .. ... ... ... | ..... | ..... | +----------+-------------------+-----------+-----------+ | Dur. | 23 21 17 | 1683 | 1683 | +----------+-------------------+-----------+-----------+ | | | AQUARIUS. | | | +----------+-------------------+-----------+-----------+ | ε | 10^s 8° 56′ 0″ | -20444 | -13964 | | β | 10 20 36 30 | -21285 | -14805 | | α | 11 0 34 0 | -22001 | -15521 | | ζ | 11 6 7 0 | -22400 | -15920 | | 2 ψ | 11 13 56 12 | -22963 | -16483 | | 5 Α | 11 18 3 28 | -23260 | -16780 | +----------+-------------------+-----------+-----------+ | Dur. | 39 7 28 | 2816 | 2816 | +----------+-------------------+-----------+-----------+ | | | PISCES. | | | +----------+-------------------+-----------+-----------+ | β | 11^s 15° 49′ 0″ | 23095 | 16615 | | λ | 11 23 49 0 | 23675 | 17195 | | δ | 12 11 22 0 | 24939 | 18459 | | σ | 12 24 26 0 | 25879 | 19399 | | α | 12 26 34 58 | 26034 | 19554 | | |... ... ... ... | ..... | ..... | | |... ... ... ... | ..... | ..... | +----------+-------------------+-----------+-----------+ | Dur. | 40 45 58 | 2939 | 2939 | +----------+-------------------+-----------+-----------+ | | | 0° | 270^s | |Sirius | 3 11 20 10 | -5487 | -18447 | +----------+-------------------+-----------+-----------+

_Construction and Use of the Table._

“The longitudes of the stars, for 1800, have been taken from the Berlin Tables, and are those of Lacaille, Bradley, or Flamstead. The first and the last of each constellation have been taken, as well as some of the brightest of the intermediate stars. The third column indicates the year in which the longitude of the star was 0′, that is to say, that in which the star was in the equinoxial colure of spring. The last column indicates the year when the star was in the solstitial colure, whether of winter or of summer.

“For Aries, Taurus, and Gemini, the winter solstice has been chosen; for the other constellations the summer solstice has been chosen, for the sake of not receding into too remote antiquity, and of not approaching too near modern times. It will be easy to find the opposite solstice, by adding the semiperiod of 12,960 years. The same rule will serve for finding the time when the star has been, or will be, at the autumnal equinox.

“The sign - indicates the years before our era, the sign + the year of our era; and the last line, at the end of each sign under the title of _duration_, gives the extent of the constellation in degrees, and the time which the equinox, or the solstice, occupies in traversing the constellation from one end to the other.

“The precession of 50″ yearly has been supposed, this being the result of the comparison of the catalogue of Hipparchus with the modern catalogues. We have thus the advantage of round numbers, and a general accuracy that may be relied upon. The entire period is thus 25,920 years; the semiperiod, 12,960 years; the quarter period, 6480 years; the twelfth, or a sign, 2160 years.

“It is to be remarked, that the constellations leave empty spaces between them, and that sometimes they encroach upon each other. Thus, between the last star of Scorpio, and the first of Sagittarius, there is an interval of 6⅔ degrees. On the other hand, the last of Capricorn is more advanced by 14° in longitude, than the first of Aquarius. Hence, even independently of the inequality of the sun’s motion, the constellations would afford a very unequal and very erroneous measure of the year and its months. The signs of 30° furnish a more convenient and less defective one. But the signs are merely a geometrical conception; they can neither be distinguished nor observed; and they are continually changing place from the retrogradation of the equinoxial point.

“We have at all times been able to determine, in a rough manner, the equinoxes and solstices; at the long run it has been remarked, that the appearance of the heavens was no longer exactly the same that it anciently was at the times of the equinoxes and solstices. But we have never been able to observe exactly the heliacal rising of a star, being always necessarily some days wide of it; and people frequently speak of it, without possessing a fixed datum on which to count. Before Hipparchus, we find nothing, either in books or in traditions, that can be submitted to calculation; and it is this which has given rise to so many systems. Controversies have arisen without a sufficient knowledge of the subject. Those who are not astronomers may form ideas as beautiful as they please of the knowledge of the Chaldeans, Egyptians, &c.; no real inconvenience will result. The enterprise and knowledge of the moderns may be lent to these nations, but nothing can be borrowed from them; for they have either had nothing, or they have left nothing. Astronomers will never derive from the ancients any thing that can be of the slightest utility. Let us leave to the learned their vain conjectures, and confess our utter ignorance respecting things of little use in themselves, and of which no monument remains.

“The limits of the constellations vary according to the authors which we consult. We find these limits extend or contract, as we pass from Hipparchus to Tycho, from Tycho to Hevelius, from Hevelius to Flamstead, Lacaille, Bradley, or Piazzi.

“I have said elsewhere, the constellations are good for nothing, unless at the most to enable us to mark the stars with more ease; whereas the stars in particular afford fixed points to which we can refer the motions, whether of the colures or of the planets. Astronomy commenced only at the period when Hipparchus made the first catalogue of the stars, measured the revolution of the sun, that of the moon, and their principal inequalities. The rest presents nothing but darkness, uncertainty, and gross error. The time would be lost that were occupied in attempting to reduce this chaos to order.

“I have given, with the exception of a few particulars, the whole of my opinion on this subject. I am nowise anxious about making converts, for it gives me little concern whether my ideas be adopted or not; but, if my reasons be compared with the reveries of Newton, Herschell, Bailly, and so many others, it is not impossible but that, in time, these more or less brilliant chimeras will no longer be relished.

“I have attempted to determine the extent of the constellations, according to the catasterisms of Eratosthenes; but the thing is really impossible. The matter would be still worse were we to consult Hygin, and especially Firmicus. The following is what I have made out from Eratosthenes.

CONSTELLATIONS. DURATIONS. Years. Aries, 1747 Taurus, 1826 Gemini, 1636 Cancer, 1204 Leo, 2617 Virgo, 3307 The Talons, 1089[219] Scorpio, 1823 Sagittarius, 2138 Capricorn, 1416 Aquarius, 1196 Pisces, 2936

“As to the Chaldeans, Egyptians, Chinese, and Indians, there is no want of reveries among them. One can absolutely make nothing of them. My opinion with regard to them may be seen in the preliminary discourse of my History of the Astronomy of the Middle Age, p. xvii and xviii. See also the note affixed to the Report on the Memoirs of M. de Paravey, vol. viii. of the Nouvelles Annales des Voyages, and republished by M. de Paravey in his Summary of his Memoirs upon the Origin of the Sphere, p. 24, 31-36. See further the Analysis of the Mathematical Labours of the Academy in 1820, p. 78 and 79.

“DELAMBRE.”

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It would still have to be ascertained at what period the observers ceased to place the constellation in which the sun entered after the solstice, at the head of the descending signs, and whether this was done as soon as the solstice had retrograded sufficiently to touch the preceding constellation.

Thus MM. Jollois and Devilliers,--to whose unremitting zeal we are indebted for an accurate knowledge of these famous monuments, always considering the division towards the entrance of the porch as the solstice, and judging that the Virgin must have been regarded as the first of the descending constellations, insomuch as the solstice had not receded at least so far as the middle of the constellation of the Lion; and, believing that they saw farther, as we have mentioned, that the Lion is divided in the great zodiac of Esne, have not given to that zodiac a more remote antiquity than 2160 years before Christ.[220]

Mr Hamilton, who was the first that observed this division of the sign of the Lion, in the zodiac of Esne, reduced the distance of the period at which the solstice occurred there, to 1400 years before Christ. A great many other opinions have appeared on the same subject. M. Rhode, for example, has proposed two. The first refers the zodiac of the portico of Dendera to a period of 591 years before Christ; the second, to 1290[221]. M. Latreille has fixed the period of this zodiac at 670 years before Christ; that of the planisphere at 550; that of the zodiac of the great temple of Esne at 2550; and that of the small one at 1760.

But a difficulty inherent in all the dates, which proceed on the double supposition, that the division marks the solstice, and that the position of the solstice marks the epoch of the monument, is the unavoidable consequence that the zodiac of Esne must have been at least 2000, and perhaps 3000, years[222] older than that of Dendera, a consequence which evidently involves the supposition in ruin; for no one, in any degree acquainted with the history of the arts, could believe, that two edifices, so similar in their style of architecture, could have been erected at periods so remote from each other.

The feeling of this impossibility, joined always to the belief that this division of the zodiacs indicates a date, has given rise to another conjecture, namely, that the intention had been to mark the particular sacred year of the Egyptians, in which the monument had been erected. As these sacred years consisted only of 365 days, if the sun, at the commencement of one occupied the commencement of a constellation, he would be nearly six hours later in returning to the commencement of the following year, and, after 121 years, he would only be at the commencement of the preceding sign. It seems natural enough that the builders of a temple might wish to indicate about what period of the great, or Sothian year, it had been erected; and the indications of the sign, by which the sacred year then commenced, was a good enough means. It will be perceived, that, calculating upon this assumption, there will be an interval of from 120 to 150 years between the temple of Esne and that of Dendera. But, in his mode of solving the problem, there remained to be determined in which of the great years these buildings had been erected, whether in that which ended in the year 138 after, or in that which ended in 1322 before Christ, or in some other.

The late Visconti, who was the first author of this hypothesis, taking the sacred year, whose commencement corresponded with the sign of the Lion, and judging from the resemblance of the signs, that they had been represented at a period when the opinions of the Greeks were not unknown to the Egyptians, was naturally led to make choice of the end of the last great year, or the space that elapsed between the year 12 and the year 138 after Christ[223], which appeared to him to accord with the Greek inscription, of which, however, he knew little more than that it was said to make mention of one of the Cæsars.

M. Testa, seeking the date of the monument in another order of ideas, went so far as to suppose that since the Virgin is seen at Esne, at the head of the zodiac, it was meant thereby to represent the era of the battle of Actium, such as it had been established with regard to Egypt, by a decree of the senate, mentioned by Dion Cassius, and which commenced in the month of September, the day on which Alexandria was taken by Augustus.[224]

M. de Paravey considered these zodiacs in a new point of view, which embraced at once both the revolution of the equinoxes, and that of the great year. Supposing that the circular planisphere of Dendera must have been set to the east, and that the axis from north to south is the line of the solstices, he found the summer solstice at the second of the Twins, and that of winter at the buttock of the Sagittary, while the line of the equinoxes would have passed through the Fishes and the Virgin, from which he obtained for date the first century of our era.

According to this method, the division of the zodiac of the portico could no longer refer to the colures, and the mark of the solstice must be sought for elsewhere. M. de Paravey having remarked that there are between all the signs figures of women bearing a star upon their heads, and marching in the same direction, and observing that the one which comes after the twins, is alone turned in a direction contrary to the others, judged that it indicates the _conversion_ of the sun or the tropic, and that this zodiac corresponds in this way with the planisphere.