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These ancient gnomons were moreover greatly inferior to those invented in our times. To convince us of this, it is sufficient to cast our eyes on those which still subGift. They are cut in the form of quadrangular pyramids cut off at the top; it was impossible of consequence to determine any way the meridian, the point of the shadow formed by the summit of the obelisk : that point made part of an impefect hadow very difficult to distinguish. It must then, in many cases, be confounded with the body of the obelisk*. But even supposing that they could come to determine this point with exactness, they could not give the true height of the sun at noon, that is to say, that of its centre. They could only obtain the height of the north fide of that star.

An ingenious people, such as the Egyptians were, must have perceived, almost from the first moment in which they employed obelisks to measure shadows, the inconveniencies of that sort of gnomon. The early knowledge which the Egyptians had acquired in geometry, fuggested to them, without doubt, the ways to remedy the imperfection of their astronomic instruments. They contrived to přit to the top of the obelisks a ball supported by a very small fhaft, and elevated sufficiently, that the shadow which it formed should find itself abfolutely disengaged from the shadow of the obelisk. The projection of that Madow on the ground near the gnomon, formed an ellipsis, by which the middle determined, by its position, exactly enough the height of the centre of the sun.

We do not find, it is true, in ancient authors any direct proof that the Egyptians were accustomed to place balls on the summit of their obelisks; but we know that Augustus had one put upon the top of the obelisk transport

This must happen every time that the meridian height of the sun, that is to say, the arch of the meridian compreliended between the horizon and the sun's place, surpassed the angle which the sides of the obtuse pyramid formed, which terminated the obelisk, with the plane of its base. And it must be observed, that in Egypt, at the fuminer-solstice, the height of the fun must be more than 83 degrees.

ed by his order into the Campus Martius *. The same reafons which have determined me believe that that Emperor only imitated the practice of the Egyptians, in destining that obelisk to astronomical observations, make me think that it was also from their example that he added the ball of which I have spoke. Besides, we sec on very ancient Greek medals, obelisks topped with a ball. We are not ignorant that the Greeks had from the Egyptians all their astronomic knowledge. Thus the academy of inscriptions, consulted by that of the sciences, about the antiquity of that usage in Egypt, have not hesitated to make it ascend to the most remote ages y,

I think then we may refer to the times which at present employ us, not only the invention of

invention of gnomons, but more. over the practice of terminating them with balls. It is probable that to this discovery we ought to attribute the reform which the Egyptians made in the duration of their solar year; a reforin which had constantly taken place in the ages which elapsed from the death of Jacob to the e. stablishment of monarchy among the Jews. This is what remains for ine to discuss,

I have said before, that in the time of Moses, that is to fay, about 1480 years before Christ, the Egyptian year was composed only of twelve months, of thirty days each ?. The advantage which these people drew from their indu. stry, by being able to procure instruments more exact than natural gnomons, was to perceive that 360 days did not contain the whole duration of the annual revolution of the fun. They estimated at first that excess to five days which they added to their year. Let us try to find in history some facts which may enable us to fix the epoch of this reform,

If we should refer to the ancient traditions of the Egyptians, we must make the establishment of the year of

x Plin. 1. 36. fect. 15. p. 737.

Memotres de l'acad. des inscript, t. 3. hift, p. 166. Supra, p. 249

365 days ascend to the most remote times. This is the fable they have propagated on this subject.

They say, that Rhea having had a secret commerce with Saturn, fell with child. The Sun, who perceived it, loaded her with maledi&tions, and pronounced that she should not be brought to bed in any of the months of the year. Mercury, who was also in love with Rhea, likewise fuca ceeded to gain her good graces. She communicated to him the embarrassment in which she found herself. In acknowledgment for the favours which he had obtained, Mercury undertook to defend that goddess from the ef: fects of the malediction of the Sun. That quickness of mind by which he is so well known, supplied him with a very singular expedient to do it. One day that he played at dice with the Moon, he proposed to play for the 72d partof each day of the year. Mercury won, and profiting by his gain, he composed five days, which he added to the twelve months of the year. It was during these five days that Rhea was brought to bed. She brought into the world Osiris, Orus, Typhon, Isis, and Nephthe ..

I shall not endeavour to explain the mystic sense of this fable : I have only reported it to fhew to what antiquity the Egyptians made the establishment of their year of 365 days afcend.

They must nevertheless have preserved some tradition of that event, less altered than that which I have just spoke of. Syncellus attributes to a monarch' named Aseth, the reform of the ancient Egyptian calendar. Under that prince, says that author, the Egyptian year was regulated to 365 days, for till that time it only had 360 days. This fact does not furnish us with any great lights about the time in which this form of the year began to have place. We know very well, it is difficult to fix the reigns of the ancient sovereigns of Egypt. Nevertheless, in collecting

• Plut. t. 2. p. 355. D. Diodorus seems also to have had some knowledge of this allegorical fable. See l. 1. p. 17, P, 123. D.

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the different facts which history can furnish, and by examining the form of the principal cycle which the Egyptians used, known by the name of the canicular cycle, we may determine the precise date of the institution of the year of 365 days.

In the description which Diodorus makes of the tomb of Osymandes, King of great Thebes, he speaks of a circle of gold whose circumference was 365 cubits, and one cubit in breadth. Each of the 365 cubits answered, says he, to a day of the year: they had marked there for each day, the rising and setting of the stars, with the prognostic of the times, conformable to the ideas of the Egyptian astrolo. gers e. Osymandes is called lsmandes by Strabo, who adds, that the prince called Ismandes by the Egyptians, was the same as the Memnon : who is so often spoke of by the historians of antiquity, as sovereign of Ethiopia. It is very probable, that Osymandes, a very warlike prince, had conquered that kingdom *; an event, which may have thrown thc ancients into an error. Whatever it be, we find this Memnon in some lists of the kings of Egypt', And we know moreover, that he was extremely revered under that name among the Egyptians. His reign falls about the time of the war of Troy. We may prove this as well from the authority of Homer, of Hesiod, of Pindar, and of Virgil, as by the testimony of the most ancient monuments, such as the coffer of Cypselides, the throne of the Amyclean Apollo, the statues of Lycias, the pictures of Polygnotus, &c. 6. Thus we have been before affured, that,

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L. 1. p. 59. This circle was taken away by Cambyses, when he made the conquest of Egypt. Diod. ibid. d L. 17. p. 1167.

e See Diod. 1. 1. p. 57, * Ancient inscriptions, of which Tacitus speaks, atteft, that Rhampses, King of Thebes, had conquered Ethiopia. Annal. I. 2. c. 63.

I Mould think, that this prince might well be the Ofymandes of Diodorus. We know how much the Greek and Latin hiftorians have disfigured the names of the Egyptians.

f Syncell. p. 72. & 151.

& Odyll. 1.4. v. 188. 1. 11. V. 521.; Hesiod. Theogon. V. 984. ; Pind. Olymp. 2. V. 148. ; Pyth. 6. V. 30.; Virgil. Æneid. l. 1. V. 489.; Paus, l. 5. c. 19. & 22. 1. 10.Ç. 31.1. 3. C. 3.

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at the time of the war of Troy, the solar year of the Egyptians was of 365 days, and by consequence that the reign of Aseth must have preceded that epoch. But the examen of the cycle that the Egyptians called the caniculary cycle, will furnish us with a much more precise date.

The ancients speak very often of the great year of the Egyptians nominated by some authors the year of God. Censo. rinus and many other writers inform ns, that this year of God, which some authors also call the heliac year, commenced every 1461 years. It was nothing else but a canicular cycle*. We see very plainly, that they only spoke of the duration of this cycle in the number of 1461 years, so ill applied by Tacitus for the duration of the life of Phoenix, by Dio to the Roman calendar, and by Firmicus to the general revolution of the planets.

This being granted, we find from the year 1322 before Christ to the year 139 of the Christian æra, a canicular cycle well attested by the authorities and by the calculations of a number of authors. There is not then any thing farther to be done at present, but to see if the establishment of the year of 365 days agrees with the commencement of the cycle. For it is evident, chat in the times which the Egyptians give for the first time of 365 days for their year; Thoth was canicular, and one of the characters of that first year ought to have commenced with the rising of the canicular. This is a fact of which we may acquire sufficient proofs, by, collecting what is said by the ancients of the manner in which the Egyptians regulated their" years by the rising of the

The first month of the Egyptian year was called Thoth. When the he. liac rising of the canicule fell on the first day of the month, they faid that Thoth was canicular, and they comprehended under the name of canicular cycle, the time which clapsed from one canicular Thoth to the succeeding one. That interval was necessarily 146. Julian years. For the Egyptian year of 365 days being too short by about fix hours, the riling of the canicule would anticipate a day every four years, and running retrograde all the days of those yeirs one after another during four times 365 years, or 1463 years. Thus it was only after 146! Egyptian years, equivalent to 1467 Julian years, that the heliac rising of the canicule would return to the first day of the month Thoth, and would commence a jew canicular cycle.

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