There is great room to think, that to meafure the different heights of these meridian fhadows they had used originally the gnomons which nature had fhewn to them, fuch as trees, mountains, edifices, &c.

But natural gnomons could not furnish the means of exactly measuring the duration of a folar year; the Egyptians foon perceived their imperfection and infufficiency, nevertheless, without knowing the utility thefe forts of inftruments might be of. This double confideration led them to invent artificial gnómons. We cannot conteft with thefe people the merit of having brought them first into use. It is impoffible not to recognife in the obelisks, gnomons conftructed, with fo much care, expense, and study. For to imagine that the Egyptian monarchs, in caufing these enormous maffes to be cut, propofed no other end, but a foolish oftentation of their riches and their power; this is what I cannot perfuade myfelf of. The choice of this fort of monuiment does not appear to me to have been made by chance. The form of the obelisks was not folely owing to caprice and fancy. The fovereigns who had caufed them to be made, tried moft certainly to immortalize themfelyes by thefe grand enterprises; but it was the motive of public utility, and the glory of contributing to the advancement of the fciences, which muft have directed the form and choice of thefe forts of monuments.

It is not, even here, a fimple conjecture on our part. We have a glimpfe, in a paffage of Arpion reported by Jofephus, that at all times the obelifks had been destined by the Egyptians for aftronomic ufes. This grammarian gives a defcription of a fort of gnomon, fingular enough, which he attributes to the invention of Mofes. The legislator of the Jews had invented it, fays he, to answer the fame purposes as the obelisks. Nothing truly can be more ill founded or more abfurd, than all that Appion has related

* Adverf. App. 1. 2. p. 469. edit, of Havercamp.

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on the account of Mofes; but this paffage at leaft proves, that, in antiquity, they were perfuaded that the obelisks had been originally raised to ferve for gnomons; and this is all that I pretend to establish.

To the testimony of Appion let us join the authority of Pliny. According to that author, the Egyptians had cut their obelisks in imitation of the rays of the fun.

He

adds, that this was the name by which they defigned these grand fpires. This denomination, without doubt, was relative as much to the form of thefe monuments as to the ufe for which they employed them *.

Even though we had not precife teftimonies about the ufe for which the Egyptians had deftined their obelisks, what a nation has done which was never diftinguished by its astronomic knowledge, will fuffice to inftruct us of it. Augustus, after having fubdued Egypt, caused to be trans ported to Rome two grand obelisks: he fet up one in the Circus, and the other in the Campus Martius. He took all the neceffary precautions, that it might ferve for a gnomon. Auguftus, in making this obelifk ferve for aftronomic observations, probably only imitated the practice of the Egyptians. These people had not invented thefe fort of monuments only to procure more fure and exact instruments than natural gnomons, to determine the duration of the folar year by the measure of the meridian fhadows. I do not think I need repeat what I have faid elfewhere of the antiquity of obelifks. I have fhewn that we must fix the epoch to the reign of Sefoftris, that is to fay, about 1640 years before Christ.

Plin. 1. 36. fect. 14. p. 735.

* The Egyptians had apparently given the name of the rays of the fun to obelifks, because they could conceive the sphere of that ftar, as being divided into an infinity of pyramids which had their fummit at the furface of his disk, and their bafe at the circumference of that fphere. Daviler, in his dictionary of architecture, on the word obelisk, advances, that the Egyptian priests called thefe oblifks the fingers of the fun, because these grand fpires ferved for a ftyle to mark on the earth the different heights of that ftar. I am ignorant from what author of antiquity Daviler has drawn this fact. "Sufra, bock 2. chap. 3. p. 13г. Thefe

t

Plin. 1. 36. fest. 15. p. 736.

These ancient gnomons were moreover greatly inferior to thofe invented in our times. To convince us of this, it is fufficient to caft our eyes on those which still fubfift. They are cut in the form of quadrangular pyramids cut off at the top; it was impoffible of confequence to determine any way the meridian, the point of the fhadow formed by the fummit of the obelisk: that point made part of an impefect fhadow very difficult to distinguish. It must then, in many cafes, be confounded with the body of the obelifk*. But even fuppofing that they could come to determine this point with exactnefs, they could not give the true height of the fun at noon, that is to fay, that of its centre. They could only obtain the height of the north fide of that ftar.

An ingenious people, fuch as the Egyptians were, must have perceived, almost from the first moment in which they employed obelisks to measure shadows, the inconveniencies of that fort of gnomon. The early knowledge which the Egyptians had acquired in geometry, fuggefted to them, without doubt, the ways to remedy the imperfection of their aftronomic inftruments. They contrived to put to the top of the obelifks a ball fupported by a very small fhaft, and elevated fufficiently, that the fhadow which it formed fhould find itself abfolutely difengaged from the fhadow of the obelifk. The projection of that fhadow on the ground near the gnomon, formed an ellipfis, by which the middle determined, by its pofition, exactly enough the height of the centre of the fun.

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

This must happen every time that the meridian height of the fun, that is to say, the arch of the meridian comprehended between the horizon and the fun's place, furpaffed the angle which the fides of the obtufe pyramid formed, which terminated the obelisk, with the plane of its base. And it must be observed, that in Egypt, at the fummer folftice, the height of the fun must be more than 80 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 deftining that obelisk to aftronomical obfervations, make me think that it was alfo from their example that he added the ball of which I have spoke. Befides, we see on very ancient Greek medals, obelisks topped with a ball. are not ignorant that the Greeks had from the Egyptians all their aftronomic knowledge. Thus the academy of infcriptions, confulted by that of the fciences, about the antiquity of that ufage in Egypt, have not hesitated to make it afcend to the moft remote ages.

We

It is

I think then we may refer to the times which at prefent employ us, not only the invention of gnomons, but moreover the practice of terminating them with balls. probable that to this discovery we ought to attribute the reform which the Egyptians made in the duration of their folar year; a reform which had conftantly taken place in the ages which elapfed from the death of Jacob to the establishment of monarchy among the Jews. This is what remains for me to difcufs,

I have faid before, that in the time of Mofes, that is to fay, about 1480 years before Chrift, the Egyptian year was compofed only of twelve months, of thirty days each. The advantage which thefe people drew from their indu ftry, by being able to procure inftruments 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 firft that excefs to five days which they added to their year. Let us try to find in history fome 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 eftablishment of the year of

365 days afcend to the most remote times. fable they have propagated on this subject.

This is the

They fay, that Rhea having had a fecret commerce with; Saturn, fell with child. The Sun, who perceived it, loaded her with maledictions, and pronounced that the fhould not be brought to bed in any of the months of the year. Mercury, who was alfo in love with Rhea, likewife fuc ceeded to gain her good graces. She communicated to him the embarraflment in which fhe found herself. In acknowledgment for the favours which he had obtained, Mercury undertook to defend that goddefs from the ef fects of the malediction of the Sun. That quickness of mind by which he is fo well known, fupplied him with a very fingular expedient to do it. One day that he played at dice with the Moon, he proposed to play for the 72d part of each day of the year. Mercury won, and profiting by his gain, he compofed 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 Ofiris, Orus, Typhon, Ifis, and Nephthe..

I fhall not endeavour to explain the myftic fenfe 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 preferved fome tradition of that event, lefs altered than that which I have just fpoke of. Syncellus attributes to a monarch named Afeth, the reform of the ancient Egyptian calendar. Under that prince, fays 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 fovereigns of Egypt. Nevertheless, in collecting

Plut. t. 2. p. 355. D. Diodorus feems also to have had some knowledge of this allegorical fable. See l. 1. p. 17.

P. 123. D.

the