LUCIUS TARUTIUS AND THE FOUNDATION OF ROME

By Eduardo Vila-Echagüe

Introduction

Even though the foundation dates of the principal cities of the ancient world are not known, Romans had the pretension of knowing theirs with remarkable precision. The scholar Varro, living in the first century BC, wrote that Rome had been founded on April 21, 753 BC, between 8 and 9 a.m. He also tells us that the illustrious mathematician Lucius Tarutius had computed the position of the celestial bodies for that date: "Jupiter in Pisces, Saturn, Venus, Mars and Mercury in Scorpius, the Sun in Taurus and the Moon in Libra."¹

It is generally acknowledged that the first usable theory of planetary movements was developed by Claudius Ptolemaeus, living in the second century AD. The aforementioned quotation shows that before that time astrologers had some means of knowing the places of celestial bodies for dates past and future. At least in principle it should be possible to use Tarutius' positions to throw light on their mathematical methods.

One problem is that we do not know the exact date considered by Tarutius. The Julian and of course the Gregorian calendars are later inventions, and from what we know of the previous calendar used by the Romans, it was totally unsuitable for computing time intervals between distant dates. But an uncertainty of a few days will not produce significant differences in the positions, except for the Moon. Assuming the validity of the Julian calendar, I calculated in which zodiacal signs the main Solar System bodies were on April 21, 753 BC, at 8:30 local time of Rome, using the procedures described in the Almagest² and also modern formulae,³⁴ which gave nearly the same results.


Heavenly Body	Tarutius' Sign	Computed Sign	Almagest Position	Modern Formulae
Sun	Taurus	Aries	25° 52'	23° 8'
Moon	Libra	Aquarius	316° 52'	313° 15'
Mercury	Scorpius	Aries	5° 0'	5° 0'
Venus	Scorpius	Pisces	358° 44'	359° 43'
Mars	Scorpius	Pisces	352° 50'	350° 38'
Jupiter	Pisces	Aries	12° 30'	10° 57'
Saturn	Scorpius	Scorpius	227° 21'	225° 28'

To my surprise, there was no match between Varro's quotation and my own calculations, with the exception of Saturn. Additionally, on closer examination I found that some of Varro's positions are impossible. Even a second class astrologer should know that under no circumstances can Mercury and Venus be seen in opposition to the Sun, which means that Mercury and Venus cannot be in Scorpius while the Sun is in Taurus, the opposite sign in the sky. It would seem that there is something wrong either with this third hand quotation, with the date we used or with Tarutius' abilities. Have we reached a dead end in our investigation? Before abandoning it, let us do some additional research to see if we can find a way out.

Lucius Tarutius Firmanus

Who was this Lucius Tarutius? Observers of the Moon may remember the beautiful crater Taruntius, placed between Mare Fecunditatis and Mare Tranquillitatis, and may even think that Varro or myself have misspelled his name. They are in fact the same person, but apparently Riccioli's nomenclature is using a variant of the name.⁵ There are at least three other references to Tarutius in the classical literature, and none of them spells his name with 'n'. Cicero tells us that his friend Lucius Tarutius, native of the Italian town of Fermo and an expert in the science of the Chaldeans, had no doubts that Rome had been born when the Moon was in Libra, and that from that circumstance he dared to predict its future.⁶ Pliny the Elder, some 100 years later, mentions Tarutius as one of his sources, saying that he wrote in Greek about the heavenly bodies.⁷ This is probably the reason why Tarutius' writings are not extant; usually the Greeks did not appreciate and therefore did not preserve books written by Romans in their language.

The last reference is by far the most interesting. It is found in the Life of Romulus written by Plutarch in the second century AC. Let us quote it in full:

'In the times of Varro the philosopher, a man deeply read in Roman history, lived one Tarutius, his familiar acquaintance, a good philosopher and mathematician, and one, too, that out of curiosity had studied the way of drawing schemes and tables, and was thought to be a proficient in the art; to him Varro propounded to cast Romulus's nativity, even to the first day and hour, making his deductions from the several events of the man's life which he should be informed of, exactly as in working back a geometrical problem; for it belonged, he said, to the same science both to foretell a man's life by knowing the time of his birth, and also to find out his birth by the knowledge of his life. This task Tarutius undertook, and first looking into the actions and casualties of the man, together with the time of his life and manner of his death, and then comparing all these remarks together, he very confidently and positively pronounced that Romulus was conceived in his mother's womb the first year of the second Olympiad, the twenty-third day of the month the Aegyptians call Choeac, and the third hour, at which time there was a total eclipse of the sun; that he was born the twenty-first day of the month Thoth, about sunrising; and that the first stone of Rome was laid by him the ninth day of the month Pharmuthi, between the second and third hour.''⁸

In the last lines we are presented with three very precise dates. The first one is complete, including the year, which we can reasonably infer for the other two. Also, the times of day are give, with an accuracy of about one hour. Are these dates of any use to us?

Some modern commentators of this passage⁹ think that Plutarch was simply giving the Greek equivalents of the Roman months, as used in Egypt in later times.¹⁰ But to anyone familiar with the Almagest, it is immediately apparent that these dates may correspond to the Egyptian mobile year of 365 days in use among Hellenistic astronomers. As the first date is associated with an astronomical event, it should be possible to check this assumption.

Romulus' Conception

The first year of the second Olympiad is our year 772 BC.¹¹ Therefore, Choiak 23 of that year in the Egyptian calendar corresponds to June 24, 772 BC in the Julian calendar.¹² In Rome the time of day was reckoned from sunrise to sunset, which means that the third hour would be 9 a.m., if we assume sunrise at 6 a.m. and 12 hours of daylight. But if we consider Rome's latitude (42°N), sunrise near the summer solstice would happen at 4:30 a.m., and there would be 15 hours of daylight, making the length of each 'seasonal' hour equal to 15/12 of one regular hour. Adding 3 of these hours to 4:30 a.m. gives 8:15 a.m. in the local time of Rome. To obtain Universal Time 0:50 hours must be subtracted, to take account for Rome's longitude (12°30'E), leaving the time of the eclipse either at 8:10 UT or 7:25 UT, depending on which type of hours were considered by Tarutius.

Was there a total eclipse of the sun on that date, as Plutarch tells us? The answer is yes and no. There was a solar eclipse, visible from the Arctic and Northern Europe. If computed according to the methods of the Almagest, a partial eclipse should have been barely visible from Rome. In that city, the minimum distance between the centers of the Sun and the Moon would have been 31' at 7:45 UT, producing only a very small notch in the Sun's disk. The timing, however, is very accurate, implying that our assumption relative to the Egyptian calendar is correct. In fact, the timing is so accurate that we must think Tarutius was using the same Hipparchus' algorithms that Ptolemaeus transcribes in the Almagest. Perhaps even including how to compute the local circumstances of the eclipse (that is, considering the Moon's parallax), because his timing is closer to the previously mentioned 7:45 UT than to the geocentric conjunction of the Sun and the Moon, which happened at 9:08 UT, using those same algorithms.
If Tarutius was so accurate in the timing of the eclipse, why did he not realize that the eclipse was only partial and almost invisible at Rome? Perhaps he was using incorrect values for the latitudinal passages of the Moon, but it is more probable that he 'fabricated' the total eclipse because he needed some special sign to have happened at Romulus' conception. After all, the availability of special events visible from Central Italy some 18 years before Rome's foundation was not very high, and this one was the best he could find.

The Birth of Romulus

According to Tarutius, Romulus was born on Thoth 21 at sunrise, presumably in the year following that of his conception. He spent 9 months less 2 days in the womb of his mother. This is neither an integer number of months nor of weeks. Tarutius must have had some special reason to choose this date, either astrological or astronomical. Let us investigate the second possibility.
In our Julian calendar the date is March 24, 771 BC and the time 5:10 UT. On that date the only event of astronomical significance was the Sun approaching the vernal equinox, its longitude being 358° 18', according to the algorithms of the Almagest. Is it possible that Tarutius had the intention of placing Romulus' birth exactly at the vernal equinox and that something went wrong with his numbers?
There is an additional clue in favor of this hypothesis. In the Almagest we find a long list of equinoxes observed by Hipparchus.¹³ The timings of all of them are expressed in quarter days, occurring either at midday, sunset (evening), midnight or sunrise (morning). This is not the case with Ptolemaeus, who gives the timings of the equinoxes observed by himself to the hour.¹⁴ Tarutius seems to be following Hipparchus' practice by giving us the time on this particular date as about sunrising, when for the other two dates he is precise to the hour or even to the half hour.
There is a difference of almost 2 days between his date and that of the equinox, when computed using the formulae of the Almagest, which are based on Hipparchus' value of the length of the tropical year, 365+1/4-1/300 days. My guess is that he did not use those formulae but just took the date of one of the equinoxes known to him, perhaps one of Hipparchus, and computed back with the usual value for the tropical year, 365+1/4 days. This value was still current in his time and is quoted, for instance, by Geminos, writing around 70 BC.¹⁵ Taking Hipparchus equinoxes and using this method, we find that the equinox would have fallen at midnight on March 24, 771 BC, and at sunrise of the same day in 770 BC. An error of one year is quite understandable considering that the Roman, Olympic and Egyptian years did not commence all at the same time of the year.

Rome's Foundation

Let us review first what is known about Rome's foundation date from other sources. A long established tradition placed the birthday of Rome on the eleventh day before the calends (first day) of May, in coincidence with the festival of the Parilia.¹⁶ This corresponds to April 21 in the Julian calendar. The Parilia was a spring festival in honor of Pales, god (or goddess) of shepherds and herds, and was obviously related to the solar agricultural calendar. There was no such consensus, however, about the foundation year. Various ancient authors gave dates ranging from 813 BC to 728 BC, while the more reliable clustered around 750 BC.¹⁷ Cicero and his friend Atticus favored 754 BC,¹⁸ while Varro himself preferred the year 753 BC¹⁹ for reasons that are unknown to us; in later times that date became the 'official' foundation date, because of his great authority in all fields of knowledge.

Tarutius gives us a precise day for this event, Pharmouthi 9 in the Egyptian calendar. What about the year? Varro tells us that Romulus was 17 years old (literally 'in his 18th year') when he founded Rome,²⁰ which brings us to 754 BC. The same year is mentioned by Plutarch in the passage coming just before the one previously transcribed, though he seems to be quoting other sources unrelated to Varro or Tarutius:

"The Roman and Greek months have now little or no agreement; they say, however, the day on which Romulus began to build was quite certainly the thirtieth of the month, at which time there was an eclipse of the sun which they conceived to be that seen by Antimachus, the Teian poet, in the third year of the sixth Olympiad." ²¹

It is therefore very probable that the date Tarutius considered for the foundation of Rome was Pharmouthi 9 of the third year of the sixth Olympiad, between the second and third hour, which is equivalent to October 4, 754 BC at 7:40 UT of the Julian Calendar. With this assumption, let us check again the positions on that date of the Sun, Moon and planets quoted by Varro, using as before the algorithms of the Almagest, which are probably closer to those used by Tarutius than our modern formulae:


Heavenly Body	Tarutius' Sign	Computed Sign	Mean Longitude	First Anomaly	Second Anomaly	Real Longitude
Sun	Taurus	Libra	187° 13'	-2° 4'		185° 9'
Moon	Libra	Libra	206° 53'	1° 33'	0° 4'	208° 30'
Mercury	Scorpius	Pisces	187° 13'	-0° 16'	-9° 12'	177° 46'
Venus	Scorpius	Scorpius	187° 13'	-1° 31'	29° 29'	215° 11'
Mars	Scorpius	Libra	218° 45'	-10° 57'	-8° 16'	199° 32'
Jupiter	Pisces	Pisces	350° 25'	1° 44'	-3° 42'	348° 27'
Saturn	Scorpius	Scorpius	218° 28'	0° 36'	-2° 51'	216° 14'

This time the coincidence is much better. Not only is the Moon in Libra, as in Varro's and Cicero's quotations, but also Venus, Jupiter and Saturn are in the right zodiacal signs. Mars is not too far (11°) from the beginning of Scorpius (210°), while Mercury and the Sun are wide off the mark. The table also shows how the real longitude is obtained from the mean longitude through the addition of the first and second anomalies. For the planets, the first anomaly represents the eccentricity of the orbits and the second the epicyclical motion. It is difficult to know from the data if Tarutius was considering the anomalies in the determination of his positions. For the Moon, Jupiter and Saturn it is indifferent, because the mean and the real longitudes give the same zodiacal sign. Venus requires the anomaly, while Mars would have a better fit without the anomaly. To bring Mercury to Tarutius' sign, it should be in a totally different position within its epicycle. As Mars and Mercury are the 'enfants terribles' of the Solar System, due to the high eccentricity of their orbits, probably there was no good approximation of their movements available at that time.

I have no explanation for the mismatch of the Sun's positions. Perhaps a later copyist, remembering that Rome had been founded in spring, realized that the Sun could not be in Libra at that time of the year and replaced that sign with another more appropriate for the season.

This brings us to the biggest mystery. If Tarutius knew that Rome had been founded in April, why did he choose a date in October, almost in the opposite season? If there was an astrological reason, I am not qualified to say. The astronomical reason I shall give, probably will not convince many of my readers, but I do not have a better one available. Tarutius selected Pharmouthi 9 as the foundation day, simply because it was the Greek equivalent of April 21! But have we not said that it was the equivalent of October 4? Yes, indeed, but that was in the year 754 BC. Because of the mobile nature of the Egyptian year, around 90 BC the Egyptian date for the Parilia would have been Pharmouthi 9, if Romans had been using the Julian calendar. But Julius Caesar was only a young boy then, and his reforms were many years in the future. The calendar Romans used in those days was highly irregular, and it is quite possible that when Tarutius composed Rome's horoscope, the ninth day of the month Pharmouthi coincided with the eleventh day before the calends of May. This may seem surprising to many, but is not very different to Orthodox Christians celebrating Christmas some day in January of their civil calendars, only because they keep to the Julian calendar for their religious festivals.

Conclusion

Astronomy was a subject of interest to Romans. Almost every writer with some concern about nature included a few descriptive chapters on the subject, from the times of Cicero to Isidorus of Seville at the close of antiquity. There were even some specialized works as those of Manilius and Censorinus. None of them, however, seems to have understood in detail the complexities of mathematical astronomy. The only well known exception is that of the patrician Sulpicius Gallus, who successfully predicted a lunar eclipse the night before the battle of Pydna, on June 21, 168 BC.²² The present article provides us a glimpse of the state of the art in Rome one hundred years later, which probably was the same as that of the rest of the classic world. There is a gap of almost 300 years between Hipparchus and Ptolemaeus, for which there is a complete lack of primary sources. Tarutius may help us a little in disentangling the specific contributions of those two summits of ancient astronomy, a question that has been always of the highest importance for the history of science.

Considering how little information we have about Tarutius' methods and numerical results, it should not be a surprise to anybody if many of the explanations given above are highly speculative. But at least some of them are in a more solid ground. It is almost sure that Tarutius used the Egyptian mobile year as a base for his calculations. He also shows very good skills at calculating a solar eclipse which, of course, is much more difficult than a lunar one. If it is true that Tarutius considered its local circumstances, then we should credit Hipparchus not only with the general theory but also with the preparation of procedures and tables to compute solar eclipses, for the use of later astronomers.

If Tarutius really tried to place Romulus' birth at the vernal equinox, as said before, this would show that Hipparchus' length of the tropical year (365 + 1/4 - 1/300 days) did not gain general acceptance and was in fact ignored by astronomers until Ptolemaeus brought it back to light.

Tarutius' performance with planetary positions is not very good. He gets acceptable results for the 'well-behaved' planets only. His positions expressed in terms of zodiacal signs, 30° broad, are too vague to check the theory he was using, but the general impression is that he either had nothing comparable to the calculation procedures we find in the Almagest, or that he was very careless in using them.

A final remark about Tarutius himself. The passage of Plutarch previously quoted says that from the deeds of Romulus and the history or Rome he worked out a horoscope, and then tried to find a date and time when the celestial bodies were in the positions required by it. This would explain his seemingly arbitrary dates, not even compatible with Rome's traditions about its foundation. Our study shows, in stead, that he had mostly astronomical reasons for the dates he chose. This would make him more of an astronomer than as the astrologer described by our sources. Perhaps, as many others in later times, he used astrology as the means to attract people's attention, while his main concern was with the movement of the stars. If that was the case, Lucius Tarutius is closer to our hearts and he certainly deserves that crater in the Moon named after him.

Notes

¹ M. Terentius Varro, Antiquitates Rerum Humanorum, Book XVIII. Frag. 65, quoted by Solinus (I,18):

'Ut affirmat Varro auctor diligentissimus, Romam condidit Romulus ..., duodeviginti annos natus undecimo kalendas Maias hora post secunda ante tertiam plenam: sicut Lucius Tarutius prodidit mathematicorum nobilissimus Iove in Piscibus, Saturno, Venere, Marte, Mercurio in Scorpione, Sole in Tauro, Luna in Libris constitutis.'

² Claudius Ptolemaeus, Almagest, Books III-V and IX-XII, (Encyclopaedia Britannica), 1952.
³ Pierre Bretagnon and Jean-Luis Simon, Planetary Programs and Tables..., (Willmann-Bell), 1986.
⁴ M. Chapront-Touzé and J. Chapront; Lunar Tables and Programs..., (Willmann-Bell), 1991.
⁵ Riccioli, Almagestum Novum, 1651.
⁶ Cicero, de Divinatione, Book II, xlvii 98:

'L. quidem Tarutius Firmanus, familiaris noster, in primis Chaldaicis rationibus eruditus, urbis etiam nostram natalem diem repetebat ab iis Parilibus, quibus eam a Romulo conditam accepimus, Romamque, in iugo cum esset luna, natam esse dicebat, nec eius fata canere dubitabat'

⁷ Plinius, Historia Naturalis, Book I, ex auctoribus libri xviii

'L. Tarutio qui Graece de astris scripsit.'

⁸ Plutarch, Life of Romulus, chapter xii, 5-9, Translation by John Dryden, with two amendments.

Tarutius, as in the Greek original, in stead of Dryden's Tarrutius.
Choeac, and the third hour, in stead of Dyrden's Choeac, and the third hour after sunset,. There is no reference to the sunset either in the Greek original nor in other translations I have seen, and it does not make any sense to have a solar eclipse 'after sunset'.

⁹ Plutarco; Vidas Paralelas, volumen I. (Gredos), 1996.
Choiak is equated to November-December, Thoth to August-September and Pharmouti to March-April.
¹⁰ E. J. Bickermann, Chronology of the Ancient World, (Dover 1989), p. 50, quoting H. Gundel (APF 1956,13).
¹¹ ibid., Table III.
¹² Ptolemaeus, op. cit., Appendix A, p. 466.
¹³ Ptolemaeus, op,cit., Book III, p. 78-79.
¹⁴ ibid., p. 82.
¹⁵ Geminus, Elementa Astronomiae, I, 7.
¹⁶ See Note 1 and also Ovid, Fasti, IV, 155-181
¹⁷ Discussion in Dionysius of Halicarnassus, Roman Antiquities, Book I, Chapters 74-75.
¹⁸ C. Julius Solinus Polyhistor, Book I, Basel, 1543, probably quoting Varro.

"...Pomponio Attico et M. Tullio, Olympiadis sextae anno tertio. Collatis igitur nostris et Graecorum temporibus, invenimus incipiente Olympiade septima Romam condita, anno post Ilium captum CCCCXXXIII."

¹⁹ Varro, op,cit., Book XVIII. Frag. 64, quoted by Censorinus (21,5):

"Varro ... nunc diversarum civitatium conferens tempora, nunc defectus, eorumque intervalla retro di numerans, eruit verum, lucemque ostendit per quam numerus certus non annorum modo sed et dierum perspici possit. Secundum quam rationem nisi fallor, hic annus, cuius velut index et titulus quidem est, Vlpii et Pontiani consulatus, ab Olympiade prima millesimus est, et quartus decimus (239 AD), ex diebus dumtaxat aestivis, quibus agon Olympicus celebratur, a Roma autem condita DCCCCLXXXXI, et quidem ex Palilibus unde urbis anni numerantur."

²⁰ See Note 1.
²¹ Plutarch, op,cit., chapter xii, 4.
²² Livy, Ab Urbe Condita, Book XLIV, 37