The „Compendium“ of Antonius Lilius

Berlin · 2009  Uwe Topper

The „Compendium“ of Antonius Lilius: Blueprint for the Calender Reform of Pope Gregory XIII

Our hypothesis of precession jolts, as proposed by Ilya Topper and the author in 2004, brings a new solution to the problems of how our calendar and modern chronology were developed, yet still it has to be regarded as a first sketch which needs continuous research. In the article of Ilya Topper „Kalender und Präzessionssprung“ (2009, see the English abstract) the „Compendium“ of Antonius Lilius has been mentioned briefly, and on this subject I shall elaborate now.

Lately we had stated that the date in the Julian Calendar had jumped by seven days due to the hypothetical precession jolt and that additionally it had moved steadily over three days due to regular precession untill the distance to the traditional vernal equinox (21st March) in the late 16th century amounted to around ten days, which Gregory XIII eliminated in 1582 and thus put the equinox right back to where it had been „in the time of the Fathers at the Council of Nicæa“.
The correction of the Calendar was anounced in the papal bull „Inter Gravissimas“ based on the „Compendium novae rationis“ of Antonius Lilius from 1577 which has been neglected by recent scholars and shall be consulted now. This Compendium is an concise version of the book written by Antonius‘ brother Aloysius Lilius, Italian astronomer and medicus who was working with the Calendar Commission till his death in 1576. This book was never printed and is still not published. It was abridged by his brother Antonio on eleven pages (which is the now called Compendium) and was sent „to the Christian princes and famous academies … and competent mathematicians“ („ad principes christianos et celeberrimas quasque academias… peritis mathematicis“). This text is well known and accessible.
The content of this short introduction into the method of the planned Calendar Reform brings some surprises to the unaware reader which are the reason I shall go into detail.
The original handwritten book of Aloysius had been brought to the pope and is regarded as easy reading („… dum Gregorio XIII pontifex … allatus est illi liber ab Aloysio Lilio conscriptus, que neque incommodam, neque dificilem viam ac rationem eius rei perficiendae proponere videbatur.“) yet – so the text – as it is not necessary for the understanding of the reform-project and would take time to be printed, the Compendium will serve as well („sed cum liber nondum typis excusus sit, operosum id atque impeditum futurum erat et peritis astrologis, cum quibus ea ratio communicanda est, minus fortasse necessarium.“)
Further we learn from the Compendium, that the pope, who in this script never talks personally but through Antonius, did not intend to act without the consent of Christiandom but wanted instead to consult with the learned men of his time so that the aim could be reached in concordance, and if there would arrise some objection or possible improvement it would be taken into consideration („visum est prudentissimo pontifici de ea re peritissimos quosque huius scientiæ viros consulendos esse, ut res, quæ omnium communis est, communi etiam omnium consilio perficiatur. Cogitarat itaque eum librum cunctis christianis principibus mittere ut ipsi, adhibitis peritioribus mathematicis, illum aut sua sententia comprobarent, aut si quid deesse videretur, id omne absolverent atque perpolirent. Simul ut si qui modus aptior alicubi (quod non desperat) repertus foret, eo communicato, illum potius ipse sequeretur.“)
Later, however, after the reform of the pope had been rejected by the protestants, it could have been helpful to persuade the opponents if the whole book of Aloysius was finally published but this has never been undertaken and even now its text is not extant as far as I could find out. This adds weight to the thought that it contained more treacherous material which was deemed heretical to the Catholic dogma. So the Compendium must serve the purpose, and all other things be left aside („Quare satis esse putavit, reliquis omnibus prætermissis, summa tantum capita, quæ maxime rem causamque contineant, breviter indicare.“)

And with this we enter in medias res:
As Holy Easter is the highest feast for all Christians, it has to be celebrated unanimously on the date the Holy Fathers of the Council of Nicæa had prescribed, that is between the 14th and 21st days of the first full moon which follows the spring equinox or soon after. Therefore the Fathers had to fix the date of the spring equinox in the calendar in order to avoid quarrels of the type that had arisen off and on. As the problem of adjusting the moon to the actual state is not of interest for our question here, I leave all discussion pertaining to the moon aside and concentrate on the sun. Lilius is telling us something very peculiar about the movement of the sun. First of all, he states that the Fathers were quite convinced that the date of the equinox (March 21st) was correct and would stay fixed („Et quidem æquinoctii sedes in eo concilio ad XII Kalendas Aprilis collocata et constituta est; quam fore stabilem et certam propemodum sibi persuaserunt“) which is not the case. To the contrary, the equinox has moved by unequal steps and erred around to the 11th or even 10th of March, and if one does not object to this it might even wander as far as the winter solstice or earlier without end („verum æquinoctium locum suum non facile tenuit, sed statione deserta, incertis passibus, ad ante diem quintum iam aut etiam sextum Idus Martii errans usque pervenit. Cui errori nisi mature obviam eatur, ad id tempus quo nunc bruma conficitur, accedet aliquando; neque tamen ibi terminus statuetur, quin in infinitum procedat.“)
The expression „they were quite convinced“ sounds a bit strange and might hint at some hidden fact that in reality is all too obvious: The length of the solar year and the length of the Julian Year are not equal, the latter being a tiny fraction longer. As commonly known it was already Hipparch who had noticed this discrepancy, and Ptolemy had pointed to it with clear words in the Almagest, the most important book on astronomy from classical times till Renaissance. The Fathers must have known that by fixing the equinox to the Julian Calendar it would wander if not corrected every now and then. Even more: It was also known that the length of the tropical year was not steady – which is contained in the words „incertis passibus“ (unequal steps) and „errans“ (erring) – but variable. Therefore, Lilius continues, no rule had been found that would fix the date for ever.
Now the Compendium becomes very explicit: Already since pope Nicolaus V when science and free arts which had been laying neglected so long were resuscitated again, it had been the aim and worry of the popes to find a remedy to the uncorrect date, but nothing was found that would not lead into further trouble (atque equidem ea iam inde a felicis recordationis Nicolao Quinto, cuius ætate meliores literæ et liberalium artium studia, quæ diu neglecta iacuerant, reviviscere et recreari cœperunt, magna summorum pontificum cura atque studio tentata est, sed nihil constitui posse videbatur, quod non in magnam aliquam difficultatem incurreret.)
I am surprised that Nicolaus V (1447-1455) is mentioned, the one who cleansed Rome from the ruins and debries and procured resettling the nearly deserted town by clearing the pavement, reconstructing aquæducts, and searching for old books that would restore knowledge of bygone times. It is since his time, says Lilius, that the church intended to reform the calendar. The thought comes to mind that Nicolaus was the first bishop of Rome after the collapse and thus did not reign 800 years after the destruction by barbaric peoples like Goths or Vandals (as now is commonly taught) but a generation or two after a general catastrophy. As we have established this since quite some years as fact, it does not surprise me, the only thing that strikes me is that one can read it plainly in this Compendium.
The new length of the tropical year after the catastrophy was measured by the Persian prince Ulugh Beg in his magnificient observatory (around 1440), and it was this value that was trusted by all western astronomers. When Nicolaus of Cues proposed the correction of the calendar at the Council of Basle (as is the common lore) the exact value of Ulugh Beg‘s measurements were not yet known here, and his proposal to eliminate seven days was rejected. (The book on correcting the Calendar ascribed to Cusanus has to be dated in connection with the papal Calendar Commission after 1560).
Thus the text of the Compendium describes very well the situation of its time, namely the uncertainty of the astronomical dates in regard to the traditional ones: The tropical year is variable, and therefore the equinox erres about. So it was by no means the fault of Julius Cæsar who was the last to reform the calendar but the irregularity of the movement of the sun in the meantime which hindered a steady form of updating.
As far as astronomy is concerned, Lilius goes on, one sees two mighty difficulties. First of all that the length of the year is not constant, as the most learned mathematicians of different epochs had found different lengths and were convinced that they don’t stay equal for all time, and for this reason there was no possibility to install a rule which would fix the date of the equinox forever in the calendar („nam quod ad astrologiam attinet, duæ potissimum res obstare atque officere videbantur. Primum ipsius anni vertentis iusta certaque mensura, quæ quoniam a doctissimis ac diligentissimis mathematicis diversis temporibus alia atque alia reperta est, non eadem semperque sui similis esse convincitur. Cum ergo sol tam vaga et mutabili ratione labatur, difficillimum factu erat intercalationes ita dispensare ut æquinoctia ævo perpetuo certas ac fixas habeant in calendario sedes“). The second difficulty concerns the full moon problem and is left out in this short article here.
Now Lilius proposes a remedy which would provide the long wanted rule for the future. He proposes a so called Alfonsine year to be used as base as it is an averrage measure and therefore keeps the error minimal. The spring equinox is coming every 134 years by one day early („proponit enim sibi anni Alfonsini mensuram, quæ inter varias media est, atque ideo errori minus obnoxia; ex qua subductis calculis efficitur ut in annis plus minus CXXXIIII æquinoctiorum loca integrum antevertant diem.“)
This date has moved since Julius Cæsar by 13 days, says Lilius, that is why the thirteen days or – what is more apt to the dignity of the church – ten days that make out the difference to the date of the Council of Nicæa have to be removed now. This could be done by omitting the intercalary day for the next forty years so that by 1620 the calendar would have come back to rule, or as others proposed, the ten days should be jumped right next year (1582). The last proposal was finally adopted.
The same measure, namely the omission of the intercalary day every 134 years, was introduced for the future by suppressing the intercalary day in every full century whose basic number is not divisible by four (i.e. 1700, 1800 and 1900). By this procedure the calendar would stay correct if nothing else happened.
It should be noted that the Compendium – just like the papal bull – does not mention any dates or chronographical moment for the ‚historical‘ events of the reform of Julius Cæsar or the Council of Nicæa but only relativ distances by giving the amount of the error: thirteen days for the first one, ten days for the other. The problem of chronology was still all but solved and the impossibility to retro-calculate such faraway dates into the past was known. To introduce wrong dates in such an important matter would have made the proposal unacceptable.
Between the ‚historical‘ Julius Cæsar’s solstice date (at December 25th, sol invictus) and the
Nicæan Father’s equinox (March 21st which would correspond to December 21st) are not three but four days which did not go unnoticed by the Calendar Commission, and this cannot be explained by the simple fluctuation of the date which the intercalary day causes. Jesus‘ passion is adjusted to March 24th while his incarnation lies on March 25th corresponding to his birth on December 25th. 130 years would have to pass to account for one day.
With all this rather heavy discussion of the employed calendar makers it is difficult to ascertain why not March 24th or 25th had been chosen for corrected equinox. Possibly the time lapse between the two events supposed to have historical reality, i.e. Cæsar and Nicæa, was not known then. Finally the church adopted the Council of Nicæa as starting point, as is neatly expressed in the Compendium: not the dignity of God is to be restored, but that of the church (ex ecclesiastica dignitate).
From what we read so far it is obvious that Lilius did not believe in a steady precession that allowed retro-calculation over a greater amount of time. That is why he mentions no dates for Cæsar or Nicæa but points to the fact that the equinox over longer times is not calculable. This idea is said more than once in the Compendium, and its reason expressed as well: Since the sun is moving in such irregular way, it was not possible to introduce a rule that would keep the equinox steady. The length of the tropical year is variable which has been found out by the greatest astronomers, he adds.
Those „greatest and most diligent astronomers“ Lilius refers to are probably the ones known in his time as outstanding capacities in these questions as are the Greeks (Hipparch and Ptolemy among others) and the Arabs (for example al-Battani, i.e. Albategnius, whose works were even translated into Spanish and well published). They all had given differing results of the tropical year length: Hipparch measured 365 ¼ days minus 1/300 part of a day, which means six minutes longer than today, while Battani’s year was two minutes shorter than today, eight minutes shorter than Hipparch’s.
Lilius projects a „medium value“ and calls it ‚Alfonsine year‘, which is a wrong designation (it is Ulugh Beg’s year) but serves the purpose. The year that became known as that of Alfonso X the astronomer king of Castilia is only 27 seconds longer than today and thus exact enough. The designation probably was a courtesy to the church because they would have disliked to use a heretic‘s or heathen‘s value but were glad to mention a Spanish Christian as originator.
Precession is understood to be the difference between the sidereal and the tropical year, the first one measured against the background of the stars, the second as distance from one spring equinox to the next averraged for a long time. So only when knowing both values the amount of precession can be measured. Battani (880 AD) calculated a precession value of 66,4 years per one degree and all his contemporaries had similar results (sometimes one year more or less) after painstaking observations: Kushair gives 66,25, Sufi 65,4, Biruni (1031 AD) 68,7, Haraqi (around 1112 AD) 65,7 years.This value was used by Alfonso X (1270) in the books ascribed to him.
From this we can deduce that real observations were involved, and that the differencc to the modern value (roughly 72) implies a sudden leap caused by the irregularity of the sun like Lilius argues. We can also surmise that this was general knowledge at his time. Between the Council of Nicæa and pope Gregory XIII a sudden rupture must have taken place which changed the smooth flow of the calendar. We call this the ‚precession jolt‘ and put it somewhere from six to seven centuries ago. In our first model (2004) we described it thus: The axis of the Earth which usually retrocedes by a tiny fraction every year (precession) once in a while jumps in the same direction by a bigger leap or jolt. After some decades of irregular movement (called trepidation) the precession swings down to a new regular speed which is near to the one before the leap but measurably different. On account of the unknown amount of the jolt itself and the swaying movement after a jolt (trepidation) it is impossible to tell by astronomical calculation the exact amount of years that have elapsed between two events before and after the jolt if there are no other critieria. If the last jolt corresponded to a week in the calendar (as we think to have reasonably shown 2004) and the intercalational error amounts to two days (from 1300 AD to pope Gregory) than there remains one more day to be reckoned with, possibly hidden in the uncalculable time span of trepidation.
Our first draft (2004) included two jolts near to each other, some 650 and 740 years ago. We now have come to the conclusion that we confounded those traditions and that they really refer to one and the same jolt not more than 700 years before present between the reform of pope Gregory and the Council of Nicæa which was the starting point for Gregory. By using archaeological results we might get closer to a definite dating but for the moment we have to leave it that vague.

The onsuing parts of the Compendium are concerned with the moon and give final tables for calculating the Easter dates on the ground of the new reform. As year for the introduction of the reform 1582 is given, the month is still open to discussion and should be chosen according to suitability. For the future there are tables presented which run until 2199 (for more than six centuries!) while for the past they only go back until 1500 AD. This is another hint that retro-calculation was not regarded as providing any sensible result if the time span is exceeding a certain limit. Our hypothesis since some years projects that counting in AD years had been introduced after 1500.
At the end of the Compendium Lilius makes a rather generous move towards the protestants and professional astronomers by proposing: If anyone thinks the calculations of Alfonso unreliable and prefers younger values, he may know that the way of using the cycle of epacts Lilius has invented can be easily adapted to the calculations of Copernicus or any other by simply substituting the tables to those of Copernicus which are added here, too (quod si alicui Alfonsi calculi incertiores esse videbuntur quam ut illis fidendum putet, potiusque recentioribus adhærendum existimet, is profecto intelliget eam esse huius artificiosi cycli tabulæque epactarum a Lilio excogitatæ dispositionem ac digestionem, ut nullo negotio sive Copernici, sive cuiusvis alterius calculis possit aptari, si tabella æquationis ex illis confecta, pro ea, quam ad marginem scripsimus, substituatur veluti hæc, quam exempli gratia a Copernici ratione non multum distantem apposuimus.)
Indeed, the tables of Copernicus of whom we know that he, too, regarded the length of the tropical year as not always having been the same, are included in the Compendium. In this he coincided with Lilius, and it seems that this still was the general conviction. In his „Comentariolus“ Copernicus says: „As the cornerpoints of the year such as the equinox are wandering considerably, everyone who thinks that the seasons are uniformely constant, is in error. By many observations at different epochs they have been found different.“ He then brings the known examples of the Greek and Arab astronomers and goes on: „These differences do not seem to be due to errors in observation because if one regards the observations more closely one finds that their differences are coherent to the movement of the equinoxes“.

The possibility that the Compendium has been fabricated some time later and could be a clerical fiction (like the afore mentioned script of Cusanus) should be pondered but after thourough deliberation I have come to the conclusion that this cannot be the case. It is the contrairiness to Catholic dogma that induces me to believe in its authenticity. Not only the benign mentioning of the Copernican tables but the basic idea of a differing year throughout history which is opposite to later teachings of the Vatican would have been banned. Moreover there are said to exist a great number of documents refering to the Compendium and its reception before 1582. I shall mention them according to the Catholic Encyclopedia. (Protestant testimonies I could not find so far.)
The members of the Calendar Commission are mostly known and named, some remain obscure or uncertain while there was a remarkable fluctuation. Even the year of Aloysius Lilius death (1576) has been doubted, and it is somewhat awkward that his book has never been published, a veritable desiderate. Yet there are two more texts like the Compendium, one being the handwritten report of the Commission to pope Gregory, the other the Compendium of Ciaconus, put to print by Clavius, the later chief of the Commission and last surviver. Those two texts are still unknown to me and should be scrutinized.
The following phrase in the Encyclopedia is doubtful: „Certain it is that Aloisius Lilius commenced his work before the accession of Gregory XIII to the throne and even before the publication of the new Breviary, spending ten years on it.“ This may be true but when someone starts his phrase with „Certain it is …“ than caution has to be observed. The refered Breviary is that of Gregory’s predecessor Paul V.
The following books should be consulted: That of Alexander Piccolomini, coadjutor Bishop of Siena who supposedly was not a member of the commission but was requested to express an opinion which he did in his „Libellus on the new form of the ecclesiastical calendar“ (Rome, 1578). And two books of Teofilus Martius from Siena: „Treatise on the Reform of the Calendar“ (after 1578) and „Short Narration of the Controversy in the Congregation of the Calendar“. This influential person accused the Commission of innovation and a lack of reverence towards the Council of Nicæa, yet the date of the equinox at Nicæa is not really known. Still it is conventional to believe it on March 21st, even the Oriental Christians held to this date. The proposal of Martius to put it on March 24th, or of the Veronese mathematician Petrus Pitatus, to put it on March 25th and delete 14 days, had no success.
The last mentioned date corresponds to the common day of the winter solstice at Cæsar’s time which seems to be a very ancient tradition because the church celebrates the anunciation to Mary on March 25th .
According to the cited Catholic Encyclopedia „answers to the Compendium are on record from Emperor Rudolf, from the Kings of France, Spain, Portugal, from the Dukes of Ferrara, Mantua, Savoy, Tuscany, Urbino, from the Republics of Venice and Genoa, from the Universities or Academies of Paris, Vienna, Salamanca, Alcalá, Cologne, Louvain, from several bishops and a number of mathematicians.“
The article goes on saying that the Catholic princes did approve of the proposed reform while most mathematicians objected on scientific grounds which led nowhere. And since a new research would have consumed more time it was a clever political move to install the new calendar right in 1582 as intended.
There were basically three suggestions among which the final solution had to be selected: In regard to the solar year, the date of the equinox should be March 25th, where Julius Cæsar had put it — this was the wish of the Humanists — or on March 24th, where it was at the time of Christ’s resurrection — this was the proposal of Salamanca — or March 21st, where the Council of Nicæa had put it, or finally should be left on March 11th, where it was at the time of the Commission. Several letters to this effect are said to be extant. Those answers are said to have postponed the introduction of the reform by one year, which must be a mistake since the intended year 1582 is mentioned in the Compendium itself. Some answers reached Rome after this date.
Pope Gregory signed the bull on February 24th 1581 and published it on March 1st 1582, New Years day in the Vatican. In October of the same year it was put into action and ten days were eliminated.

If we read the Compendium this way it delievers a sequence of arguments for our hypothesis. Lilius and his contemporaries knew very well what could be said without violating the then valid knowledge. The Compendium was directed to all Europe and therefore foul play could not be tolerated. Only after it became clear that the Protestants did not follow suite, the Catholic church could sweep scientific standards and hide ideas that were contrary to the dogma. The Compendium may be regarded as one of the last open minded documents of the church after the Tridentinum.
After 1700 the Protestant churches by and by implemented the Gregorian Calendar and from then on safegarded the same dogma of uniformity and invariability of the planetary system.
The Orthodox churches have so far not joined the plot but some (like the Greek) have promised to do so in the near future.

Uwe Topper 25. 11. 2009

References:
Cusanus, Nicolaus: De emendatione Kalendarii (Latin and German by Victor Stegemann, Heidelberg 1955)
Copernicus, Nikolaus (around 1514): Commentariolus (German transl. by F. Rossmann, Darmstadt 1986)
Lilius, Antonius (1577): Compendium, as edited by Clavius, Christopherus (1603): Romani calendarii … restituti explicatio (Rome)