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Aloisius Lilius, principal author of the Gregorian Calendar, was a native of Cirò or Zirò in Calabria. His name was originally Aloigi Giglio, from which the Latinized form now used is derived. Montucla (Histoire des Mathématiques, I, 678) erroneously calls him a Veronese, and Delambre (Histoire de l'Astronomie moderne, 1812, I, 5 and 57) calls him Luigi Lilio Giraldi, mixing up Aloigi with Lilius Gregorius Giraldi, the author of a work "De Annis et Mensibus". Of Lilius's life nothing is known beyond the fact that he was professor of medicine at the University of Perugia as early as 1552. In that year he was recommended by Cardinal Marcello Cervini (afterwards Pope Marcellus II) for an increase of salary as an eminent professor and a man highly esteemed by the entire university. This date may explain why Lilius did not live to see his calendar introduced thirty years later. The statement in Poggendorff's "Handwörterbuch", that Lilius was a physician in Rome and that he died in 1576, is apparently not supported by recent researches. In that year, 1576, his manuscript on the reform of the calendar was presented to the Roman Curia by his brother Antonius, likewise doctor of arts and medicine. Antonius was probably many years younger, as he survived the reform, and owned the copyright of the new calendar, until, by retarding its introduction, he lost that privilege, and its printing became free. Mention is made of a Mgr Thomas Giglio, Bishop of Sora, as first prefect of the papal commissions for the reform. If he was a relative of the two brothers, he was not guilty of family favouritism, as he proved himself an obstruction to Aloigi's plans. Lilius's work cannot be understood without a knowledge of what was done before him and in what shape his reform was introduced.

From the Council of Nicæa to that of Constance

The reform of the calendar was from the start connected with general councils, viz. those of Nicæa (325), of Constance (1414-1418), of Basle (1431), the Fifth of the Lateran (1512-1517), and that of Trent (1545-1563). The double rule, ascribed to the first council, that the vernal equinox shall remain on 21 March, where it then was, and that Easter shall fall on the Sunday after the first vernal full moon, was not respected by all those that planned reforms, but was strictly adhered to in the Gregorian Calendar. It was well known, at the time of the Council of Nicæa, that both the Julian year and the lunar cyclo of Meton were too long; yet a remedy could not be adopted until the errors were more exactly determined. This state of knowledge lasted throughout the first twelve hundred years of our era, as is testified by the few representatives of that period: Gregory of Tours (544-595), Venerable Bede (c. 673-735), and Alcuin (735-804). Some progress was made during the thirteenth century. In the computus of Magister Chonrad (1200) the error of the calendar was again pointed out. A first approximation of its extent was almost simultaneously given by Robert Grosseteste (Greathead, 1175-1253), Chancellor of Oxford and Bishop of Lincoln, and by the Scottish monk Joannes a Sacrobosco (Holywood or Halifax). According to the former one leap day should be omitted every 300 years; according to the latter 288 Julian years were just one day too long, and 19 Julian years were one and one-third hours shorter than the lunar cycle. While the latter error is estimated correctly, the other two numbers 300 and 288 should be replaced by 128. The Franciscan friar, Roger Bacon of Ilchester (1214-1294), basing his views on Grosseteste, recommended to the pope a series of reforms, the merits of which he did not decide. Campanus (between 1261 and 1264) made to Urban IV the specific proposition to replace the lunar cycle of 19 years by two others of 30 and 304 years. The most important step in the thirteenth century was made by the appearance, in 1252, of the astronomical tables of King Alphonsus X of Castile.

The fourteenth century is remarkable for an astronomical conference held at the papal court in Avignon. In 1344 Clement VI sent invitations to Joannes de Muris, a canon of Manières (Canton Bourges), who was held to be no mean astronomer, and to Firminus de Bellavalle (Beauval), a native of Amiens, and others. The result of the conference was a treatise written by the two authors just mentioned: "Epistola super reformatione antiqui Calendarii". It had four parts: the solar year, the lunar year, the Golden Number, Easter. A third author was the monk Joannes de Thermis. Whether he was a member of the same conference or not, certain it is that he was charged by Clement VI to write his "Tractatus de tempore celebrationis Paschalis". It appeared nine years after the conference (1354) and was dedicated to Innocent VI, successor to Clement VI. In the same century other treatises on the errors and the reform of the calendar are recorded: one of Magister Gordianus (between 1300 and 1320) and one of a Greek monk, Isaac Argyros (1372-3).

The Councils of Constance and Basle

The fifteenth century marks an epoch in the reform of the calendar by two scientific authorities, Pierre d'Ailly and Nicolas de Cusa, both cardinals. Pierre d'Ailly (1350-1420), Bishop of Cambrai and Chancellor of the Sorbonne, followed the views of Roger Bacon. After advising Pope John XXIII in 1412, he pointed out to the Council of Constance, in 1417, the great errors of the calendar. He suggested different remedies: first, to omit one leap day every 134 years, thereby correcting the solar year; second, to omit one day of the lunar cycle every 304 years; or third, to abandon all cyclical computation and follow astronomical observation. It must be noticed that the first and third proposition of Cardinal d'Ailly are reiterated in our own days (substituting for 134 the correct number 128). The first and second of d'Ailly's propositions were elaborated and again proposed by Cardinal de Cusa (1401-1446) to the Council of Basle. The error should be corrected by omitting 7 days in the solar cycle (passing, in 1439, from 24 May to 1 June) and 3 days in the lunar cycle. His "Reparatio Calendarii" furnished much information to subsequent reformers. He was the first to take into account differences of longitude for various meridians. The two councils wisely postponed the reform of the calendar to some future time. The fifteenth century was not to close, however, without considerable progress connected with the names of Zoestius, John of Gmund, George of Purbach, and John of Koenigsberg (Regiomontanus). A treatise on the reform of the calendar by Zoestius appeared after 1437. The first printed almanacs were issued by John of Gmund (d. 1442), dean and chancellor of the University of Vienna. His disciple was Purbach, afterwards professor of mathematics at the same university and teacher of John Müller, called Regiomontanus after his native place in Franken. The latter (1435-1476) continued the work of the chancellor in publishing calendars that served as models for a century to come. The Golden Numbers of the lunar cycle were retained, but the lunations were taken from observation. This combination made the errors of Easter more and more manifest. Regiomontanus was called to Rome by Sixtus IV, for the purpose of reforming the calendar, but died shortly after his arrival at the age of forty-one.

The Councils of the Lateran and of Trent

The two councils of the sixteenth century were finally to pave the way for the long desired reform. The efforts made at the Lateran Council are described by Marzi. From the twelve or more authors enumerated by him it will suffice to mention the two that exercised a decisive influence: Paul of Middleburg, who started the proceedings, and Copernicus, who brought them to a temporary conclusion. The life of the former is described by Baldi in Appendix I to Marzi. Paul born in 1445, died as Bishop of Fossombrone in 1534. He was called from Louvain to Italy by the Republic of Venice, became professor of mathematics at Padua, and physician and astrologer to the Duke of Urbino. Before the opening of the council in 1512 he asked Julius II to attend to the calendar. Leo X sent out briefs to Maximilian I, the princes, bishops, and universities, to obtain their opinion on the calendar, and appointed the Bishop of Fossombrone as president of the commission for the reform. The treatise which Paul of Middelburg laid before the council is entitled: "Paulina sive de recta Paschæ celebratione etc." (Fossombrone, 1513). He was against bringing the equinox back to 21 March, and opposed the idea of abandoning the lunar cycle or putting Easter on a fixed Sunday of the year. He proposed, however, a change in the cycle by reducing the seven embolismic months to five. Emperor Maximilian charged the Universities of Vienna, Tübingen, and Louvain, to express an opinion. Vienna supported the first and third propositions of Cardinal d'Ailly at the Council of Constance, viz. to correct the Julian intercalation by omitting a leap day every 134 years, and to abandon the lunar cycle. Tübingen was of the same opinion, and agreed with Bishop Paul in leaving the equinox where it was.

Copernicus had been asked by the papal commission in 1514 to state his views, and his decision was, that the motions of sun and moon were not yet sufficiently known to attempt a reform of the calendar. The commission was to make definite propositions in the tenth session of the council. Although this was postponed from 1514 to 1515, no conclusion was reached. After the Lateran Council considerable progress was made. Copernicus had promised to continue the observations of sun and moon and he did so for more than ten years longer. The results laid down in his immortal work "De Revolutionibus Orbium Cœlestium" (1543) enabled Erasmus Reinhold to compute the Prutenic Tables (Wittenberg, 1554), which were afterwards made the basis of the Gregorian reform. The principal writers at the time are the following: Albertus Pighius, magister at the University of Louvain, who dedicated to Leo X, in 1520, a treatise in which he supported Cardinal d'Ailly's intercalation, omitting a leap day every 134 years, but, on the other hand, recommended the retention of the lunar cycle. About the equinox he committed an error, reckoning it from the constellation of Aries and advising the omission of 16 days. The two Florentine monks, Joannes Lucidus and Joannes Maria de Tholosanis, may be mentioned in passing. The latter pleaded for cyclic reckoning but was opposed to changing the date of the equinox. During the Council of Trent a number of plans were written and proposed to the council and to the pope. Cardinal Marcellus Cervinus, president of the council, summoned to Trent the Veronese Girolamo Fracastoro, a physician and renowned astronomer, and had several conferences with him on the subject of the calendar. In 1548 Bartholomeus Caligarius, a priest in Padua, offered a memorandum to the Bishop of Bitonto, wherein he based his plans on Paul of Middelburg, Stoeffler, and Joannes Lucidus. The Spanish Franciscan Joannes Salon, addressed a proposition to Cardinal Gonzaga, first president of the council under Pius IV. An abridgment of it he offered, immediately after the council, in 1564, to Pius IV, and, on the advice of Sirleto, also to Gregory XIII, in 1577. His memorandum is remarkable for the reasons he puts forth against an immovable Easter, and for the advice that a leap day should be omitted by the pope on the occasion of general jubilees.

Other memoranda were that of Begninus, a canon of Reims, which was handed to on his way to the council; that of Lucas Gauricus, who signed himself Episcopus Civitatensis, and based his "Calendarium Ecclesiasticum" of 1548 on Paul of Middelburg; that of the Spanish priest Don Miguel of Valencia, which was presented to Pius IV in 1564. More important than all these was a plan proposed by the Veronese mathematician Petrus Pitatus. Basing his ideas likewise on Paul of Middelburg he wanted the lunar cycle retained and the equinox restored to Cæsar's date, by the omission of fourteen days, which for two years should be taken from the seven months having 31 days each. His original idea, which took final effect in the Gregorian reform, was to correct the Julian intercalation of the solar year, not every 134 years, but by full centuries. No earlier writer seems to have called attention to the fact, that applying the rule of 134 years three times comes, within a small error, to the same thing as omitting three leap days in 400 years. His "Compendium" was published and offered to Pius IV in 1564. The Council of Trent was the first since that of Nicæa that took a positive step towards a reform of the calendar. In the last session, 4 December, 1563, it charged the pope to reform both Breviary and Missal, which included the perpetual calendar.

After the Council of Trent

Pius V published a Breviary (Rome, 1568), with a new perpetual calendar, which was faulty and soon discarded. Gregory XIII, the immediate successor of Pius V, charged Carolus Octavianus Laurus, lector of mathematics at the Sapienza, with working out a plan of reform. It was completed in 1575, and it again recommended the correction of the intercalations by full centuries. A certain Paolo Clarante also composed a calendarium and offered it to the pope for examination. In 1576 the famous manuscript of the late Aloisius Lilius was presented to the papal Curia by his brother Antonius.

Whether Antonius acted in response to the pope's request is not known. 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. Gregory then organized a commission to decide upon the best plan of reform. During the many sessions the members of the commission changed several times. From the names of those who signed the report offered to Gregory XIII it may be inferred that its composition was intended to represent various nations, grades, and rites of the Church. Besides four Italians there was the French Auditor of the Rota Seraphinus Olivarius, the German Jesuit Christoph Clavius, the Spaniards Petrus Ciaconus, and the Syrian Patriarch Nehemet Alla. Religious Orders were represented by Clavius, by the celebrated Dominican friar Ignatius Dantes and, for a while, by the Benedictine monk Teofilus Martius. The hierarchy we find represented by Vincentius Laureus, Bishop of Mondovì, by the Patriarch of Antioch, and by Cardinal Sirleto. The laity was represented by Antonius Lilius, doctor of arts and medicine, and, as it seems, collaborator of his brother Aloisius in the reform. About the Spaniards Ciaconus or Chacon nothing seems to be known.

The first president of the commission, Bishop Giglio, did not succeed in securing a majority. He favoured the corrections suggested for Lilius's manuscript by the two professors of the Roman Sapienza, the mathematician Carolus Laurus and the professor of Greek, Giovanni Battista Gabio. The commission, however, condemned the corrections as false and addressed itself directly to Gregory XIII. Thomas Giglio, being promoted to the See of Piacenza in 1577, was superseded as president by the learned and pious Cardinal Sirleto, a native of Calabria like Lilius. Another disagreement was caused by the Sienese Teofilus Martius, who was mentioned above. He blamed the commission for the spirit of innovation and for lack of reverence towards the Council of Nicæa; he wanted the equinox restored to the older Roman date 24 or 25 March; he rejected the new cycle of Lilius, and wanted the old cycle corrected; he accepted neither the Alphonsine nor the Prutenic Tables and he desired a leap day to be omitted every 124 years or ten years sooner than the Alphonsine Tables required. Teofilus put his dissent on record in a "Treatise on the Reform of the Calendar" (after 1578) and in a "Short Narration of the Controversy in the Congregation of the Calendar". This would seem to show that he was a member of the commission; at least for a time, for he did not sign the report of the latter to the pope. It was probably owing to his objections that the new cycle of Epacts was changed at least twice and recommended by the commission in a third or even later form.

The opposition of the Sienese Teofilus against the innovation of the Epacts was supported by Alexander Piccolomini, coadjutor Bishop of Siena. If he was not a member of the commission, he was at least requested to express an opinion. He laid down his theories in a "Libellus on the new form of the ecclesiastical calendar" (Rome, 1578). He was influenced by the "Epitoma" of the Florentine Joannes Lucidus (1525). Underrating the exactness of the Alphonsine Tables he gave preference to Albategni's length of the year and advocated the correction of the Julian intercalation once in every hundred years (thinking the error to amount to one day in 106 years). Piccolomini's name is not among the eight that recommended the official report of the commission to Gregory XIII in 1580; they are: Sirleto, Ignatius, Laureus, Olivarius, Clavius, Ciaconus, Lilius, Dantes, all mentioned above. The last mentioned, usually called Ignazio Danti, was afterwards made Bishop of Alatri. His scientific reputation may be inferred from the praises given to him more than a hundred years later (1703) by Clement XI for his large solar instruments in Rome, Florence, and Bologna, which affirmed the correctness of the Gregorian equinox. The instruments consisted of meridian lines and gnomons. The former were usually strips of white marble inset in stone floors. The gnomon was sometimes replaced by a small opening in a wall which projected the image of the sun on the meridian line. An arrangement of this description is visible in the old Vatican Observatory, called the Tower of the Winds. It was on this line that, according to Gilii and Calandrelli, the error of ten days was demonstrated in the presence of Gregory XIII.

The manuscript of Lilius was never printed and has never been discovered. Its contents are known only from the manuscript report of the commission and from the "Compendium" of Ciaconus, which was printed by Clavius. The request of Charante, that his "Calendarium" be distributed together with the "Compendium", was not granted by the commission. The "Compendium" was sent out in 1577 to all Christian princes and renowned universities, to invite approbation or criticism. With Lilius, it left open the questions, whether the equinox should be placed on 24 March or 21 March, following the old Roman Calendar or the Council of Nicæa; and if the latter (which seemed preferable), whether the ten days should be omitted at once, in some suitable month of 1582, or gradually by declaring all of the next forty years common years and thus completing the reform in 1620. That the error from the Nicæan regulation of the equinox had amounted to ten days, was sufficiently known from various observers, like Toscanelli, Danti, Copernicus (Calandrelli, "Opuscoli Astronomici", Rome, 1822, 30). The motions of sun and moon were taken from the Alphonsine Tables. Whether the Prutenic Tables of 1554 were at the time known to Lilius may be doubted. He could be no stranger, however, to Cardinal d'Ailly's "Exhortatio ad Concilium Constantiense", in which the Julian intercalation was shown to be one day in error every 134 years, or to the proposition of the Veronese mathematician Pitatus, who wanted the correction applied by a cycle of four centuries. Lilius considered fractions of centuries unfit for all cyclic or non- astronomical reckoning and used centurial corrections for both solar and lunar motions.

Lilius's masterpiece is the new "Nineteen Years' Cycle of Epacts", by which he kept the Nicæan Easter regulation apace with the astronomical moon. The old lunar cycle gave the lunations four or more days in error, and Easter could thus (by taking the Sunday after Luna XIV) fall on Luna XXVI, within a few days of the astronomical new moon. Lilius brought the new cycle of Epacts in harmony with the year by two equations so called, the solar and the lunar. The solar equation diminishes the epacts by a unit whenever a Julian leap day is omitted, as in 1900; the lunar equation increases the epacts by unity every 300 years, or (after seven repetitions, the eighth time) in 400 years. The former equation accounts for the error in the Julian year and the latter for the error in the Metonic cycle. The Greek cycle is longer than 19 years and the surplus amounts to one day in 310 years. This will explain the lunar equation, and also show that greater exactness could be reached by applying the interval of 400 years the tenth time. It may happen that the two equations cancel each other and leave the epacts unchanged, as happened in 1800. The new cycle of epacts, with the two equations, were joined to the "Compendium". 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 bull "Inter Gravissimas"

The contents of the answers are not officially recorded, but in the Bull of Gregory they are called concordant. How the concordance is to be understood may be illustrated by the answers from Paris and from Florence. While the Sorbonne not only rejected the "Compendium" but condemned every change in the calendar, the king's Parlement fully adopted the reform proposed by Lilius. The Duke of Tuscany forwarded to the pope the judgments of several Florentine mathematicians, no two of which agreed among themselves, while he himself gave full approval to the Gregorian reform. The King of Portugal presented two professional answers without adding a judgment of his own. The emperor also confined himself to forwarding the reply from the University of Vienna. The answers from Savoy, Hungary, and Spain were in approbation of Lilius's plan. All the princes may have seen the necessity of a reform and desired it. This is confirmed by a letter of the Cardinal Secretary of State to Charles Borromeo, Archbishop of Milan, dated 16 June, 1582, in which the statement is made that the reform of the calendar was concluded with the approbation of all Catholic princes. The consent of the princes had more influence with the pope than the opinion of scientists. To bring about an agreement of the latter was utterly hopeless, and, in view of the labours of the papal commission, unnecessary. The variety of opinion, collected by Kaltenbrunner and Schmid, bears testimony to this, quite apart from the bitter polemics that followed the Gregorian reform and which does not concern us in this article.

The propositions made in answer to the "Compendium" may be summed up as follows. In regard to the solar year, the date of the equinox should be 25 March, where Julius Cæsar had put it — this was the wish of the Humanists — or on 24 March, where it was at the time of Christ's resurrection — this was the proposal of Salamanca — or 21 March, where the Council of Nicæa had put it, or finally should be left on 11 March, where it was at the time. Those who would not accept the correction of the Julian intercalation by full centuries wanted a leap day omitted as often as the error amounted to a full day — by the Alphonsine Tables every 134 years — or, as the theological faculty of the Sorbonne demanded, no correction at all. As to the lunar cycle, no university attempted an improvement on Lilius's epacts. Salamanca and Alcalá, as we know from a letter of Clavius to Moleto in Padua, fully approved Lilius's reform. Vienna rejected all cyclical computation, while the theological faculty of the Sorbonne pleaded for the retention of the old cycle, uncorrected. The answers from Louvain deserve special mention because of the full approval of Lilius's calendar by the famous astronomer Cornelius Gemma, while Zeelstius (1581) sided with the University of Vienna. The answers from Padua were peculiar. Macigni, in a letter to Sirleto (1580), accepted the idea of the Spanish Franciscan Salon and proposed that during general jubilees a number of mathematicians be called to Rome by the pope to decide upon the date of the equinox. Apparently the first to advocate an immovable Easter Sunday was Sperone Speroni, who calls himself a layman in mathematics. According to him Easter should be fixed on the Sunday nearest to the 25 March; or, as the Spaniards Franciscus Flussas Candalla proposed, on the Sunday nearest the equinox.

Thus, every imaginable proposition was made; only one idea was never mentioned, viz. the abandonment of the seven-day week. The answers delayed the publication of the papal Bull from 1581 to 1582, and some arrived even later. The consent of the Catholic princes on the one side and the variety of scientific opinions on the other left to the papal commission no alternative, but forced it to follow its own judgment. The final framing of the reform seems to have been in great part the work of Clavius; for he alone afterwards took up its defence and furnished full explanations ("Apologia", 1588; "Explicatio", 1603; see CLAVIUS). Sirleto writes of him that he was among the foremost workers in the reform (cum primis egregie laboravit), and Clement VIII says, in his Bull "Quæcumque" (17 March, 1603), that Clavius did signal services for the calendar. The papal commission decided, 17 March, 1580, that out of reverence for ecclesiastical tradition, the equinox should be restored to the decree of the Council of Nicæa. The majority, under the leadership of the Bishop of Mondovì, declared itself against astronomical lunations and for the cycle of Epacts. Lilius's century rule for the ommission of leap days was adopted, but his lunar cycle was modified. The Prutenic Tables were made the basis, and the epacts were all diminished by unity, in other words, Luna XIV was put one day later, to remove all danger of Easter ever being celebrated on the day of the astronomical full moon, as was forbidden by the old canons. It is known that the month of October, 1582, was to have twenty-one days (not twenty, as Montucla says) and the ten days should be expunged by passing from 4 October to 15 October. The reform, as recommended by the commission on 14 September, 1580, received papal sanction by the Bull "Inter Gravissimus", dated 24 February, 1581, and published on 1 March, 1582. The decrees of the Council of Nicæa were in this manner put on a cyclical basis that secured their correctness for nearly four thousand years, a space of time more than long enough for any human institution. The original task of the papal commission seems to have exceeded its strength and time. The dates of Easter were actually computed for the next three thousand years; the "Liber Novæ Rationis Restituendi Calendarii", which was to accompany the reform, was never written, and the Martyrology did not appear until 1588 under Sixtus V. In 1603, Clavius was the only surviving member of the papal commission. It was by command of Clement VIII that he composed his "Explanation of the new Calendar".

For the technical part of the Gregorian reform see CALENDAR, REFORM OF THE; CHRONOLOGY.