SOURCE: “Solving the Riddle of Time,” in Calendar: Humanity's Epic Struggle to Determine a True and Accurate Year, Avon Books, Inc., 1998, pp. 187-208.

[In the following essay, Duncan recounts the efforts of those involved in the Gregorian calendar reform, the technical difficulties they faced, and the reaction to their work.]

The patriarch has also subscribed to our calendar and admitted that it is very good. I hope that it will soon be published, because the Pope is quite eager.

—Christopher Clavius, 1581

None of the three men responsible for fixing the calendar was a conqueror, notorious lover, heretic, or lone monk pondering the cosmos from a cell in a monastery. They were not even particularly flamboyant, and certainly not free thinkers in the spirit of a Bacon or even a Paul of Middelburg—all of which might account for their success.

They included an obscure physician from the toe of Italy who was the genius behind the reform, a Jesuit astronomer famous for being wrong about many of his most cherished theories, and a lawyer turned pope remembered as much for his failures as for his successes. Each contributed to the reform named for one of them, and each in the story of his role offers an explanation for why the calendar was finally fixed 1,627 years after Caesar launched it, and after so many centuries of false tries and frustrations.

The doctor was Aloysius Lilius. Born about 1510 to a family of modest means, little is known about Lilius—the “primus auctor” of the Gregorian reform, according to a prominent member of the calendar commission. He is said to have studied medicine and astronomy at Naples, settled in Verona, and taught at the University of Perugia before returning late in life to his hometown of Ciro, in southeastern Italy, where he concocted the solution to the calendar conundrum and designed the reforms. Indeed, if the pope had offered a prize for solving this age-old problem—as the British later offered a prize of £20,000 to anyone who solved the ancient puzzle of determining longitude at sea—Aloysius Lilius could have rightly claimed it. But this forgotten man never had the chance. For before his solution could be presented in 1576 to the pope's commission in Rome, Lilius took ill and died.

After Lilius's death, his brother Antonio, also a physician acquainted with astronomy, presented Aloysius's plan to the calendar commission. They quickly embraced it as their leading proposal, admiring it for its simplicity, elegance, and avoidance of controversy. Antonio stayed on in Rome as his brother's representative. Later he was the recipent of what passed for a discoverer's “prize” in the sixteenth century: a 1583 bull from Pope Gregory that granted him the exclusive right to publish the reformed calendar and its new rules for a period of ten years. This potentially lucrative license was later rescinded when Antonio failed to produce enough copies fast enough to meet the demand, a delay that nearly derailed the reform.

The second prime mover was the Jesuit astronomer Christopher Clavius (1538-1612), the man behind the scenes who championed Lilius's ideas (after an initial skepticism) and shepherded the reform through the minefields of scientific and ecclesiastic controversy before and after 1582. Until he died in 1612, Clavius worked hard to defend and explain the new calendar, ensuring that it would spread beyond the handful of countries that initially accepted it.

As a prominent public figure in Rome during the late sixteenth and early seventeenth centuries, more is known about Christopher Clavius than about Lilius. Yet little exists to flesh out who he really was. In a portrait of Clavius rendered in 1606 he is dressed in a simple Jesuit robe and a four-cornered hat. A portly, satisfied-looking man with a pudgy, bearded face, he looks sympathetic, even kind—the sort of scholar who is serious but never stuffy, smart but not precocious; one that students are fond of, and one that politicians and prelates feel comfortable assigning to commissions.

To his contemporaries Clavius was a revered sage of math and astronomy, acclaimed as “the Euclid of his times” in part because he penned a widely used translation of the original Euclid, along with several other works considered important in his day. Even the era's greatest scientific firebrand, Galileo Galilei, came to him for validation of his telescopic observations of the moon, sun, and planets. Clavius hailed them as important to astronomy, but since he was a confirmed defender of Ptolemy he disagreed with Galileo's interpretation that craters on the moon, Venus passing through its phases, and moons around Jupiter suggested Copernicus was correct. Clavius also has the distinction of having his face inscribed on a marble relief on the base of Gregory XIII's imposing statue in St. Peter's (probably Clavius) which shows a priest handing the pope a copy of the calendar reform.

Yet Clavius today is nearly as obscure as Aloysius Lilius. In part this comes from the bad luck to have lived between Copernicus—Clavius was five years old when De revolutionibus was published—and the young Galileo, who burst onto the scene in Clavius's final years. But more than anything, Christopher Clavius is obscure because he adhered to a worldview that turned out to be wrong. This made him a hero to traditionalists while he was alive, but a fool to those who came later.

Clavius was surprisingly young when Pope Gregory named him to his new calendar commission, convened in the mid-1570s. Born on March 25, 1537, in the Bavarian town of Bamberg, Clavius's life to us is a blank page until he joined the recently formed Society of Jesus—the Jesuits—in Rome on April 12, 1555. Studying in Rome and then at the University of Coimbra in Portugal, Clavius returned to Rome in the early 1560s to finish his education and then to teach at the Jesuits' own Collegio Romano, where he became a professor of mathematics. But for a few short trips, he would remain in Rome until his death.

As a mathematician and astronomer, Clavius was a minor figure, notable mostly for his work on Euclid, algebraic notation, and the calendar—and for his staunch defense of an earth-centered universe. Yet Clavius was flexible enough to constantly update his own theories to incorporate Copernican data and Galileo's observations, attempting to squeeze it into an increasingly strained Ptolemaic interpretation.

Clavius's willingness after 1582 to at least consider new ideas as Rome's senior astronomer seems to have exercised a restraining influence on the inevitable showdown between the ideas of Copernicus and those of Ptolemy, primarily benefiting the young Galileo, whose reputation was enhanced by Clavius's support of his telescopic discoveries. Galileo judged Clavius to be “worthy of immortal fame,” and forgave him for rejecting the Copernican theory, a shortcoming he blamed on the old man's age.

Others were not so forgiving. In 1611 the England poet and satirist John Donne (1572-1631), a former Catholic in this sometimes virulently anti-Catholic kingdom, penned a vicious satire of the Jesuits and their founder, Ignatius Loyola (1491-1556), titled Ignatius His Conclave. Donne describes Loyola in hell trying to convince Satan to reject Copernicus because the Polish astronomer had not done enough to obfuscate the minds of men and therefore keep them from the truth. In the midst of this the poet mentions Clavius, whom he could not place in hell because in 1611 the old astronomer was still alive. But Donne did have his Loyola tell the dead Copernicus about a candidate possibly more “worthy” for the netherworld, describing among other things Clavius's work on calendar reform, which the English, as Protestants, considered tainted because it came from Rome:

If therefore any man have honour or title to this place in this matter, it belongs wholly to our Clavius who opposed himselfe opportunely against you, and the truth, which at that time was creeping into every man's minde. Hee only can be called the Author of all contentions, and schoole-combats in this cause; and no greater profit can bee hoped for heerein, but that for such brabbles, more necessarie matters bee neglected. And yet not onely for this is our Clavius to be honoured, but for the great paines also which hee tooke in the Gregorian Calendar, by which both the peace of the Church, and Civill businesses have beene egregiously troubled: nor hath heaven it selfe escaped his violence, but hath ever since obeied his apointments: so that S. Stephen, John Baptist, & all the rest, which have bin commanded to worke miracles at certain appointed dates … do not now attend till the day come, as they are accustomed, but are awaked ten daies sooner, and constrained by him to come downe from heaven to do that businesse.

The final person in our troika was born Ugo Buoncompagni (1502-1585). The son of a noble family in Rome, he became a prominent ecclesiastic lawyer and senior papal official before being elected Pope Gregory XIII at age 70, on May 14, 1572. One of several pontiffs in the sixteenth century who worked to rebuild the authority of the Church and to reform its worst excesses, he was zealous in trying to stamp out Protestantism, chiefly by lavishing money on building up Catholic colleges across Europe, and by launching Church reforms in Germany, Poland, and Belgium. He also dispatched Jesuit missionaries to countries such as India, the Philippines, and China, where European ships had begun to sail with some regularity.

But Gregory also suppressed knowledge that failed to agree with Church dogma, establishing an infamous index of banned books that later listed Copernicus's De revolutionibus. He also supported military efforts by Catholic monarchs against Protestants, and connived in attempts to undermine England and Queen Elizabeth I—including ill-conceived military ventures to thwart English efforts to conquer and dominate Ireland. But all this pales against Gregory's infamous response to the slaughter of thousands of Huguenots in Paris that began on St. Bartholomew's Day, 1572. Hearing the news, the newly installed pope is said to have ordered a Te Deum—a hymn of praise to God—and issued a medal.

In Rome Gregory supported grandiose building projects; he also was known as a man who enjoyed pomp and celebration, nearly bankrupting the Vatican treasury with his edifices and fetes. His tenure as ruler of the papal state—a swath of land running across the middle of Italy and governed directly by the Vatican—was marked by peasant riots over steep taxes and by a rise in banditry and lawlessness, which he proved incapable of stopping.

But most of this has been forgotten, with Gregory chiefly remembered as the pope who finally corrected time, a feat that begs the question: why this pope?

Probably his motivation came from the same zeal he devoted to promoting education and putting the Church back onto a more sound intellectual track. But it also came from the lawyer Ugo Buoncompagni's systematic attempts as pontiff to enact reforms approved by the various church councils, particularly those passed at the various sessions of the Council of Trent (1545-1563), where Buoncompagni served as Pius IV's deputy and may have drafted some of the decrees. One of these ordered the reissuance of the mass book and breviary—the Catholic list of daily hymns and ceremonies—which implied the need for an updated calendar. Indeed, the first words in the momentous 1582 bull announcing the calendar reform do not claim the authority of science, the Church, or even God, but the decree of Trent, as if this legalistic sanction mattered most to this old lawyer-pope:

Among the most serious tasks, last perhaps but not least of those which in our pastoral duty we must attend to, is to complete with the help of God what the Council of Trent has reserved to the Apostolic see.

As the pace of reform quickened, the story of the calendar returns to the same city where Julius Caesar had launched his calendar 16 centuries earlier—though it could hardly have been more different.

Rome in the sixteenth century had ceased long before to be important as a commercial, political, or intellectual center. Nor did the Roman Church wield the all-embracing authority it once had enjoyed as Europe's religious overlord, now that Protestantism had broken up its monopoly of the spirit, and kings and princes had eclipsed its influence in the realms of politics and finance. Still, the Church remained the only force in Western Europe capable of exerting anything like a universal authority. It also had been the guardian of the calendar for centuries, for better or for worse, and was now riding a certain momentum from years of reform talk and council decrees aimed at making a fix.

Rome itself in the 1570s looked ruined and exhausted, its ancient monuments, palaces, and temples shattered and half buried by dirt and rubbish, its ancient walls and columns picked apart for centuries and incorporated into disconcerting hodgepodge of old and new. Even the once mighty Forum, where 16 centuries earlier Caesar had stood up to announce that he was establishing a new calendar, was now called the Campo Vaccino, the “Cow Pasture.” Buried under eons of trash and dust, and mostly dismantled for its marble and bricks, this place that had been the center of the Roman world was now the domain of bovines chewing tufts of grass growing around broken columns and archways.

The Eternal City that Clavius and Gregory lived in during the years of the calendar commission stood inside the sprawling ancient walls built in the third century by Emperor Aurelian. Diminished now from as many as a million people in imperial times to perhaps sixty thousand—though in the 1570s it was beginning to grow again—the city's inhabited areas were clustered near the Tiber, where those who stayed through the barbarian invasions had moved for easy access to water after the aqueducts were cut. This left large sections inside the walls empty of people. These vast stretches of space were used for vineyards, gardens, garbage dumps, and pastureland, and were marked here and there by scattered farmhouses and convents. Forests grew on the slopes of the Palatine, Caelian, and Aventine Hills. Deer and boar ran wild amidst the ruins of ancient villas covered with ivy and trees in which hundreds of pigeons squawked and fluttered.

Because of the water problem and the location of St. Peter's near the river, Rome's center had shifted north from the Forum to the C-shaped bend in the river between the Capitoline Hill to the south (just above the Forum-turned-pasture) and the Piazza del Popolo to the northwest. Still very much a medieval city, Rome in those days was a confusing knot of narrow, winding, fetid streets filled with people, animals, dung, dust, and sewage and edged by brick houses, shops, stalls, and offices. This was broken up here and there by piazzas and by a scattering of new Renaissance churches, including St. Peter's Basilica with its half-finished dome by Bramante and Michelangelo. Rome's fractious noble families had recently erected a number of splendid new palaces and villas, many of them on hills with breathtaking views of the city.

Another new building project was an extensive upgrading of Christopher Clavius's own Collegio Romano, which Gregory XIII took on as part of his efforts to improve Catholic universities. He lavished funds and support on the previously struggling Collegio, in part because of his close ties to his favorite astronomer, who made a special pitch for improvements in the departments of mathematics and astronomy.

The pope's attention to Roman education was long overdue. Before his improvements, the Collegio Romano had been one of two clearly second-rate outposts of learning in a city known for raucous local politics, pilgrimages, indulgences, and papal fetes, but not for intellectual pursuits. Rome in the 1570s still lacked any meaningful tradition of universities and scholarship. Nor did its officials offer much public support for scientific or technical research—unlike cities such as Florence, where the ruling Medicis hired Galileo as their court mathematician in 1610, or the Holy Roman Imperial court, which commissioned the astronomers Tycho Brahe (1546-1601) and later Johannes Kepler (1571-1630) to advise Emperor Rudolph II of Bohemia.

In the lovely Tuscan village of Siena is a painting of Pope Gregory XIII crowned and enthroned, leaning forward and listening intently to a scholar on the calendar commission describe the error in Caesar's calendar. This man looks like Clavius as depicted when he was older, with a white beard and four-cornered hat. Pointing to a picture of the zodiac on the wall he is explaining to the pope the difference between the Julian calendar, marked on a band outside the zodiac, and the true seasonal year, portrayed on the inside. He stands amidst members of the commission, some of whom are dressed in the flowing robes, broad-brimmed hats, and priestly hoods popular at that time in Italy. Seated around a table, the commission is surrounded by books and astronomic tools, including an armillary sphere the scholarly speaker is manipulating with his left hand as he points to the zodiac chart with his right.

The names of the members of the commission that worked through the 1570s and early 1580s were not recorded, except in the final report presented in 1581 to the pope—which is probably the meeting depicted in the Siena painting. Nine individuals signed this report, presumably all of them members of the commission, though one seems to have been simply a witness. The signatories included a cardinal, a bishop, a former Syrian patriarch, a man from Malta, a French lawyer, a Spanish historian and theologian, a physician, and two scholar-scientists.

The cardinal and the bishop were senior church officials now all but forgotten. They are Cardinal Guglielmo Sirleto (1514-1585), a scholar, Hellenist, and contender for the papacy, who served as president of the commission, and Bishop Vincenzodi Lauri of Mondovì. Why they were chosen is unknown, though in Sirleto's case the appointment of someone so senior and respected was clearly a signal by the pope to the Vatican bureaucracy and to everyone else within the Church that Gregory was serious about reform. Sirleto and Lauri may also have been experts on the Church calendar and its history, and on the deliberations of Church councils.

The patriarch was Ignatius of Antioch, a Jacobite Christian from Syria who had arrived in Rome in 1577 or 1578 to seek a personal reconciliation with the Roman Church. A refugee from the still-mysterious East whom some suspected was a fake—until he was confirmed as genuine—Ignatius was knowledgeable in mathematics and medicine, and he brought to the commission an Eastern perspective on astronomy and the calendar. He provided Clavius and the scientists with useful comments on their proposed reforms, written in Arabic and translated into Latin. He signed the 1581 report in Arabic and Syriac.

The man from Malta, Leonardo Abel, seems to have signed the final report just to serve as a witness to Ignatius's signatures, apparently because he was fluent in Arabic. The French lawyer signed his Latinized name as Seraphinus Olivarius Rotae, an auditor Gallus who may have been summoned to help the commission sort through the many legal implications of the reform for both canon and civil law. The Spaniard was Pedro Chacón, who probably advised the committee on past and present papal and Church pronouncements on the calendar, and on the critical issues of Easter and saint's days. He also authored some of the key documents of the commission.

The scholar-scientists included the Dominican friar Ignazio Danti (1536-1586), the second most famous commission member after Clavius. A mathematician, astronomer, cartographer, and artist, Danti was a professor of mathematics at Pisa and later at Bologna. Summoned to Florence he also worked on astronomic projects under Grand Duke Cosimo I (Cosmos de' Medici), preparing maps, an enormous terrestrial globe, and instruments he used to observe the vernal equinoxes in 1574 and 1575. From this he came up with the length of the year as 365 days, 5 hours, and 48 minutes. Comparing this to Ptolemy's erroneous calculation of 365 days, 5 hours, and 55 minutes, Danti joined Copernicus and other astronomers by concluding that the tropical year was variable. After a falling-out with Cosimo's son, Danti relocated to Bologna, where he measured the solstices in 1576 with a gnomon he built in the church of St. Petronius. He used this data to confirm the error in the Julian calendar and its drift against the true year.

In 1580 Danti was summoned to Rome by the pope to join the commission, and also to design the frescoes and astronomic instruments in a new building devoted to astronomy and to calendar reckoning. Known as the Tower of the Winds, this 240-foot tower north of St. Peter's dome and above the Vatican archives, was built between 1578 and 1580 and decorated with Danti's designs between 1580 and 1582. These included a series of enormous frescoes of the four winds, rendered in the style of Titian as voluptuous cupids flanked by images of astronomers at work. Danti also equipped the main room of the tower with an enormous anemometer (wind gauge) attached to a weathervane. He etched into the floor a map of the stars and zodiac, situated so that a small hole in the wall would shine a ray of sunlight onto the map, varying according to the seasonal angle of the sun. This created in the Tower of the Winds a crude seasonal calendar. In 1583, after the reform, Danti was named bishop of Alatri in Italy, where he died in 1586.

The final member of the commission was Antonio Lilius, who represented his late brother's interest after presenting Aloysius's ideas in 1576—an event Gregory mentions in his 1582 bull by recalling that “a book was brought to us by our beloved son Antonio Lilio, doctor of arts and medicine, which his brother Aloysius had formerly written.”

This “book,” still in manuscript form, was easily the most important document in the entire reform process. Yet over the centuries it has disappeared without a trace. What survives is a short booklet issued by the commission, titled Compendium novae rationis restituendi kalendarium, “Compendium of the new rational for reforming the calendar.” This is a synopsis of Lilius's plan sent out to various experts and important princes, monarchs, and prelates for comment.

The Compendium was also believed lost until the historian Gordon Moyer located not one but several copies in 1981—all printed in Rome in 1577. The booklet is a short quarto volume containing 24 pages, with a title page that prohibits the selling or reprinting of the book “under penalty of excommunication.” All of the copies of the Compendium found by Moyer in archives in Florence, Siena, and Rome are attached to other short volumes critiquing Lilius's ideas—with some offering modified plans of their own.

The controversies that continued to swirl around talk of changing the calendar broke down along the familiar lines of science, theology, Church doctrine, and the practical impact of reform on the lives of people, governments, and the economy. By the 1570s, however, the emphasis was different, with the once potent theological concerns of God and time weighing in far less than debates about astronomic theory, Church cosmology, and how to mechanically come up with the best solution for fixing the calendar.

First on the list of contentious issues was the age-old conundrum: what is the true length of the year?

No one had yet come up with a method for determining the true year beyond a doubt—an issue still not entirely resolved today, given the variability of the earth's movements—even if the science of astronomy in the sixteenth century was slowly improving. Indeed, by the late 1570s it had become refined enough that Clavius and the commission could seriously consider whether the calendar should be changed to a system based on the actual motions of the earth (or the sun, if you were a follower of Ptolemy), instead of one that used a mean value of measurements. The latter was the method employed in both the Julian calendar, with its leap-year system, and by the Church's lunisolar calendar for determining Easter. Neither calendar had ever been linked to planetary theory; this had long appalled astronomers, who thought that the only way to create an error-free calendar was to drop the idea of a mean and to go on “real time,” so to speak.

Clavius, for one, initially hoped to link up the reformed calendar as closely as possible to the true astronomic year. “I should think that in order to restore and keep account of astronomy it would be rather important to adopt the true motion,” he wrote to a friend in Padua on 24 October 1580, “but these gentleman [of the commission] do not understand this for several reasons.”

Lilius, however, argued in favor of a mean, insisting that astronomic theory remained too uncertain despite its advancements. He also believed that trying to devise a calendar based on planetary theory would be far too complicated for people who were not astronomers. What was needed, he said, was a mean calculated to be as close as possible to the true motions of the moon and the perceived motions of the sun.

Apparently the commission agreed, concluding that a calendar must be simple enough for all to understand and use, even if it is slightly off the true astronomic year—the challenge being to make the margin of error as small as possible. Even Clavius evidently came around and was persuaded to go with Lilius, since he later defended this choice after the reform was introduced.

That issue settled, the commission's next task was to decide which of the many measurements of the year they believed to be most reliable.

A half century earlier Copernicus had scratched his head and pondered the same question. He had decided that there were no good measurements for the tropical year, which seemed to him to speed up and slow down with no discernible pattern. This led him to rely on the more stable sidereal year in De revolutionibus. Calendar makers did not have this option, however, since their concern was with creating a “year” that matched the seasons, not the position of the earth in space—the two being slightly different, given that pesky phenomenon known as the precession of the equinoxes.

To understand this problem, and how it is possible to have two different kinds of years, first visualize the earth as a simple sphere or ball circling the sun. The sidereal year is the amount of time it takes for the earth to circle the sun relative to a fixed celestial object, such as a star; in other words, to reach the exact point in the orbit where it began.

That's easy. Where it gets tough is when you realize that the earth not only spins around like a top—this is where we get our day and night—but also “tilts,” its plane of rotation on its axis tilting relative to the plane of its orbit around the sun (the ecliptic).

To imagine this, think of the globe that sat in the front of your classroom in grammar school, with a line drawn around the fattest part: the equator. Without any tilt, the equator would always be the closest place on the earth to the sun, and we would have no seasons. But in fact the earth does tilt—so that in June the northern hemisphere is aligned with the sun on its ecliptical plane, when it is summer in the north. Roughly six months later the earth tilts so that the southern hemisphere is aligned relative to the plane, making it summer in the south and winter in the north. In between the tilt brings the equator into perfect alignment with the ecliptic, marking the equinoxes that occur in March and September.

Hipparchus in Alexandria was one of the first astronomers to notice the difference between the two types of years when he took measurements of the year according to the equinoxes on his skaphe, from 141 to 127 b.c. He then must have compared this to the year as measured by the Egyptians, who for centuries had been measuring sidereal year rather than a tropical year. This is because they used as their time “ruler” the annual rise of the Dog Star, Sirius, catching it at the moment it could be seen crossing the peaked point of an obelisk.

Based on Hipparchus's observations, Claudius Ptolemy three centuries later proposed a simple formula for the precession, hypothesizing that the drift of the tropical year against the stars was fixed, and amounted to one degree per century.

By the time of the calendar commission this had been proven wrong beyond a doubt, first by Arab astronomers and then by others, as the Patriarch Ignatius, the commission's expert on the Islamic scientific tradition, pointed out to the pope in a letter in 1579 and in his comments on the Compendium in 1580. The Arabs, however, had also believed in a fixed rate of precession—coming up with different numbers than Ptolemy—while Copernicus and others had concluded the tropical year was indeed variable, though there was significant disagreement about how much.

This scientific debate over how to calculate a true year was further complicated by the ancient cosmologic theory that most educated people, as well as the Church, still considered true in the sixteenth century. This was that the heavens were composed of a series of concentric spheres, with the earth in the center and the moon, sun, planets, and stars orbiting in successive spheres—a precise and unchanging configuration that could not easily accommodate the possibility of a variable year, or of a starfield that seemed to be drifting slightly each year.

One explanation was that another, even higher sphere of stars might exist, or perhaps several more. This possibility created a great deal of muddle and confusion as traditional astronomers and ecclesiastics struggled mightily to make new and still sketchy data fit into their age-old conception of the universe.

The two astronomers on the calendar panel, Clavius and Danti, each had to convince himself that the year was in fact variable at a time when this was still controversial. For Danti the confirmation came when he took his measurement of the equinoxes in Florence in 1574 and 1575 and found that the length of the year differed from Ptolemy's measurements. The proof for Clavius came when he constructed a celestial globe for the Collegio Romano and calculated the rate of precession for the years between Copernicus's observations in 1525 and the year Clavius built his contraption in 1575. This was a change from his earlier blanket acceptance of all things Ptolemaic. Indeed, Clavius kept an open mind about the precession during the commission's debates, once referring the members to an unpublished essay by a certain Ricciardo Cervini, written in 1550, which argued that there was no precession at all, though Cervini failed to convince anyone.

Given the turmoil over the precession—and the larger controversy looming over Copernicus versus Ptolemy—Aloysius Lilius wisely ignored the entire issue in his solution. According to Clavius—our major source, along with the Compendium, for what Lilius was thinking, since Lilius's own manuscript is lost—the old physician opted simply to choose a value for the year based on what was then one of the more popular astronomical tables. These were the Alfonsine Tables, originally written in 1252 and updated over the years. They gave a mean tropical year of 365 days, 5 hours, 49 minutes, and 16 seconds. This was some 30 seconds slower than the true year, but still quite close. The mean value for the year used in the reform itself, which is our calendar year today, is slightly more accurate at 365 days, 5 hours, 49 minutes, and 12 seconds—a year that runs only 26 seconds slower than the true year.

This final mean for the Gregorian year allows us to summarize some key measurements, estimates, and guesses of the length of the tropical year taken over the centuries, most of which the commission had access to during the decade of their deliberation.

Once Lilius had decided on his mean year, he pondered the next crucial problem of reform: how to close the gap between Caesar's year and the “true” year. This meant comparing the Alfonsine year of 365 days, 5 hours, 49 minutes, and 16 seconds to the Julian year of 365 days, 6 hours. The Alfonsine runs short of the Julian by 10 minutes 44 seconds—equal to a day lost every 134 years.

Lilius seems to have tried different ideas to work this cumbersome measurement into a simple formula for dropping an appropriate number of leap days from the calendar. He rejected the long-standing proposal advocated by Bacon and others to drop a day roughly every 134 years. Instead Lilio took as his inspiration the simplicity of the Julian leap-year formula, with its easy-to-remember four-year rule, hoping to come up with a similarly convenient dictum to solve the Julian gap.

As the good doctor tinkered with various solutions shortly before his death, he discovered that the gap amounted to three days gained against the true year every 402 years (134 years x 3). This he rounded off to three days every 400 years, a more accessible number that became the basis for the leap-century rule—which drops three days from the calendar every four hundred years by canceling the leap year in three out of four century years. This formula, based on tables not entirely precise and a base number that is rounded off, ended up being remarkably accurate, running ahead of the seasons by only one day every 3,300 years.

Lilius also proposed two well-known options to recoup the days already lost due to the drift of the Julian calendar, which he thought should be cut by ten days to restore the equinox to the time of Nicaea. He suggested making up the days either by skipping 10 leap years over the course of 40 years, or—more radically—by removing ten days all at once.

The other big problem for Lilius and the calendar commission was repairing the Catholic lunar calendar used to determine Easter. Indeed, for the pope and other Christians the project of cinching up the solar calendar—and restoring the spring equinox to its proper place in the tropical year—was never an end in itself, but part of a religious fix required to restore the Feast of the Passion to its “proper” date.

Easter, of course, is supposed to fall on the first Sunday after the first full moon after the spring equinox—a seemingly straightforward formula, except for the ancient problem that the moon and sun do not match up in their respective years. To compensate for this Christian time reckoners had long used the 19-year Metonic cycle—which theoretically brought the sun and moon into sync because every 19 years of solar time equaled 235 lunar months.

Well, almost. In reality the moon's cycles run roughly an hour and a half behind the 19-year solar cycle, a mismatch that had been alarming computists and astronomers for some time.

Lilius calculated that the lunar-solar gap equals about 1 hour 27.5 minutes, which meant that the moon was drifting against the Church's lunisolar calendar by a whole day every 312.7 years. By the 1570s this error had amounted to more than four complete days.

To halt this lunisolar mayhem, Lilius and the commission scrapped the old Metonic assumption that the phases of the moon, particularly the critical full moon, always matched up in the 19-year cycle with the solar year. Instead Lilius concentrated on trying to work out a new method for keeping the lunar calendar from sliding a day every 312.7 years.

Again, this was no easy task, given that 312.7 is hardly an easy number to divide into a Gregorian calendar of 365 days, 5 hours, 48 minutes, and 20 seconds. But once more Lilius came through, with a simple discovery that eight periods of 312.7 years equal almost 2,500 years—a number that can be divided almost perfectly into seven periods of 300 years plus one period of 400 years. This was Lilius's lunar solution: dropping one day from the lunar calendar every 300 years seven times, and then an additional eighth day after 400 years. For simplicity's sake Lilius and the commission again proposed making the corrections and dropping the days at the end of appropriate centuries.

Lilius's manuscript was initially received with some doubts and resistance, but soon it became the panel's lead proposal as Clavius and company studied it and sent it to various experts for comments. One so-called expert, Giovanni Carlo Ottavio Lauro, at one point seems to have tried to slow up the review process by taking Lilius's manuscript—and holding it for several months. Supposedly this was to make unspecified “corrections,” though Lauro actually used the time to delay action so that he could finish his own proposal. His tactics so infuriated Lilius's supporters on the commission that they appealed directly to the pope, asking that the manuscript be returned—which it was—and the “chimeras” of Lauro be ignored.

Lilius's solution won out at last when the pope issued on January 5, 1578, the Compendium of the doctor's manuscript to universities, heads of state, and important prelates for their comments. The Compendium was sent rather than Lilius's much longer manuscript to save time now that calendar reform fever had struck Rome—or at least the small group of people who cared about such matters in the Eternal City. It also allowed the calendar committee to add its own remarks and amendments, which Clavius later says were minimal. The 20-page Compendium was written by the commission member from Spain, Pedro Chacón, presumably with input from Lilius's brother, Antonio.

After the publication, more comments poured into the commission. It received a vigorous response compared to past reform efforts, such as the one initiated earlier in the sixteenth century by Paul of Middelburg. This time the Compendium attracted dozens of letters, still preserved in the Vatican. Most simply gave their nod of approval; others contained comments, proposals, and counterproposals, some of them fascinating. The court mathematician for the duke of Savoy, Giovanni Battista Benedetti, made a number of suggestions in an April 1578 letter—including a calendar correction of 21 days, which would land the winter solstice on the first of January. Benedetti further proposed changing the length of the months to coincide with the presence of the sun in each of the 12 zodiac signs. Other commentators advocated various dates for the equinox and complained about using a mean for the length of the year. Some went to the trouble of publishing their alternative plans and circulating them, hoping to get a hearing with the commission and the pope.

Royalty also responded. For instance, King Philip II of Spain, in a short letter signed with a flamboyant El Rey, “The king,” approved of the plan, but insisted that the equinox be kept on March 21—out of deference for Nicaea, but also for the practical reason that a great expense would be spared if the date did not have to be changed in mass books and breviaries.

The complaints of astronomers and other scientists would continue over the next several decades as the new calendar took hold. Most agreed with the technical side of the reform, including the Protestants Tycho Brahe and Johannes Kepler. Both found the reform scientifically sound and the best they had seen. Brahe from the beginning dated his letters using the new calendar, and Kepler in a posthumous article offered his arguments in the form of a dialogue between a Protestant chancellor, a Catholic preacher, and an expert mathematician. In the end he concluded that Easter, which was causing so much consternation among opponents and proponents of the calendar, “is a feast and not a planet.” In 1613, Kepler argued in support of the reforms, but failed to persuade the Protestant sovereigns, a resistance that lasted until 1700. Even then Kepler's own Rudolphine Tables were substituted for the Gregorian values when determining Easter. In some years, this caused Germany to celebrate Easter on a different day than Catholics and other Protestants.

A great many astronomers found fault with the new calendar, including several mathematicians in Prague who refused to help the bishop there revise the calendar of feasts because they claimed to find the science unsound. Others disagreed, sometimes vehemently, for religious reasons. These included the Protestant astronomer Michael Maestlin (1550-1631), a professor at Tübingen in southern Germany and one of the teachers of Johannes Kepler. He insisted that the pope had no authority to institute such a reform, and also criticized Gregory for calling the new calendar “perpetual,” because this denied the coming of the last Judgment. This argument was later refuted by another German defender of the calendar, who suggested that by Maestlin's reasoning people should also stop building houses.

Maestlin and others repeated criticisms that the reform should adhere more closely to the true movements of the sun (i.e., the earth) and moon. They complained about the methods used to determine Easter in the lunar reforms, worried over whether the equinox under the reform would always fall on March 21, and challenged the sources for the length of the year. Many astronomers and mathematicians—including several assigned by monarchs and bishops to prepare the reforms for public dissemination—not only offered criticism but published their own solutions, sometimes side by side with the new calendar, to the confusion of anyone trying to understand the pope's reforms.

Other astronomers, led by Christopher Clavius, defended the new calendar. In 1595 he wrote a refutation of Maestlin, directed at the calendar's many critics, called Novi calendarii Romani apologia, adversus Michaelem Maestlinum—“Defense of the new Roman calendar, in reply to Michael Maestlin.” He explained, among other things, why the commission adopted a system of mean rather than absolute motions.

Clavius also defended the use of a mean by pointing out that it was impossible for all Christians to celebrate Easter at exactly the same moment given the spread of Christians across several meridians. In 1606 Clavius answered his critics in the 800-page Explicatio (Explanation). In all, Clavius penned six treatises on the calendar, characteristically well-reasoned and scientifically sound documents that went a long way toward quieting the criticism and smoothing the way for reform in countries that initially hesitated to go along with the new calendar.

One of the most well known scholarly critics of the calendar was a bitter rival of Clavius, the French scholar and Calvinist Joseph Justus Scaliger (1540-1609). He found the reform littered with supposed errors and even stooped to name-calling, referring to Clavius as a “German fat-belly.” But this did not keep Scaliger from later using the Gregorian system for his most famous project: creating a timeline of historical events according to the rules of astronomy. This was a monumental task, one that modernized the old medieval preoccupation with chronology and brought together all of the historical timelines and descriptions of events he could find. Indeed, he and Clavius were not so far apart in their respective tasks, the portly German setting out to align the calendar as closely as possible with the movements of the sun and moon, and Scaliger trying to get the past and future to correspond with a generally accepted standard. The year after the calendar reform Scaliger published Opus de emendatione tempore (1583), establishing chronology as a science.

Scaliger invented his own chronological calendar: the Julian day calendar, an ingeneous if complex system that does not use individual years at all, but a cycle of 7,980 astronomic years that counts a day at a time, with no fractional days, no mean year, and no leap years. He came up with his number by multiplying three chronologic cycles: an 18-year solar cycle, a 19-year lunar cycle, and the 15-year indiction period used by the Romans. All three cycles began together at the same moment at the start of his “Julian cycle,” but would not converge again until the end. This was useful for anyone trying to create a uniform timeline, since the date from any one of the three base cycles could be translated into the two other cycles.

This may sound far too obtuse for the average person. However, Scaliger's calendar lives on today among astronomers, who do not need a calendar based on a mean of the tropical year but one that is astronomically exact. How else could one properly measure the time between, say, two appearances of the comet Hale-Bopp, or two pulses of a quasar? Scaliger began his Julian cycle at noon on January 1, 4713 b.c., which he based on calculations concerning Christ's birthdate.

The other great chronologist of the early modern era was Sir Isaac Newton (1642-1727), whose work in astronomy finally demolished what was left of the Ptolemaic school in planetary theory, and whose work on light, gravity, and mathematics launched modern physics. A man of many interests, Newton later in life became obsessed with properly dating the past. This included an elaborate attempt to correlate biblical events with those recorded in civilizations ranging from Assyria to Rome.

His astronomy and methods of dating long-ago events were brilliant, using recorded eclipses, the rate of drift in the precession of the equinoxes, and careful measurements of stars, equinoxes, comets, and novas. But his attempt to date myths and legends of dubious historic validity and his adamant piety about using the Bible to date events tainted his actual timeline. He insisted, for instance, that the world was created by God in 4004 b.c., as determined by Irish archbishop and student of the Scriptures James Ussher (1581-1656). He attempted to establish the entire timeline based on the voyage of Jason and the Argonauts in search of the Golden Fleece—an effort admirers called “masterly” and the work of “genius,” but others dismissed as “no better than a sagacious Romance.”

On September 14, 1580, the commission signed its official report to Gregory XIII, with Aloysius Lilius's solutions largely intact. They also added a clause to standardize New Year's Day on January 1, the date used by Julius Caesar.

Gregory enthusiastically approved the plan, which was set for implementation in October 1581—October being a month with few holy days. A final delay kept this from happening when the commission waited for a Flemish scholar named Adriaan van Zeelst to deliver promised improvements on Lilius's solution, though all he seems to have accomplished was to cause the postponement of the reform until 1582.

The bull itself was written in the fall of 1581, mostly by Pedro Chacón. On October 20, 1581, he sent a draft from Turino to Cardinal Sirleto in Rome. Chacón then died a few days later, leaving the final version of the bull to be written by commission member Vincenzo di Lauri. Sirleto also dispatched Antonio Lilius, Aloysius's brother, to work with the pope's aides on the final bull at Mondragone, Gregory's favorite villa outside of Rome.

On February 24, 1582, the 80-year-old Pope Gregory XIII sat down at a table that is still preserved at Mondragone and signed the bull that would make this the last year of Julius Caesar's calendar, at least for those staunchly Catholic countries still willing to accept a decree from the much-deflated authority of the Roman See.

On March 1 the text was posted at the doors of Saint Peter's, the chancellery of Rome, and other locations in the city. Printed together with the new perpetual calendar and the basics of the new system, copies were dispatched to every Catholic country through the papal nuncios as everything was prepared for a new calendric era, named for the pope who made the reform possible.

Gregory deserved this honor for the sheer bureaucratic feat of pushing through the reform when so many others had failed. Still, it seems unfair that the mysterious doctor who actually devised the reform didn't get some small measure of immortality for his troubles—perhaps a star named for him. Or, like Clavius, Copernicus, and Tycho Brahe, a crater on the moon.