The Calendar

by David Ewing Duncan

  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 gentlemen [of the commission] do not understand this for several reasons.’

  Lilius, however, argued in favour 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.

  Half a century earlier Copernicus had scratched his head and pondered the same question. He had decided that there were 110 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 tiresome 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 BC. 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 centre 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 t
ook 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 cancelling 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 equalled 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 5 January 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 Chacon, 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 flamboyan
t El Rey, ‘The king’, approved of the plan, but insisted that the equinox be kept on 21 March--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 Tubingen 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.