I took this photograph of the clock in the old town square in Prague a few years ago. The clock dates from 1410 and was made by Mikuláš of Kadaň, clockmaker and Jan Šindel, astronomer and mathematician. It is an amazing work of art and science. In addition to the time, the clock shows the relative positions of the sun, moon, and constellations of the zodiac. It is the oldest working astronomical clock.
It takes about 365.2422 days for the Earth to revolve around the sun, not something that has always been well reflected in the calendar. The calendar of the Roman Republic fell short more than 10 days each year which meant that the seasons drifted against the calendar. The years were periodically reconciled with the addition of a “mensis intercalaris” – a.k.a. Mercedonius from merces for wages - although it was not systematically applied, and even used by the pontifex maximus for political reasons.
For not only in very ancient times was the relation of the lunar to the solar year in great confusion among the Romans, so that the sacrificial feasts and festivals, diverging gradually, at last fell in opposite seasons of the year, but also at this time people generally had no way of computing the actual solar year;
-Plutarch, (late 1st century - early 2nd AD) The Life of Julius Caesar 59.2 Ovid, in the first book of Fasti describes the New Year in Rome. January first starts the new year and the month is named for Janus who can see both ahead and behind. The Kalends was the first day of the month.
KALENDS IAN. 1st: See Janus comes, Germanicus, the herald of a lucky year to thee, and in my song takes precedence. Two-headed Janus, opener of the softly gliding year, thou who alone of the celestials dost behold thy back, O come propitious to the chiefs whose toil ensures peace to the fruitful earth, peace to the sea.
-Ovid (published 8 AD), Fasti Book 1.63 
Ovid goes on to have a conversation with Janus asking questions about various New Year’s traditions – worth a visit to the link above. I am intrigued by the sky sparkling with fragrant fires, and Cilician saffron crackling on kindled hearths. Also interesting to note that January 1 was a workday for the Romans, "assigned the birthday of the year to business, lest from the auspice idleness infects the whole".
Roman Republican Didrachm or Quadrigatus 225-212 BC 6.4g, 22mm
Obv: Laureate head of Janus.
Rev: Jupiter, holding sceptre and thunderbolt, in quadriga driven by Victory; incuse ROMA on raised rectangle.
In 46 BC - the calendar was off by 90 days. Julius Caesar was exposed to more functional calendar systems in Egypt and one of his enduring changes was the Julian calendar, only slightly adjusted as the Gregorian calendar that we use today. From 46 BCE, The Julian calendar added days to the months to get to 365 days in the year and created the leap year every 4 years to stay aligned with the sun.
Caesar laid the problem before the best philosophers and mathematicians, and out of the methods of correction which were already at hand compounded one of his own which was more accurate than any. This the Romans use down to the present time, and are thought to be less in error than other peoples as regards the inequality between the lunar and solar years.
-Plutarch, The Life of Julius Caesar 59.5 The Julian calendar was still in use when Mikuláš of Kadaň and Jan Šindel built their clock in 1410. However, the calendar was running fast by 11 min and 14 seconds a year, which by AD 1582 had become 10 days and needed adjustment by Pope Gregory and Christopher Clavius, a Jesuit astronomer. There was a 3 day discrepancy every 400 years, they adjusted the leap days put in place by Julius Caesar and Sosigenes of Alexandria, to have leap days in years ending in 00 only if they are divisible by 400 (eliminating 3 leap years every 400 years) – he also took 10 days out of October 1582 by jumping from the 4th to the 15th. Pope Gregory’s calendar took a while to be adopted – the British Empire didn’t adopt it until the 18th century.
The calendar that Sosigenes and Caesar created aligned against the backdrop of the stars.
Between the winter solstice and the period when the west winds begin to prevail, the following, according to Caesar, are the more important signs afforded by the constellations: the Dog sets in the morning, upon the third day before the calends of January; a day on the evening of which the Eagle sets to the people of Attica and the adjoining countries. On the day before the nones of January, according to Caesar's computation, the Dolphin rises in the morning, and on the next day, the Lyre, upon the evening of which the Arrow sets to the people of Egypt.
-Pliny the Elder (1st Century AD), Natural History, 18.64 Julius Caesar had to add 90 days as 2 "intercalary months" and an extra 23 days to February to the year 46 BCE – to realign – making the year 46 BC, 445 days long – the longest year.
Caesar therefore began the new arrangement of the calendar by using up all the days which could still have caused confusion, with the result that the last of the years of uncertainty was prolonged to one of four hundred and forty-three days. Then, copying the Egyptians – the only people who fully understood the principles of astronomy – he endeavored to arrange the year to conform to the duration of the course of the sun, which it takes three hundred and sixty-five days and a quarter to complete.
-Macrobius, (5th century AD) Saturnalia XIV Macrobius seems to have made a 2 day math error and 445 is accepted based on other sources including Censorinus – who describes in this way Caesar's correction of the calendar in 46 BC.
The confusion was such that Caius (Julius) Cæsar, sovereign-pontiff, resolved in his third consulate and that of M. Emilius Lepidus to destroy the effects of past abuses by placing between the months of November and December, two intercalary months of 67 days, although he had already intercalated 23 days in the month of February, which gave 445 days to that year; and at the same time to prevent the return of similar errors, he suppressed the intercalary month, and established the civil year after the course of the sun.
-Censorinus, (3rd century AD) De Die Natali XX Given this large shift it is surprising how little comment there is about difficulty with new calendar – perhaps that is because the Roman economy already found the calendar an unreliable and inconvenient tool. I suspect that today we would find a 445 day year a little more disruptive. Plutarch does relate that some were irritated:
"However, even this furnished occasion for blame to those who envied Caesar and disliked his power. At any rate, Cicero the orator, we are told, when some one remarked that Lyra would rise on the morrow, said: "Yes, by decree," implying that men were compelled to accept even this dispensation."
-Plutarch, The Life of Caesar 59.6Here are three Roman Republican denarii from the longest year, 46 BC.
Mn. Cordius Rufus, c. 46 BC, AR Denarius, Rome mint
Obv: RVFVS IIIVIR, Conjoined heads of the Dioscuri right, wearing filleted pilei surmounted by stars
Rev: MN CORDI downwards (mostly off-flan), Venus Verticordia standing left, holding scales and scepter; Cupid on her shoulder
Ref: Crawford 463/1b; Sear, CRI 63a; Cordia 1
Mn. Cordius Rufus, c. 46 BC, AR denarius, Rome mint
Obv: RVFVS Corinthian helmet with crest, owl standing above / MN CORDIVS
Rev: Aegis of Minerva, head of Medusa at center
Ref: Cordia 4; Syd. 978; C463/2
T. Carisius, c. 46 BC, AR Denarius, Rome mint
Obv: Diademed and winged bust of Victory right, S.C. behind, wearing earring and necklace; jeweled hair pulled into knot
Rev: T. CARISI in exergue, Victory driving galloping biga right, holding reins and wreath
Ref: Crawford 464/4; CRI 72; Sydenham 986
I have seen 46 BC referred to as teh "last year of confusion" and to add to the confusion.
Apparently the first implementation of the Julian calendar was misunderstood and added a leap year every three years, which was corrected by Augustus who omitted the leap days between 8 BC and 8 AD to get back on track. Leap days added every four years after that. The month of Sextilius was eventually named for Augustus - it is fitting that the 8th month was named for Octavian, the month whne he first became consul and when Egypt came under the control of Rome.
"Augustus deinde est qui Sextilis antea vocabatur, donec honori Augusti daretur ex senatusconsulto cuius verba subieci: CUM IMPERATOR CAESAR AUGUSTUS MENSE SEXTILI ET PRIMUM CONSULATUM INIERIT. ET TRIUMPHOS TRES IN URBEM INTULERIT. ET EX IANICULO LEGIONES DEDUCTAE SECUTAEQUE SINT EIUS AUSPICIA AC FIDEM. SED ET AEGYPTUS HOC MENSE IN POTESTATEM POPULI ROMANI REDACTA SIT. FINISQUE HOC MENSE BELLIS CIVILIBUS INPOSITUS SIT. ATQUE OB HAS CAUSAS HIC MENSIS HUIC IMPERIO FELICISSIMUS SIT AC FUERIT. PLACERE SENATUI UT HIC MENSIS AUGUSTUS APPELLETUR."
-Macrobius, XII.35-36 Note: first published 9/16/202 and revised 12/31/2023