Church Disagreements Around the Calculation of Easter

My last post, The Calculation of Easter, featured an encyclopedia article showing the commonly accepted Western calculation for the holiday. This has not, however, always been the method employed, and throughout the history of Christianity, different regions and denominations came up with their own method for determining when the holiday should occur. The 11th edition of the Encyclopædia Britannica's entry on "Easter" presents a detailed history of these disagreements (including some amusing anecdotes, like a royal household which was split on when to celebrate the holiday). The entry can be found in volume 8, pages 828 - 829; it starts with a discussion of the meaning of the word itself. This is then followed by the aforementioned history of the controversy surrounding the setting of the date, and the article then finishes with a few notes on church ritual, including a discussion of candle sizes.

EASTER, the annual festival observed throughout Christendom in commemoration of the resurrection of Jesus Christ. The name Easter (Ger. Ostern), like the names of the days of the week, is a survival from the old Teutonic mythology. According to Bede (De Temp. Rat., c. xv.) it is derived from Eostre, or Ostâra, the Anglo-Saxon goddess of spring, to whom the month answering to our April, and called Eostur-monath, was dedicated. This month, Bede says, was the same as the mensis paschalis, "when the old festival was observed with the gladness of a new solemnity."

The name of the festival in other languages (as Fr. pâques; Ital. pasqua; Span. pascua; Dan. paaske; Dutch paasch; Welsh pasg) is derived from the Lat. pascha and the Gr. πάσχα. These in turn come from the Chaldee or Aramaean form פַסְהָא pascha', of the Hebrew name of the Passover festival פֶסַח pesach, from פָּסַח "he passed over," in memory of the great deliverance, when the destroying angel "passed over the houses, of the children of Israel in Egypt when he smote the Egyptians" (Exod. xii. 27).

An erroneous derivation of the word pascha from the Greek πάσχειν, "to suffer," thus connected with the sufferings or passion of the Lord, is given by some of the Fathers of the Church, as Irenaeus, Tertullian and others, who were ignorant of Hebrew. St Augustine (In Joann. Tract. 55) notices this false etymology, shows how similarity of sound had led to it, and gives the correct derivation.

There is no indication of the observance of the Easter festival in the New Testament, or in the writings of the apostolic Fathers. The sanctity of special times was an idea absent from the minds of the first Christians. "The whole of time is a festival unto Christians because of the excellency of the good things which have been given" is the comment of St Chrysostom on I Cor. v. 7, which has been erroneously supposed to refer to an apostolic observance of Easter. The ecclesiastical historian Socrates (Hist. Eccl. v. 22) states, with perfect truth, that neither the Lord nor his apostles enjoined the keeping of this or any other festival. He says: "The apostles had no thought of appointing festival days, but of promoting a life of blamelessness and piety"; and he attributes the observance of Easter by the church to the perpetuation of an old usage, "just as many other customs have been established."

This is doubtless the true statement of the case. The first Christians continued to observe the Jewish festivals, though in a new spirit, as commemorations of events which those festivals had foreshadowed. Thus the Passover, with a new conception added to it of Christ as the true Paschal Lamb and the first fruits from the dead, continued to be observed, and became the Christian Easter.

Although the observance of Easter was at a very early period the practice of the Christian church, a serious difference as to the day for its observance soon arose between the Christians of Jewish and those of Gentile descent, which led to a long and bitter controversy. The point at issue was when the Paschal fast was to be reckoned as ending. With the Jewish Christians, whose leading thought was the death of Christ as the Paschal Lamb, the fast ended at the same time as that of the Jews, on the fourteenth day of the moon at evening, and the Easter festival immediately followed, without regard to the day of the week. The Gentile Christians, on the other hand, unfettered by Jewish traditions, identified the first day of the week with the Resurrection, and kept the preceding Friday as the commemoration of the crucifixion, irrespective of the day of the month. With the one the observance of the day of the month, with the other the observance of the day of the week, was the guiding principle.

Generally speaking, the Western churches kept Easter on the first day of the week, while the Eastern churches followed the Jewish rule, and kept Easter on the fourteenth day. St Polycarp, the disciple of St John the Evangelist and bishop of Smyrna, visited Rome in 159 to confer with Anicetus, the bishop of that see, on the subject; and urged the tradition, which he had received from the apostle, of observing the fourteenth day. Anicetus, however, declined to admit the Jewish custom in the churches under his jurisdiction, but readily communicated with Polycarp and those who followed it. About forty years later (197) the question was discussed in a very different spirit between Victor, bishop of Rome, and Polycrates, metropolitan of proconsular Asia. That province was the only portion of Christendom which still adhered to the Jewish usage, and Victor demanded that all should adopt the usage prevailing at Rome. This Polycrates firmly refused to agree to, and urged many weighty reasons to the contrary, whereupon Victor proceeded to excommunicate Polycrates and the Christians who continued the Eastern usage. He was, however, restrained from actually proceeding to enforce the decree of excommunication, owing to the remonstrance of Irenaeus and the bishops of Gaul. Peace was thus maintained, and the Asiatic churches retained their usage unmolested (Euseb. H.E. v. 23-25). We find the Jewish usage from time to time reasserting itself after this, but it never prevailed to any large extent.

A final settlement of the dispute was one among the other reasons which led Constantine to summon the council of Nicaea in 325. At that time the Syrians and Antiochenes were the solitary champions of the observance of the fourteenth day. The decision of the council was unanimous that Easter was to be kept on Sunday, and on the same Sunday throughout the world, and "that none should hereafter follow the blindness of the Jews" (Socrates, H.E. i. 9). The correct date of the Easter festival was to be calculated at Alexandria, the home of astronomical science, and the bishop of that see was to announce it yearly to the churches under his jurisdiction, and also to the occupant of the Roman see, by whom it was to be communicated to the Western churches. The few who afterwards separated themselves from the unity of the church and continued to keep the fourteenth day, were named Quartodecimani, and the dispute itself is known as the Quarto-deciman controversy. Although measures had thus been taken to secure uniformity of observance, and to put an end to a controversy which had endangered Christian unity, a new difficulty had to be encountered owing to the absence of any authoritative rule by which the paschal moon was to be ascertained. The subject is a very difficult and complex one (see also Calendar.) Briefly, it may be explained here that Easter is the first Sunday after the full moon following the vernal equinox. This, of course, varies in different longitudes, while a further difficulty occurred in the attempt to fix the correct time of Easter by means of cycles of years, when the changes of the sun and moon more or less exactly repeat themselves. At first an eight years' cycle was adopted, but it was found to be faulty, then the Jewish cycle of 84 years was used, and remained in force at Rome till the year 457, when a more accurate calculation of a cycle of 532 years, invented by Victorius of Acquitaine, took its place. Ultimately a cycle of 19 years was accepted, and it is the use of the cycle which makes the Golden Number and Sunday Letter, explained in the preface to the Book of Common Prayer, necessary. Owing to this lack of decision as to the accurate finding of Easter, St Augustine tells us (Epist. 23) that in the year 387 the churches of Gaul kept Easter on the 21st of March, those of Italy on the 18th of April, and those of Egypt on the 25th of April; and it appears from a letter of Leo the Great (Epist, 64, ad Marcian.) that in 455 there was a difference of eight days between the Roman and the Alexandrine Easter. Gregory of Tours relates that in 577 "there was a doubt about Easter. In Gaul we with many other cities kept Easter on the fourteenth calends of May, others, as the Spaniards, on the twelfth calends of April."

The ancient British and Celtic churches followed the cycle of 84 years which they had originally received from Rome, and their stubborn refusal to abandon it caused much bitter controversy in the 8th century between their representatives and St Augustine in Canterbury and the Latin missionaries. These latter unfairly attempted to fix the stigma of the Quartodeciman observance on the British and Celtic churches, and they are even now sometimes ignorantly spoken of as having followed the Asiatic practice as to Easter. This, however, is quite erroneous. The British and Celtic churches always kept Easter according to the Nicene decree on a Sunday. The difference between them and the Roman Church, at this period, was that they still followed the 84 years' cycle in computing Easter, which had been abandoned by Rome for the more accurate cycle of 532 years. This difference of calculation led to Easter being observed on different Sundays, in certain years, in England, by the adherents of the two churches. Thus Bede records that in a certain year (which must have been 645, 647, 648 or 651) Queen Eanfleda, who had received her instruction from a Kentish priest of the Roman obedience, was fasting and keeping Palm Sunday, while her husband, Oswy, king of Northumbria, following the rule of the British church, was celebrating the Easter festival. This diversity of usage was ended, so far as the kingdom of Northumbria was concerned, by the council of Streaneshalch, or Whitby, in 654. To Archbishop Theodore is usually ascribed the credit of ending the difference in the rest of England in 669.

The Gregorian correction of the calendar in 1582 has once more led to different days being observed. So far as Western Christendom is concerned the corrected calendar is now universally accepted, and Easter is kept on the same day, but it was not until 1752 that the Gregorian reformation of the calendar was adopted in Great Britain and Ireland. Jealousy of everything emanating from Rome still keeps the Eastern churches from correcting the calendar according to the Gregorian reformation, and thus their Easter usually falls before, or after, that of the Western churches, and only very rarely, as was the case in 1865, do the two coincide.

Easter, as commemorating the central fact of the Christian religion, has always been regarded as the chief festival of the Christian year, and according to a regulation of Constantine it was to be the first day of the year. This reckoning of the year as the beginning of Easter lingered in France till 1565, when, by an ordinance of Charles IX., the 1st of January finally took its place.

Four different periods may be mentioned as connected with the observance of Easter, viz. (1) the preparatory fast of the forty days of Lent; (2) the fifteen days, beginning with the Sunday before and the Sunday after Easter, during which the ceremonies of Holy Week and the services of the Octave of Easter were observed; this period, called by the French the Quinzaine de Pâques, was specially observed in that country; (3) the Octave of Easter, during which the newly-baptized wore their white garments, which they laid aside on the Sunday after Easter, known as Dominica in albis depositis from this custom; another name for this Sunday was Pascha clausum, or the close of Easter, and from a clipping of the word "close" the English name of "Low" Sunday is believed to be derived; (4) Eastertide proper, or the paschal season beginning at Easter and lasting till Whit Sunday, during the whole of which time the festival character of the Easter season was maintained in the services of the church.

Many ecclesiastical ceremonies, growing up from early times, clustered round the celebration of the Easter festival. One of the most notable of these was the use of the paschal candle. This was a candle of very large dimensions, set in a candlestick big enough to hold it, which was usually placed on the north side, just below the first ascent to the high alter. It was kept alight during each service till Whitsuntide. The Paschal, as it was called at Durham cathedral, was one of the chief sights of that church before the Reformation. It was an elaborate construction of polished brass, and, contrary to the usual custom, seems to have been placed in the centre of the altar-step, long branches stretching out towards the four cardinal points, bearing smaller candles. The central stem of the candlestick was about 38 ft. high, and bore the paschal candle proper, and together they reached a combined height of about 70 ft., the candle being lighted from an opening above. Other paschal candles seem to have been of scarcely less size. At Lincoln, c. 1300, the candle was to weigh three stones of wax; at Salisbury in 1517 it was to be 36 ft. long; and at Whitsuntide what remained was made into smaller candles for the funerals of the poor. In the ancient churches at Rome the paschal candlesticks were fixtures, but elsewhere they were usually movable, and were brought into the church and set up on the Thursday before Easter. At Winchester the paschal candlestick was of silver, and was the gift of Canute. Others of more or less importance are recorded as having been at Canterbury, Bury St Edmunds, Hereford and York. The burning of the paschal candle still forms part of the Easter ceremonial of the Roman Catholic Church (see Lights, Ceremonial).

The liturgical colour for Easter was everywhere white, as the sign of joy, light and purity, and the churches and altars were adorned with the best ornaments that each possessed. Flowers and shrubs no doubt in early times were also used for this purpose, but what evidence there is goes against the medieval use of such decorations, which are so popular at the present day.

It is not the purpose of this article to enter on the wide subject of the popular observances, such as the giving and sending of Pasch or Easter eggs as presents. For such the reader may consult Brand's Popular Antiquities, Hone's Every-Day Book, and Chambers's Book of Days.

Authorities. — Bingham, Antiquities of the Christian Church; Bede, Ecclesiastical History of England; Procter and Frere, A New History of the Book of Common Prayer (London, 1901); Surtees Society, Rites of Durham, ed. J. T. Fowler (1903); De Morgan, Companion to the Almanac (1845); De Moleon, Voyages liturgiques (Paris, 1718).

(T.M.F.)

The Calculation of Easter

I find it very amusing that the entirety of the very lengthy article on "Easter" found in Johnson's Universal Cyclopædia (1887) is devoted to calculating when the holiday actually takes place. It includes a copy of an instrument called "The Churchman's Companion to the Calendar," with instructions on how to use this system of rings to calculate the date for a given year. I'll attempt to calculate Easter for the current year following the article (bottom of this post). This entry is from volume 2, pages 558 - 561:

Eas'ter [Ger. Oster; Gr. πάσχα; Lat. pas'cha; Fr. pâques; etymology doubtful], the principal festival of the Christian year, observed in commemoration of the resurrection of our blessed Lord. The returns of this anniversary were originally regulated, and in imitation of this early usage have always continued to be, by the calendar of Judea, in which the months were conterminous with the revolutions of the moon. A mean lunation being, roughly, twenty-nine and a half days long, twelve lunar months, or a lunar year, fall short of a solar year by about eleven days. The beginning of the Jewish year therefore goes backward on the natural year eleven days annually, requiring an intercalary month to be introduced in the third year, and again in the sixth, ninth, eleventh, fourteenth, and so on. Any anniversary regulated by such a calendar as this is consequently movable in reference to a calendar regulated by the sun. The Resurrection took place just after the Jewish feast of the Passover, which was held on the fourteenth day of Nisan, the first month of the year — that is to say, the fourteenth day of the moon, or not far from the time of the full moon. The Christians of Jerusalem, and after them those of the Asiatic churches generally, were accustomed to hold the feast of Easter on this same day or simultaneously with the Jewish Passover. This usage was unacceptable to the Gentile churches in Italy and the West generally, which preferred to celebrate Easter on the Sunday following the fourteenth day of the moon; and the difference of practice in this particular led to grave dissensions between the East and West, which were at length pacified by the agreement reached in the Council of Nicæa (A. D. 325), to make the Western usage universal. Since this early period Easter has always been observed throughout the world on the Sunday following the fourteenth of that lunation of which this fourteenth day falls on the 21st of March or next later. In order to find the time of Easter for any given year, it would seem that we should calculate the exact time of the new moon in that year for March, and try whether the fourteenth day of that moon (the day of new moon itself being counted the first) would all not earlier than the 21st; in which case the Sunday following this fourteenth day might be presumed to be Easter. But should this fourteenth day fall earlier than the 21st of March, we should conclude that the new moon of April must be taken. The ecclesiastical calendar, however, is only nominally dependent on the moon in the heavens, the true moon and the calendar moon sometimes differing in their age more than two days. The practical reason for this is, that if the astronomical time of new moon is taken, this time will not be the same in the local times of different longitudes; so that a meridian may always be assigned such that the same new moon may fall on different calendar days on different sides of it. And if the calculation is very nicely made, when new moon happens exactly at midnight of Saturday or Sunday in the middle of a large city like London, the east and west halves of the city may have their Easter upon two very different days. The ecclesiastical moon is therefore an ideal or artificial moon; and in determining the beginning and end of each lunation no account is taken of any differences smaller than a day. In order to divest the ecclesiastical calendar as much as possible of complexity, advantage is taken of the fact discovered by Meton, an Athenian astronomer in the fifth century before our own era, that in a period of nineteen solar years the sun and the moon return almost exactly to the same relative positions which they occupied at the beginning of this period, the difference amounting to little more than the space the moon would move over in two hours. The calendar therefore assumes that the moons determining Easter will recur in the same order every nineteen years throughout an entire century, and sometimes throughout two or three centuries. The Easters themselves do not therefore necessarily recur on the same days of the month of March or April in each of these successive series of nineteen years, but would do so if the same days of the week always corresponded to the same days of the month. This, however, is not necessarily the case; and as Easter must be a Sunday, it is necessary, in order to fix definitely the date of Easter in any given year, to know both the place of the year in the series of nineteen (or in the Metonic cycle) and also the day of the week on which the year began, or (what is practically the same thing) the dominical letter for the year. Various methods have been given for finding Easter, but all of them commence, expressly or implicitly, with the determination of these two elements. The rules given by Prof. de Morgan in the "Companion to the British Almanac" for 1845 occupy about a page. The formulæ of Delambre, in the first volume of his "History of Modern Astronomy," and those of Gauss, given in the first volume of the "Theoretical and Practical Astronomy" of the same writer, though concise as mathematical expressions, involve much laborious computation in their practical application. The following rules, however, originally devised by the writer of the present article, are very simple and easy, It is to be observed, first, that the fourteenth day of the Easter moon, being approximately the time of full moon, is called the paschal full moon. The number of the year in the lunar cycle is also called the Golden Number. (See Golden Number.) Then, supposing that we know the golden number and the dominical letter, we find, for the present century, the paschal full moon as follows:

If the golden number is odd: To four times the golden number add ten; and

If the golden number is even: To four times the golden number add twenty-five.

The result, in either case, if greater than twenty and less than fifty, is the date of paschal full moon, considered as a day of March (that is to say, if it happens to be, say, thirty-three, it is the thirty-third of March = the second of April, and so on). If not grater than twenty and less than fifty, add thirty, or subtract thirty, or twice thirty, if necessary to make it so, and the result is once more paschal full moon.

Then, to find Easter: To the constant number eighteen add the numerical value of the dominical letter (i.e. A = 1; B = 2; C = 3, etc.), and the sum, if greater than the value of paschal full moon just found, is the date of Easter; but if not, add seven, or twice seven, or three times seven, and so on till a total is obtained which exceeds that value; and this total is the date of Easter considered as a day of March.

To find the golden number and the dominical letter: In either case first separate the hundreds in the number expressing the given year of our Lord from the years less than a hundred, and treat the parts independently of each other. First, for the dominical letter: If the hundreds be dived by four, the remainder from the division will have one or other of the following values — viz., 0, 1, 2, 3. And the dominical letters belonging to the hundreds which give these remainders respectively will be A, C, E, G = 1, 3, 5, 7. These, for convenience, call centurials. Then for the years take half the largest number divisible by fouri.e. half the number of the latest leap-year — increase this by seven, and subtract the excess of fours (i.e. the remainder left in the previous division of four). To this result add the centurial, and the excess of sevens in the sum will e the value of the dominical letter; it being observed that if there is no excess the dominical letter has the value of seven itself, or is G. Leap-years have two dominical letters — one for January and February; the other, which is less than the former by a unit, for the remainder of the year. This last, which only is used in finding Easter, is that given by the rule.

To find the dominical letter for Old Style the process is the same except as to the centurial. The centurial for old style is found by adding three to the number of hundreds, and suppressing sevens. Thus, if the hundreds be fifteen, we have 15 + 3 = 18. And 18 with seven dropped as often as possible leaves 4, which is the old style centurial. If there is no excess of sevens, the centurial is seven itself.

Secondly, for the golden number: Add a unit to the number expressive of the given year; then divide the years by twenty, and add the quotient to the remainder. Next divide the centuries by four, and add the quotient to five times the remainder. Finally, add the two results, and the sum, if nineteen or less, is the golden number. If it exceeds nineteen, drop nineteen, or, if necessary, twice nineteen, and the number left, being not greater than nineteen, will be the golden number.

Take, as an example, the year 1873. For the dominical letter: 18 ÷ 4 gives 2 remainder, and the centurial is accordingly 5. The number of the largest leap-year in 73 is 72, and the half of this is 36. Then 36 + 7 = 43, and 43 - 1 = 42. Finally, 42 + 5, with the sevens suppressed, is evidently 5 = E, which is the dominical letter of 1873.

For the golden number: 1873 + 1 = 1874. Then, 74 ÷ 20 = 3, with 14 remainder, and 14 + 3 = 17. Also, 18 ÷ 4 = 4, with 2 remainder, and 2 × 5 + 4 = 14. Then, 17 + 14 = 31, and 31 - 19 = 12, the golden number for 1873.

For Easter in 1873: 12 × 4 + 25 = 73. Then 73 - 30 = 43, or paschal full moon is the 43d day of March. To 18 add 5, the value of the dominical letter, and the result, 23, is smaller than the date of the paschal full moon. But 23 + 7 + 7 + 7 = 44, which is greater than that date (43), and Easter is the 44th day of March, or the 13th day of April.

There is one case not provided for in the foregoing. If in finding the paschal full moon we obtain a result which is exactly twenty or exactly fifty, adding or subtracting thirty will not bring it between those limits. In this case paschal full moon must be taken at 49. There is also an irregularity arbitrarily introduced by the mathematicians of Pope Gregory XIII., by whom the calendar was regulated, which is this: Should the rules above laid down give forty-nine directly as the date of paschal full moon, this must be reduced to forty-eight in case the golden number is 12 or upward; not otherwise.

For centuries earlier or later than the present, the rules are the same, except that the numerical terms ten and twenty-five used in finding paschal full moon are liable to variation (but do not always vary) in passing from century to century. The second of these terms always exceeds the first by fifteen. The first may be found for any century up to the forty-second by the following rule: from the number of the centuries take its fourth part and its third part (disregarding fractions in both cases), and increase the result by two. Thus, for the twentieth century we have 20 - 5 - 6 + 2 = 11. Hence, the numerical terms for the next century will be 11 and 26. In old style dates these numerical terms are invariable, and are always two for odd golden numbers and seventeen for even. (See "Proceedings of the Protestant Episcopal Church in the United States" for 1871, Appendix.) The author of this article has also designed an instrumental contrivance for finding Easter by inspection, for any year from the beginning of the Christian era down to the end of hundredth century, in old style or new. This is constructed of card-board, and a facsimile of it, reduced in size, is given below. In the centre is a rotary disk, on the lower border or limb of which are inscribed the numbers below 100 which consist of even twenties, and also the zero. These are called vigesimals. On the upper limb appear all the numbers less than twenty, called residuals, the leap-year numbers being written twice. Around this disk is a fixed ring, bearing the dominical letters above and the centurial numbers below — the new style centurials being on the left, and the old style centurials on the right. The centurial numbers here employed are simply the remainders left in dividing the hundreds by 4 for new style and by 7 for old style. To use this for finding the dominical letter, turn the disk till the proper vigesimal of the given year stands opposite the proper centurial; then opposite the proper residual will be found the dominical letter (or letters) of the year. In case of leap-years there will be found two such letters, of which the lesser or right-hand one is the Easter dominical letter.

Around the fixed ring here described is a rotary ring bearing the numbers from 1 to 19 (the golden numbers), twice repeated, and at the left of these the vigesimals, arranged in regular order. Outside of this rotary ring is a second fixed ring, which bears on the left the numbers 0 to 19, arranged en échelon, so as to allow the natural sequence to be observed. These are called the centurials of the lunar cycle, and are simply what remains after suppressing the nineteens out of the hundreds in the given year of our Lord. Thus, in the year 4173 there are forty-one hundreds, from which, if we suppress 19 × 2 = 38, there will remain 3, which is the centurial for the forty-second century. On the right the same fixed ring bears the residuals, or excesses of twenties in the years of the incomplete century, in which it is not necessary to duplicate the leap-year numbers. When the movable ring is turned so that the proper vigesimal stands opposite the proper centurial, the golden number for the year will be found opposite the proper residual.

On this same fixed ring, outside of the numbers already mentioned, is an annular row of figures distributed without any obvious order, which embraces all the possible golden numbers from 1 to 19, each entered twice. Of these, all up to 11 are printed in full face; all from 12 to 19 inclusive in outline. Their use will presently appear.

Around this second fixed ring is a second rotary ring, on which are inscribed all the days of March and April on which paschal full moon or Easter can fall; together with the calendar letters belonging to them severally. From the 17th to the 25th of April the day numbers and letters are entered twice, the second or inner series being advanced beyond the outer by a single place. This same rotary ring also bears an arrow, which is designed to be used as an index. Finally, surrounding this rotary ring there is another fixed ring, in the several divisions of which are written the centuries from 15 up to 100, none below 15 being necessary, as the new style, or Gregorian reckoning, began in 1582. The use of the last-mentioned rotary ring is to find, first, the date of paschal full moon, and subsequently, by consequence, the date of Easter. In employing it, the ring is turned until the arrow points to the golden number for the year, when the date of paschal full moon will be found opposite the proper centurial number in the outer fixed ring. Then, looking along the series of letters to the right of the date of the paschal moon, Easter will be found immediately over the next succeeding dominical letter for the year. If the time of Easter for years before 1582 is sought, the paschal moon will be found, not opposite the century, but opposite the words "Old Style" written in one of the compartments into which the outer fixed ring is divided, and Easter will be opposite the proper dominical letter next following, as before.

As it is arbitrarily ruled that the paschal full moon shall never fall later than April 18th, and as a consistent method of computation or of instrumental determination would make it sometimes fall on the 19th, the double series of days and letters is introduced at the end of April in the outer revolving ring to meet this case. When, therefore, in the use of the instrument, paschal full moon would seem to fall on the 19th of April by the series of outer, full-faced figures, we must pass to the inner series of figures printed in outline, which will give paschal full moon on the 18th. Also, if the outer series of full-faced figures should at any time directly give paschal full moon on the 18th, we must pass to the inner series again, and make paschal full moon the 17th, provided the arrow stands opposite a golden number printed in outline, but not otherwise. When the light-faced numbers are thus used instead of the full-faced for the paschal moon, the light-faced letters must of course also be used in finding Easter. The table in figure on the preceding page is adjusted for the Easter of 1873. In 73 the vigesimal is 60 and the residual is 13. For 18 (centuries) the centurial is 2, and the Easter sought belongs to new style. It is seen that, 60 being opposite 2, the residual, 13, is opposite E; which is the dominical letter of 1873. In the first rotary ring the same vigesimal, 60, is opposite the golden number centurial, which is 18; and under the residual 13 we have 12, the golden number for 1873. Bringing, finally, the arrow of the outer rotary ring opposite to the golden number, 12, we find under 18 in the outer row of centuries, the 12th of April, which is the date of paschal full moon for 1873; and opposite E, the dominical letter of the year next following the date of the paschal full moon thus found, we have April 13th for the date of Easter.

This little instrument is useful in the solution of many questions connected with chronology and the calendar, besides that for which it was expressly constructed. Any person possessed of a little mechanical skill can construct a working instrument of this kind for himself, by copying this diagram on a scale about one-fourth larger.

The principal festivals and fasts of the Church dependent for the time of their celebration upon Easter are Septuagesima Sunday, nine weeks before Easter; Ash Wednesday, which is the Wednesday of the seventh week before Easter; Good Friday, which is the Friday next before Easter; Ascension Day, which is the Thursday of the sixth week after Easter; Whitsun Day, the seventh Sunday after Easter; and Trinity Sunday, the eighth Sunday after Easter.

F. A. P. Barnard, Columbia College.

Now an attempt at this "easy" (certainly longer than the one-pager he was complaining about) calculation for the year this post was written, 2020:

  1. The article author refers to his year (1873) as being the 18th century. So that would make our year (2020) the 20th century as he calls it. He already calculated the "numerical terms" for the 20th century to be 11 and 26.
  2. The dominical: The hundreds number, 20, is divisible by 4, which gives 0 remainder, so we start with A (1) as our centurial. The years number, 20, is the largest number in itself divisible by 4, and half of that is 10. We increase by seven: 10 + 7 = 17. Adding the centurial and reducing by sevens: 17 + 1 = 18 - 7 = 11 - 7 = 4 (D).
  3. The golden number: Add one to the year: 2020 + 1 = 2021. Taking the last two digits for the years and dividing by four: 21 + 4 = 5 with 1 remainder. Add the remainder to the result: 5 + 1 = 6. Going back to the century and dividing that by four: 20 + 4 = 5. Adding the years and century results together: 5 + 6 = 11.
  4. Our golden number is odd, so we multiply our golden number by four and add the second of the "numerical terms" from step 1: 11 × 4 + 26 = 70. This is greater than 50, so we subtract 30 until we get a number between 20 and 50: 70 - 30 = 40. This is the date of the paschal full moon (March 40 = April 9th).
  5. We then add our dominical number to the constant 18: 18 + 4 = 22. 22 is less than our paschal full moon value of 40, so we keep adding 7 until it exceeds that value: 22 + 7 = 29 + 7 = 36 + 7 = 43. 43 is greater than 40, so Easter is "March 43rd", or April 12th — which is indeed the correct date for 2020.