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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..6833f05 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,3 @@ +* text=auto +*.txt text +*.md text diff --git a/36197-8.txt b/36197-8.txt new file mode 100644 index 0000000..dc3caf4 --- /dev/null +++ b/36197-8.txt @@ -0,0 +1,5090 @@ +The Project Gutenberg EBook of Our Calendar, by George Nichols Packer + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Our Calendar + +Author: George Nichols Packer + +Release Date: May 23, 2011 [EBook #36197] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK OUR CALENDAR *** + + + + +Produced by Bryan Ness and the Online Distributed +Proofreading Team at http://www.pgdp.net (This file was +produced from images generously made available by The +Internet Archive.) + + + + + + + + + + OUR CALENDAR. + + + The Julian Calendar and Its Errors. + + HOW CORRECTED BY THE GREGORIAN. + + + Rules For Finding the Dominical Letter, + + AND THE DAY OF THE WEEK OF ANY EVENT FROM THE + DAYS OF JULIUS CÆSAR 46 B. C. TO THE YEAR OF + OUR LORD FOUR THOUSAND--A NEW AND EASY + METHOD OF FIXING THE DATE OF EASTER. + + + HEBREW CALENDAR; + + SHOWING THE CORRESPONDENCE IN THE DATE OF + EVENTS RECORDED IN THE BIBLE WITH OUR + PRESENT GREGORIAN CALENDAR. + + + ILLUSTRATED BY VALUABLE TABLES AND CHARTS. + + + BY REV. GEORGE NICHOLS PACKER, + CORNING, N. Y. + + + + + Entered according to Act of Congress, in 1890, 1892 and 1893, + BY REV. GEORGE NICHOLS PACKER, + In the Office of the Librarian of Congress, Washington, D. C. + ALL RIGHTS RESERVED. + + + WILLIAMSPORT, PA.: + FRED R. MILLER BLANK BOOK CO. + 1893. + + + + +TO HON. HENRY W. WILLIAMS, JUSTICE OF THE SUPREME COURT OF PENNSYLVANIA +WHOM I HAVE FOUND A TRUE FRIEND IN POVERTY AND IN SICKNESS, AND FROM WHOM +I HAVE RECEIVED WORDS OF ENCOURAGEMENT AND COMFORT DURING MANY YEARS OF +ADVERSITY, AND AT WHOSE SUGGESTION THIS LITTLE VOLUME HAS BEEN WRITTEN, +AND BY WHOSE ASSISTANCE IT IS NOW PUBLISHED, THIS HUMBLE VOLUME IS +DEDICATED AS A TRIBUTE OF RESPECT BY THE AUTHOR. + + + + +PREFACE. + + +Many years ago, while engaged in teaching, the writer of this little +volume was in the habit of bringing to the attention of his pupils a few +simple rules for finding the dominical letter and the day of the week of +any given event within the past and the present centuries; further than +this he gave the subject no special attention. + +A few years ago, having occasion to learn the day of the week of certain +events that were transpiring at regular intervals on the same day of the +same month, but in different years, he was led to investigate the subject +more thoroughly, so that he is now able to give rules for finding the +dominical letter and the day of the week of any event that has transpired +or will transpire, from the commencement of the Christian era to the year +of our Lord 4,000, and to explain the principles on which these rules +rest. When the investigations were entered upon he had no thought of +writing a book; but having been laid aside from active labor by ill +health, he found relief from the despondency in which sickness and poverty +plunged him by pursuing the study of the calendar, its history, and the +method of disposing of the fraction of a day found in the time required +for the revolution of the Earth in its orbit about the Sun. + +He became so much interested in the study of this subject that he +frequently spoke of it to friends and acquaintances whom he met. On one +occasion, while speaking to Hon. H. W. Williams about some of the curious +results of the process by which the coincidence of the solar and the civil +year is preserved, it was suggested to him that he should put the story of +the calendar, its correction by Gregory, and the theory and results of +intercalation, in writing. It was urged that this would give increased +interest to the study, help the writer to forget his pains, and probably +enable him to realize a little money from the sale of his work to meet +pressing wants. Acting upon this suggestion, an effort has been made to +put into this little volume some of the most interesting facts relating to +the origin, condition, and practical operation of the calendar now in use; +together with rules for finding the day of the week on which any given day +of any month has fallen or will fall during four thousand years from the +beginning of our era. + +The writer does not claim absolute originality for all that appears in the +following pages; on the contrary, he has made free use of all the +materials that came within his reach relating to the history of the +calendar and the work of its correction by Gregory. These materials, +together with his own calculations, he has arranged in accordance with a +plan of his own devising, so that the outline and the execution of the +work may be truly said to be original. Of its value the world must judge. +It has been prepared in weakness of body and in suffering, which have been +to some extent relieved by the mental occupation thus afforded, but which +may have nevertheless left their impress on the work. But let it be read +before pronouncing judgment upon it. Cicero could infer the littleness of +the Hebrew God from the smallness of the territory he had given his +people. To whom Kitto replies: "The interest and importance of a country +arise, not from its territorial extent, but from the men who form its +living soul; from its institutions bearing the impress of mind and spirit, +and from the events which grow out of the character and condition of its +inhabitants." So the value of a book does not consist in the size and +number of its pages, but from the knowledge that may be gained by its +perusal. + +THE AUTHOR. + + + + +PREFACE + +TO THE REVISED EDITION. + + +Soon after the publication of the former edition of this work, it was +suggested that a chapter be added on Easter; rules for fixing its date, +and also church festivals that depended upon the date of Easter. It was +suggested that this would add very much to the value of the work, if so +presented as to be brought within the comprehension of ordinary minds. +Knowing that the determination of Easter was an affair of considerable +nicety and complication, and had had the attention of our best minds, and +they had failed so to present it, that even among scholarly men, probably +not one in a hundred was able to determine its date without referring to +tables prepared for that purpose the author of this work felt as though he +was hardly competent for the task. Nevertheless it was undertaken, and the +work has been revised and enlarged by a Chapter on the Peculiarities of +the Roman Calendar, another on fixing the date of events prior to the +Christian era, and a third part on Easter, church festivals, and the +Hebrew Calendar. In the opinion of the author, the rules for determining +the date of Easter are so simplified by his new method that any person of +ordinary intelligence may understand them. How well he has succeeded the +public will decide. + +G. N. P. + + + + +CONTENTS. + + + PART FIRST. + + DEFINITIONS--HISTORY. + + _Pages._ + + CHAPTER I.--Definitions 11 + + CHAPTER II.--History of the divisions of time, and the old + Roman Calendar 12 + + CHAPTER III--History of the reformation of the Calendar by + Julius Cæsar 18 + + CHAPTER IV.--History of the reformation of the Julian Calendar + by Pope Gregory XIII 20 + + CHAPTER V.--Peculiarities of the Roman Calendar 26 + + + PART SECOND. + + MATHEMATICAL. + + CHAPTER I.--Errors of the Julian Calendar 36 + + CHAPTER II.--Errors of the Gregorian Calendar 38 + + CHAPTER III.--Dominical Letter 39 + + CHAPTER IV.--Rule for finding the Dominical Letter 44 + + CHAPTER V.--Rule for finding the day of the week of any given + date, for both Old and New Styles 50 + + CHAPTER VI.--A simple method of finding the day of the week of + events, which occur quadrennially; the inaugural of + the Presidents, the day of the week on which they + have occurred and on which they will occur for the + next one hundred years 61 + + Some peculiarities concerning events which fall on + the 29th of February 64 + + CHAPTER VII.--Rule for finding the day of the week of events + prior to the Christian era 68 + + + PART THIRD. + + CYCLES--JULIAN PERIOD--EASTER. + + CHAPTER I.--The Solar Cycle 73 + + CHAPTER II.--The Lunar Cycle 75 + + CHAPTER III.--The Lunar Cycle and Golden Number 77 + + CHAPTER IV.--Cycle of Indiction, and the Julian Period 79 + + CHAPTER V.--Easter 82 + + CHAPTER VI.--A new and easy method of fixing the date of Easter 88 + + CHAPTER VII.--Church feasts and fasts whose date depend on the + date of Easter 108 + + CHAPTER VIII.--Hebrew Calendar 124 + + APPENDIX 134 + + ERRATA 149 + + + + +OUR CALENDAR. + +PART FIRST. + +DEFINITIONS. HISTORY. + + + + +CHAPTER I. + +DEFINITIONS. + + +_a_--A Calendar is a method of distributing time into certain periods +adapted to the purposes of civil life, as hours, days, weeks, months, +years, etc. + +_b_--The only natural divisions of time are the solar day, the solar year, +and the lunar month. + +_c_--An hour is one of the subdivisions of the day into twenty-four equal +parts. + +_d_--The true solar day is the interval of time which elapses between two +consecutive returns of the same terrestrial meridian to the Sun, the mean +length of which is twenty-four hours. + +_e_--The week is a period of seven days, having no reference whatever to +the celestial motions, a circumstance to which it owes its unalterable +uniformity. + +_f_--The lunar month is the time which elapses between two consecutive new +or full moons, and was used in the Roman calendar until the time of Julius +Cæsar, and consists of 29d, 12h, 44m, 2.87s. + +_g_--The calendar month is usually employed to denote an arbitrary number +of days approaching a twelfth part of a year, and has now its place in the +calendar of nearly all nations. + +_h_--The year is either astronomical or civil. The solar astronomical year +is the period of time in which the Earth performs a revolution in its +orbit about the sun or passes from any point of the ecliptic to the same +point again, and consists of 365 days, 5 hours, 48 minutes and 49.62 +seconds of mean solar time. Appendix A. + +_i_--The civil year is that which is employed in chronology, and varies +among different nations, both in respect of the seasons at which it +commences and of its subdivisions. + + + + +CHAPTER II. + +HISTORY OF THE DIVISIONS OF TIME AND THE OLD ROMAN CALENDAR. + + +_Day_--The subdivision of the day into twenty-four parts or hours has +prevailed since the remotest ages, though different nations have not +agreed either with respect to the epoch of its commencement or the manner +of distributing the hours. Europeans in general, like the ancient +Egyptians, place the commencement of the civil day at midnight; and reckon +twelve morning hours from midnight to midday and twelve evening hours from +midday to midnight. Astronomers, after the example of Ptolemy, regarded +the day as commencing with the Sun's culmination, or noon, and find it +most convenient for the purpose of computation to reckon through the whole +twenty-four hours. Hipparchus reckoned the twenty-four hours from midnight +to midnight. + +The Roman day, from sunrise to sunset, and the night, from sunset to +sunrise, were each divided at all seasons of the year into twelve hours, +the hour being uniformly one-twelfth of the day or the night, of course, +varied in length with the length of the day or night at different seasons +of the year. + +_Week_--Although the week did not enter into the calendar of the Greeks, +and was not introduced at Rome till after the reign of Theodosius, A. D. +292, it has been employed from time immemorial in almost all Eastern +countries; and as it forms neither an aliquot part of a year nor of the +lunar months, those who reject the Mosaic recital will be at a loss to +assign to it an origin having much semblance of probability. In the +Egyptian astronomy the order of the planets, beginning with the most +remote, is Saturn, Jupiter, Mars, the Sun, Venus, Mercury, the Moon. Now, +the day being divided into twenty-four hours, each hour was consecrated to +a particular planet, namely: One to Saturn, the following to Jupiter, +third to Mars, and so on according to the above order; and the day +received the name of the planet which presided over its first hour. If, +then, the first hour of a day was consecrated to Saturn, that planet would +also have the 8th, the 5th and the 22d hours; the 23d would fall to +Jupiter, the 24th to Mars, and the 25th or the first hour of the second +day would belong to the Sun. In like manner the first hour of the third +day would fall to the Moon, the first hour of the fourth to Mars, of the +fifth to Mercury, of the sixth to Jupiter and the seventh to Venus. The +cycle being completed, the first hour of the eighth day would again return +to Saturn and all the others succeed in the same order. See table on the +17th page. + +It will be seen by the table, and it is also recorded by Dio Cassius, of +the second Century, that the Egyptian week commenced with Saturday. On +their flight from Egypt the Jews, from hatred to their ancient oppressors, +made Saturday the last day of the week. It is stated that the ancient +Saxons borrowed the week from some Eastern nation, and substituted the +names of their own divinities for those of the gods of Greece. The names +of the days are here given in Latin, Saxon and English. It will be seen +that the English names of the days are derived from the Saxon. + + LATIN. SAXON. ENGLISH. + _Dies Solis._ Sun's Day. SUNDAY. + _Dies Lunae._ Moon's Day. MONDAY. + _Dies Martis._ Tiw's Day. TUESDAY. + _Dies Mercurii._ Woden's Day. WEDNESDAY. + _Dies Jovis._ Thor's Day. THURSDAY. + _Dies Veneris._ Friga's Day. FRIDAY. + _Dies Saturni._ Seterne's Day. SATURDAY. + +_Month_--The ancient Roman year contained but ten months and is indicated +by the names of the last four. September from Septem, seven; October from +Octo, eight; November from Novem, nine, and December from Decem, ten; July +and August were also denominated Quintilis and Sextilis, from Quintus +five, and Sex, six. + +Quintilis was changed to July in honor of Julius Cæsar, who was born on +the 12th of that month 98 B. C. Sextilis was changed to August by the +Roman Senate to flatter Augustus on his victories about 8 B. C. In the +reign of Numa Pompilius, about 700 B. C., two months were added to the +year, January at the beginning, and February at the end of the year. This +arrangement continued till 450 B. C., when the Decemvirs (ten magistrates) +changed the order, placing February after January, making March the third +instead of the first month of the Roman year. + +_Year_--If the civil year correspond with the solar the seasons of the +year will always come at the same period. But if the civil year is +supposed to be too long (as is the case in the Julian year) the seasons +will go back proportionately; but if too short they will advance in the +same proportion. Now, as the ancient Egyptians reckoned thirty days to the +month invariably, and to complete the year, added five days, called +supplementary days, their year consisted of 365 days. + +They made use of no intercalation, and by losing one-fourth of a day every +year, the commencement of the year went back one day in every period of +four years, and consequently made a revolution of the seasons in 1460 +years. Hence the Egyptian year was called a vague or erratic year because +the first day of the year in the course of 1460 years wandered, as it +were, over all the seasons. Therefore 1460 Julian years of 365-1/4 days +each are equal to 1461 Egyptian years of 365 days each. + +The ancient Roman year consisted of twelve lunar months, of twenty-nine +and thirty days alternately, which equals 354 days; but a day was added +to make the number odd, which was considered more fortunate, so that the +year consisted of 355 days. + +This differed from the solar year by ten whole days and a fraction; but to +restore the coincidence, Numa ordered an additional or intercalary month +to be inserted every second year between the 23d and 24th of February, +consisting of twenty-two and twenty-three days alternately, so that four +years contained 1465 days, and the mean length of the year was +consequently 366-1/4 days, so that the year was then too long by one day. + +As the error amounted to twenty-four days in as many years, it was ordered +that every third period of eight years, instead of containing four +intercalary months, two of twenty-two and two of twenty-three days, +amounting in all to ninety days, should contain only three of those months +of twenty-two days each, amounting to sixty-six days, thereby suppressing +twenty-four days in as many years, reducing the mean length of the year to +365-1/4 days. + +Had the intercalations been regularly made the concurrence of the solar +and the civil year would have been preserved very nearly. But its +regulation was left to the pontiffs, who, to prolong the term of a +magistracy or hasten an annual election, would give to the intercalary +month a greater or less number of days, and consequently the calendar was +thrown into confusion, so that in the time of Julius Cæsar there was a +discrepancy between the solar and the civil year of about three months; +the winter months being carried back into autumn and the autumnal into +summer. + +A table of the order and the names of the planets in the Egyptian +astronomy illustrating the origin of the names of the days of the week: + + ---------+---------+--------+-------+-------+----------+------- + Saturn, |Jupiter, |Mars, |Sun, |Venus, |Mercury, |Moon, + Saturday.|Thursday.|Tuesday.|Sunday.|Friday.|Wednesday.|Monday. + ---------+---------+--------+-------+-------+----------+------- + 1 | 2 | 3 | 4 | 5 | 6 | 7 + 8 | 9 | 10 | 11 | 12 | 13 | 14 + 15 | 16 | 17 | 18 | 19 | 20 | 21 + 22 | 23 | 24 | 1 | 2 | 3 | 4 + 5 | 6 | 7 | 8 | 9 | 10 | 11 + 12 | 13 | 14 | 15 | 16 | 17 | 18 + 19 | 20 | 21 | 22 | 23 | 24 | 1 + 2 | 3 | 4 | 5 | 6 | 7 | 8 + 9 | 10 | 11 | 12 | 13 | 14 | 15 + 16 | 17 | 18 | 19 | 20 | 21 | 22 + 23 | 24 | 1 | 2 | 3 | 4 | 5 + 6 | 7 | 8 | 9 | 10 | 11 | 12 + 13 | 14 | 15 | 16 | 17 | 18 | 19 + 20 | 21 | 22 | 23 | 24 | 1 | 2 + 3 | 4 | 5 | 6 | 7 | 8 | 9 + 10 | 11 | 12 | 13 | 14 | 15 | 16 + 17 | 18 | 19 | 20 | 21 | 22 | 23 + 24 | 1 | 2 | 3 | 4 | 5 | 6 + 7 | 8 | 9 | 10 | 11 | 12 | 13 + 14 | 15 | 16 | 17 | 18 | 19 | 20 + 21 | 22 | 23 | 24 | 1 | 2 | 3 + 4 | 5 | 6 | 7 | 8 | 9 | 10 + 11 | 12 | 13 | 14 | 15 | 16 | 17 + 18 | 19 | 20 | 21 | 22 | 23 | 24 + ---------+---------+--------+-------+-------+----------+------- + + + + +CHAPTER III. + +HISTORY OF THE REFORMATION OF THE CALENDAR BY JULIUS CÆSAR. + + +In order to put an end to the disorders arising from the negligence or +ignorance of the pontiffs, Julius Cæsar, 46 B. C., abolished the use of +the lunar year and the intercalary month, and regulated the civil year +entirely by the Sun. With the advice and assistance of the astronomers, +especially Sosigenes of Alexandria, he fixed the mean length of the year +at 365-1/4 days, and decided that there should be three consecutive years +of 365 days, and a fourth of 366. + +In order to restore the vernal equinox to the 24th of March, the place it +occupied in the time of Numa, two months, together consisting of 67 days, +were inserted between the last day of November and the first day of +December of that year. An intercalary month of 23 days had already been +added to February of the same year according to the old method, so that +the first Julian year commenced with the first day of January, 45 years +before Christ, and 709 from the foundation of Rome, making the year A. U. +C. 708 to consist of the prodigious number of 445 days, (i. e. 355 + 23 + +67 = 445). Hence it was called by some the year of confusion; Macrobius +said it should be named the last year of confusion. + +There was also adopted at the same time a more commodious arrangement in +the distribution of the days throughout the several months. It was decided +to give to January, March, May, July, September and November each +thirty-one days; and the other months thirty, excepting February, which +in common years should have but twenty-nine days, but every fourth year +thirty; so that the average length of the Julian year was 365-1/4 days. + +Augustus Cæsar interrupted this order by taking one day from February, +reducing it to twenty-eight and giving it to August, that the month +bearing his name should have as many days as July, which was named in +honor of his great-uncle, Julius. In order that three months of thirty-one +days might not come together, September and November were reduced to +thirty days, and thirty-one given to October and December. + +In the Julian calendar a day was added to February every fourth year, it +being the shortest month, which was called the additional or intercalary +day, and was inserted in the calendar between the 23d and 24th of that +month. In the ancient Roman calendar the first day of every month was +invariably called the calends. The 24th of February then was the 6th of +the calends of March--Sexto calendas; the preceding, which was the +additional or intercalary day, was called bis-sexto calendas (from _bis_, +twice, and _sextus_, six), twice the sixth day. Hence the term bis-sextile +as applied to every fourth year, commonly called leap-year. Appendix B. + + + + +CHAPTER IV. + +HISTORY OF THE REFORMATION OF THE JULIAN CALENDAR BY POPE GREGORY XIII. + + +True enough, the year in which Julius Cæsar reformed the ancient Roman +calendar was the last year of confusion, and the method adopted by him a +commodious one, and answered a very good purpose for a short time; but as +the years rolled on and century after century had passed away, astronomers +began to discover the discrepancy between the solar and the civil year; +that the vernal equinox did not occupy the place it occupied in the time +of Cæsar, namely, the 24th of March, but was gradually retrograding +towards the beginning of the year, so that at the meeting of the Council +of Nice in 325 it fell on the 21st. Appendix C. + +The venerable Bede, in the 8th century, observed that these phenomena took +place three or four days earlier than at the meeting of that council. +Roger Bacon, in the 13th century, wrote a treatise on this subject and +sent it to the Pope, setting forth the errors of the Julian calendar. The +discrepancy at that time amounted to seven or eight days. + +Thus the errors of the calendar continued to increase until 1582, when the +vernal equinox fell on the 11th instead of the 21st of March. Gregory, +perceiving that the measure (of reforming the calendar) was likely to +confer great eclat on his pontificate, undertook the long desired +reformation; and having found the governments of the principal Catholic +states ready to adopt his views, he issued a brief in the month of March, +1582, in which he abolished the use of the ancient calendar, and +substituted that which has since been received in almost all Christian +countries under the name of the Gregorian calendar or New Style. + +The edict of the Pope took effect in October of that year, causing the 5th +to be called the 15th of that month, thus suppressing ten days and making +the year 1582 to consist of only 355 days. So we see that the ten days +that had been gained by incorrect computation during the past 1257 years, +were deducted from 1582, restoring the concurrence of the solar and the +civil year, and consequently the vernal equinox to the place it occupied +in 325, namely, the 21st of March. + +The Pope was promptly obeyed in Spain, Portugal, and Italy. The change +took place the same year in France, by calling the 10th the 20th of +December. Many other Catholic countries made the change the same year, and +the Catholic states of Germany the year following; but most of the +Protestant countries adhered to the Old Style until after the year 1700. +Among the last was Great Britain; she, after having suffered a great deal +of inconvenience for nearly two hundred years by using a different date +from the most of Europe, at length, by an act of Parliament, fixed on +September, 1752, as the time for making the much desired change, which was +done by calling the 3d of that month the 14th (as the error now amounted +to eleven days), adopting at the same time the Gregorian rule of +intercalation. + +Russia is the only Christian country that still adheres to the Old Style, +and by using a different date from the rest of Europe is now twelve days +behind the true time. The discrepancy between solar and civil time does +not effect the day, for, as has already been shown, the mean length of the +day is twenty-four hours, and is marked by one revolution of the earth +upon its axis. + +Nor does it effect the week, for the week is uniformly seven of those +days. But it effects the year, the month and the day of the month. + +Russia, by adhering to the Old Style, has reckoned as many days and as +many weeks, and events have transpired on the same day of the week as they +have with us who have adopted the New Style; as Christian nations we are +observing the same day as the Sabbath. + +When it was Tuesday, the 20th day of December, 1888, in Russia, it was +Tuesday, the 1st day of January, 1889, in those countries which have +adopted the New Style. Columbus sailed from Palos, in Spain, on Friday, +August 3d, 1492, Old Style, which was Friday, August 12th, New Style. +Washington was born on Friday, February 11th, 1732, Old Style, which was +Friday, February 22d, New Style. + +Now, the difference in styles during the 15th century is nine days; during +the 16th and 17th centuries, ten days; the 18th century, eleven days, and +the 19th, twelve days. In regard to the sailing of Columbus, the change is +made by suppressing nine days, calling the 3d the 12th of August. In +regard to the birth of Washington, the change is effected by suppressing +eleven days, calling the 11th of February the 22d. As regards Russia, she +could have made the change last year by calling the 20th of December, +1888, the 1st day of January, 1889, thereby suppressing twelve days, and +making the year 1888 to consist of only 354 days, and the month of +December twenty days. The methods of computation, both Old and New Styles, +will be explained in another chapter. + +To persons unacquainted with astronomy, the difference between Old and New +Styles would probably be better understood by the diagram on the 25th +page. The figures represent the ecliptic, which is the apparent path of +the Sun, or the real path of the Earth as seen from the Sun, in her annual +or yearly revolution around the Sun in the order of the months, as marked +on the ecliptic. + +Attention is called to four points on the ecliptic, namely, the vernal +equinox, the autumnal equinox, the winter solstice, and the summer +solstice. These occur, in the order given above, on the 21st of March, the +21st of September, the 21st of December and the 21st of June. It has +already been stated that if the civil year correspond with the solar, the +seasons of the year will always come at the same period. Julius Cæsar +found the ancient Roman year in advance of the solar; Gregory found the +Julian behind the solar year; so one reforms the calendar by +intercalation, the other by suppression. Appendix D. + +Cæsar restored the coincidence of the solar and the civil year, but failed +to retain it by allowing what probably appeared to him at the time a +trifling error in his calendar. The error, which was 11 minutes and 10.38 +seconds every year, was hardly perceptable for a short period, but still +amounted to three days every 400 years. Hence the necessity in 1582 of +reforming the reformed calendar of Julius Cæsar to restore the +coincidence. Appendix E. + +From the meeting of the Council of Nice, in 325, to 1582, a period of 1257 +years, there was found to be an error in the Julian calendar of ten days. +Now, in 1257 years the Earth performs 1257 annual and 459,109 daily +revolutions, after which the vernal equinox was found to occur on the 21st +of March, true or solar time; thus concurring with the vernal equinox of +325. But the erroneous Julian calendar would make the Earth perform +459,119 daily revolutions to complete the 1257 years, a discrepancy of ten +days, making the vernal equinox to fall on the 11th instead of the 21st. +It will be seen by the diagram that the ten days were deducted from +October, in 1582, making it a short month, consisting of only twenty-one +days. + +The discrepancy between the Julian and Gregorian calendar amounts to +thirty days in 4000 years; three months in 12,175 years. Hence, in 12,175 +years the equinoxes would take the place of the solstices, and the +solstices the place of the equinoxes. In 24,350 years, the vernal equinox +would take the place of the autumnal equinox, and the winter solstice the +place of the summer solstice. + +And in 48,700 years, according to the Julian rule of intercalation, there +would be gained nearly 365-1/4 days, or one entire revolution of the +Earth. So, to restore the concurrence of the Julian and Gregorian years, +there would have to be suppressed 365-1/4 days, calling the 1st day of +January, 48,699, the 1st day of January, 48,700. + +Thus would disappear from the Julian calendar twelve months, or one whole +year, it having been divided among the thousands of the preceding years. + + +[Illustration: The Julian calendar, reformed by Gregory XIII, Oct. 5th, +1582, by suppressing ten days, calling the 5th of Oct. the 15th, making it +a short month of 21 days, and the year to consist of 355 days. + +The Roman calendar, reformed by Julius Cæsar, 46 B. C., by intercalating +90 days, making that year to consist of 445 days, that is, 355 + 23 + 67 = +445 days, and "the last year of confusion."] + + +To make this subject better understood, let us suppose the solar year to +consist in round numbers of 365 days, and the civil year 366. It is +evident that at the end of the year of 365 days, there would still be +wanting one day to complete the civil year of 366 days, so one day must be +added to that year, and to every succeeding year, to complete the years of +366 days each, which would be the loss of one year of 365 days in 365 +years. Hence, 364 years of 366 days each are equal to 365 years of 365 +days each, wanting one day. + +Again, let us suppose the civil year to consist of 364 days. It is evident +that at the end of the supposed solar year of 365 days, there would be an +advance or gain of one day in that year and every succeeding year, so that +in 365 years there would be a gain of 365 days or one whole year. Hence, +366 years of 364 days each are equal to 365 years of 365 days each, +wanting one day. Appendix F. + + + + +CHAPTER V. + +PECULIARITIES OF THE ROMAN CALENDAR. + + +The Romans, instead of distinguishing the days of the month by the ordinal +numbers, first, second, third, etc., counted backwards from three fixed +points, namely, the Calends, the Nones, and the Ides. + +Calends (Latin _Calandae_, from _Calare_, to call,) was so denominated +because it had been an ancient custom of the pontiffs to call the people +together on that day to apprise them of the festivals, or days that were +to be kept sacred during the month. + +Nones (Latin _nonae_, from _nonus_, the ninth,) the ninth day before the +Ides. + +Ides (Latin _idus_, supposed to be derived from an obsolete verb _iduare_, +to divide,) was near the middle of the month, either the 13th or the 15th +day. + +The first day of each month was invariably called the Calends. The Nones +were the fifth, and the Ides the thirteenth, except in March, May, July, +and October, in which the Nones occurred on the seventh day and the Ides +on the fifteenth. + +From these three points the days of the month were numbered--not forward, +but backward--as so many days before the Nones, the Ides, or the Calends, +the point of departure being counted in the reckoning, so that the last +day of every month was the second of the Calends of the following month. + +It will be seen by the Roman and English calendar found on the following +pages, that there are six days of Nones in March, May, July and October, +and four of all the other months; also that all the months have eight days +of Ides. The number of days of Calends depend upon the number of days in +the month, and the day of the month on which the Ides fall. + +If the month has thirty-one days and the Ides fall on the thirteenth, +there are nineteen days of Calends; but if the Ides fall on the fifteenth, +there are only seventeen days of Calends. As the Ides fall on the +thirteenth of all the months of thirty days, they have eighteen days of +Calends. February, the month of twenty-eight days, has only sixteen, +except in leap-year, when the sixth of the Calends is reckoned twice. + +It may also be seen from the calendar that the Romans, after the first +day of the month, began to reckon so many days before the Nones, as 4th, +3d, 2d, then Nones; after the Nones, so many days before the Ides, as 8th, +7th, 6th, etc., and after the Ides, so many before the Calends of the next +month, the highest numbers being reckoned first. + +In reducing the Roman calendar to our own, it should be remembered that in +reckoning backward from a fixed point, that the point of departure is +counted; also, that the last day of the month is not the point from which +the Calends are reckoned, but the first day of the following month. We +have then this rule for finding the English expression for any Latin date: + + +RULE. + +If the given date be Calends, add two to the number of days in the month, +from which subtract the given date; if the date be Nones, or Ides, add one +to that of the day on which the Nones or Ides fall, from which subtract +the given date, and you will have the day of the month in our calendar. To +find the Latin expression for any English date, the preceding method is to +be reversed, upon the principle that if 5 - 3 = 2, then 5 - 2 = 3. + +But in reducing a Roman date to a date of February in leap-year, for the +first twenty-four days, proceed according to the preceding rule as if the +month had only twenty-eight days, and to obtain the proper expression for +the remaining five days, regard the month as having twenty-nine days, +taking the Roman date from 31 instead of 30. Thus 31 - 6 = 25, while 30 -6 += 24; the former corresponding with sexto calendas, the latter with +bis-sexto calendas of the Julian calendar. By referring to the table on +the 35th page, one may easily learn how to find the English expression for +any Latin date, or the Latin expression for any English date. + +It has already been stated that in January the Nones fall on the 5th, and +the Ides on the 13th, January then having thirty one days, the number from +which to subtract the Roman date to obtain the corresponding day of the +month is, for Nones, 5 + 1 = 6; for Ides, 13 + 1 = 14; for Calends, 31 + 2 += 33. Hence the first column in the table under January are the numbers 6, +14 and 33. February is the same as January for Nones and Ides. For Calends +in leap-year, for the first 24 days, it is 28 + 2 = 30; for the remaining +5 days it is 29 + 2 = 31. Hence for the first column under February are +the numbers 6, 14, 30 and 31. March is the same as January, except that +the Nones fall on the 7th and the Ides on the 15th, consequently we have +for Nones, 7 + 1 = 8, and for Ides, 15 + 1 = 16; hence, for the first +column under March we have the numbers 8, 16, and 33. + +In the table the three months are taken to illustrate how easily the +change may be made from Roman to English, or from English to Roman date. A +complete calendar for 1892, both in Roman and English, which will be very +convenient for reference, may be found on the four following pages. + +The first seven letters of the alphabet, used to represent the days of the +week, are placed in the calendar beside the days of the week. The letter +that represents Sunday is called the dominical or Sunday letter. The +letter that represents the first Sunday in any given year represents all +the Sundays in that year, unless it be leap-year, when two Sunday letters +are used. The first represents all the Sundays in January and February, +while the letter that precedes it represents all the Sundays for the rest +of the year. + +The reason of this is, the day intercalated, or thrust in, between the +28th day of February and the 1st day of March so interrupts the order of +the letters that D, which always represents the 1st day of March, now +represents the 29th day of February, so that in 1892 it represents Monday, +the 29th day of February, also Tuesday the 1st day of March. As it +represented all the Mondays in January and February, it will now represent +all the Tuesdays for the rest of the year, while C, the letter preceding, +represented all the Sundays, will now represent all the Mondays, and B all +the Sundays. For January and February we have then C, Sunday; D, Monday; +E, Tuesday; F, Wednesday; G, Thursday; A, Friday, and B, Saturday. For the +rest of the year we have B, Sunday; C, Monday; D, Tuesday; E, Wednesday; +F, Thursday; G, Friday, and A, Saturday. See Part Second, chapters IV and +V. + + ------------------++------------------++------------------ + JAN., 1892. || FEB., 1892. || MARCH, 1892. + ------------------++------------------++------------------ + 1|_Cal._ |a|Fri. || 1|_Cal._ |d|Mon. || 1|_Cal._ |d|Tues. + 2| 4 |b|Sat. || 2| 4 |e|Tues.|| 2| 6 |e|Wed. + 3| 3 |c|Sun. || 3| 3 |f|Wed. || 3| 5 |f|Thur. + 4| 2 |d|Mon. || 4| 2 |g|Thur.|| 4| 4 |g|Fri. + 5|_Non._ |e|Tues.|| 5|_Non._ |a|Fri. || 5| 3 |a|Sat. + 6| 8 |f|Wed. || 6| 8 |b|Sat. || 6| 2 |b|Sun. + 7| 7 |g|Thur.|| 7| 7 |c|Sun. || 7|_Non._ |c|Mon. + 8| 6 |a|Fri. || 8| 6 |d|Mon. || 8| 8 |d|Tues. + 9| 5 |b|Sat. || 9| 5 |e|Tues.|| 9| 7 |e|Wed. + 10| 4 |c|Sun. ||10| 4 |f|Wed. ||10| 6 |f|Thur. + 11| 3 |d|Mon. ||11| 3 |g|Thur.||11| 5 |g|Fri. + 12| 2 |e|Tues.||12| 2 |a|Fri. ||12| 4 |a|Sat. + 13|_Ides._|f|Wed. ||13|_Ides._|b|Sat. ||13| 3 |b|Sun. + 14| 19 |g|Thur.||14| 16 |c|Sun. ||14| 2 |c|Mon. + 15| 18 |a|Fri. ||15| 15 |d|Mon. ||15|_Ides._|d|Tues. + 16| 17 |b|Sat. ||16| 14 |e|Tues.||16| 17 |e|Wed. + 17| 16 |c|Sun. ||17| 13 |f|Wed. ||17| 16 |f|Thur. + 18| 15 |d|Mon. ||18| 12 |g|Thur.||18| 15 |g|Fri. + 19| 14 |e|Tues.||19| 11 |a|Fri. ||19| 14 |a|Sat. + 20| 13 |f|Wed. ||20| 10 |b|Sat. ||20| 13 |b|Sun. + 21| 12 |g|Thur.||21| 9 |c|Sun. ||21| 12 |c|Mon. + 22| 11 |a|Fri. ||22| 8 |d|Mon. ||22| 11 |d|Tues. + 23| 10 |b|Sat. ||23| 7 |e|Tues.||23| 10 |e|Wed. + 24| 9 |c|Sun. ||24| 6 |f|Wed. ||24| 9 |f|Thur. + 25| 8 |d|Mon. ||25| 6 |g|Thur.||25| 8 |g|Fri. + 26| 7 |e|Tues.||26| 5 |a|Fri. ||26| 7 |a|Sat. + 27| 6 |f|Wed. ||27| 4 |b|Sat. ||27| 6 |b|Sun. + 28| 5 |g|Thur.||28| 3 |c|Sun. ||28| 5 |c|Mon. + 29| 4 |a|Fri. ||29| 2 |d|Mon. ||29| 4 |d|Tues. + 30| 3 |b|Sat. || | | | ||30| 3 |e|Wed. + 31| 2 |c|Sun. || | | | ||31| 2 |f|Thur. + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + + ------------------++------------------++------------------ + APRIL, 1892. || MAY, 1892. || JUNE, 1892. + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + 1|_Cal._ |g|Fri. || 1|_Cal._ |b|Sun. || 1|_Cal._ |e|Wed. + 2| 4 |a|Sat. || 2| 6 |c|Mon. || 2| 4 |f|Thur. + 3| 3 |b|Sun. || 3| 5 |d|Tues.|| 3| 3 |g|Fri. + 4| 2 |c|Mon. || 4| 4 |e|Wed. || 4| 2 |a|Sat. + 5|_Non._ |d|Tues.|| 5| 3 |f|Thur.|| 5|_Non._ |b|Sun. + 6| 8 |e|Wed. || 6| 2 |g|Fri. || 6| 8 |c|Mon. + 7| 7 |f|Thur.|| 7|_Non._ |a|Sat. || 7| 7 |d|Tues. + 8| 6 |g|Fri. || 8| 8 |b|Sun. || 8| 6 |e|Wed. + 9| 5 |a|Sat. || 9| 7 |c|Mon. || 9| 5 |f|Thur. + 10| 4 |b|Sun. ||10| 6 |d|Tues.||10| 4 |g|Fri. + 11| 3 |c|Mon. ||11| 5 |e|Wed. ||11| 3 |a|Sat. + 12| 2 |d|Tues.||12| 4 |f|Thur.||12| 2 |b|Sun. + 13|_Ides._|e|Wed. ||13| 3 |g|Fri. ||13|_Ides._|c|Mon. + 14| 18 |f|Thur.||14| 2 |a|Sat. ||14| 18 |d|Tues. + 15| 17 |g|Fri. ||15|_Ides._|b|Sun. ||15| 17 |e|Wed. + 16| 16 |a|Sat. ||16| 17 |c|Mon. ||16| 16 |f|Thur. + 17| 15 |b|Sun. ||17| 16 |d|Tues.||17| 15 |g|Fri. + 18| 14 |c|Mon. ||18| 15 |e|Wed. ||18| 14 |a|Sat. + 19| 13 |d|Tues.||19| 14 |f|Thur.||19| 13 |b|Sun. + 20| 12 |e|Wed. ||20| 13 |g|Fri. ||20| 12 |c|Mon. + 21| 11 |f|Thur.||21| 12 |a|Sat. ||21| 11 |d|Tues. + 22| 10 |g|Fri. ||22| 11 |b|Sun. ||22| 10 |e|Wed. + 23| 9 |a|Sat. ||23| 10 |c|Mon. ||23| 9 |f|Thur. + 24| 8 |b|Sun. ||24| 9 |d|Tues.||24| 8 |g|Fri. + 25| 7 |c|Mon. ||25| 8 |e|Wed. ||25| 7 |a|Sat. + 26| 6 |d|Tues.||26| 7 |f|Thur.||26| 6 |b|Sun. + 27| 5 |e|Wed. ||27| 6 |g|Fri. ||27| 5 |c|Mon. + 28| 4 |f|Thur.||28| 5 |a|Sat. ||28| 4 |d|Tues. + 29| 3 |g|Fri. ||29| 4 |b|Sun. ||29| 3 |e|Wed. + 30| 2 |a|Sat. ||30| 3 |c|Mon. ||30| 2 |f|Thur. + | | | ||31| 2 |d|Tues.|| | | | + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + + --+---------------++------------------++------------------ + JULY, 1892. || AUG., 1892. || SEPT., 1892. + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + 1|_Cal._ |g|Fri. || 1|_Cal._ |c|Mon. || 1|_Cal._ |f|Thur. + 2| 6 |a|Sat. || 2| 4 |d|Tues.|| 2| 4 |g|Fri. + 3| 5 |b|Sun. || 3| 3 |e|Wed. || 3| 3 |a|Sat. + 4| 4 |c|Mon. || 4| 2 |f|Thur.|| 4| 2 |b|Sun. + 5| 3 |d|Tues.|| 5|_Non._ |g|Fri. || 5|_Non._ |c|Mon. + 6| 2 |e|Wed. || 6| 8 |a|Sat. || 6| 8 |d|Tues. + 7|_Non._ |f|Thur.|| 7| 7 |b|Sun. || 7| 7 |e|Wed. + 8| 8 |g|Fri. || 8| 6 |c|Mon. || 8| 6 |f|Thur. + 9| 7 |a|Sat. || 9| 5 |d|Tues.|| 9| 5 |g|Fri. + 10| 6 |b|Sun. ||10| 4 |e|Wed. ||10| 4 |a|Sat. + 11| 5 |c|Mon. ||11| 3 |f|Thur.||11| 3 |b|Sun. + 12| 4 |d|Tues.||12| 2 |g|Fri. ||12| 2 |c|Mon. + 13| 3 |e|Wed. ||13|_Ides._|a|Sat. ||13|_Ides._|d|Tues. + 14| 2 |f|Thur.||14| 19 |b|Sun. ||14| 18 |e|Wed. + 15|_Ides._|g|Fri. ||15| 18 |c|Mon. ||15| 17 |f|Thur. + 16| 17 |a|Sat. ||16| 17 |d|Tues.||16| 16 |g|Fri. + 17| 16 |b|Sun. ||17| 16 |e|Wed. ||17| 15 |a|Sat. + 18| 15 |c|Mon. ||18| 15 |f|Thur.||18| 14 |b|Sun. + 19| 14 |d|Tues.||19| 14 |g|Fri. ||19| 13 |c|Mon. + 20| 13 |e|Wed. ||20| 13 |a|Sat. ||20| 12 |d|Tues. + 21| 12 |f|Thur.||21| 12 |b|Sun. ||21| 11 |e|Wed. + 22| 11 |g|Fri. ||22| 11 |c|Mon. ||22| 10 |f|Thur. + 23| 10 |a|Sat. ||23| 10 |d|Tues.||23| 9 |g|Fri. + 24| 9 |b|Sun. ||24| 9 |e|Wed. ||24| 8 |a|Sat. + 25| 8 |c|Mon. ||25| 8 |f|Thur.||25| 7 |b|Sun. + 26| 7 |d|Tues.||26| 7 |g|Fri. ||26| 6 |c|Mon. + 27| 6 |e|Wed. ||27| 6 |a|Sat. ||27| 5 |d|Tues. + 28| 5 |f|Thur.||28| 5 |b|Sun. ||28| 4 |e|Wed. + 29| 4 |g|Fri. ||29| 4 |c|Mon. ||29| 3 |f|Thur. + 30| 3 |a|Sat. ||30| 3 |d|Tues.||30| 2 |g|Fri. + 31| 2 |b|Sun. ||31| 2 |e|Wed. || | | | + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + + ------------------++------------------++------------------ + OCT., 1892. || NOV., 1892. || DEC., 1892. + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + 1|_Cal._ |a|Sat. || 1|_Cal._ |d|Tues.|| 1|_Cal._ |f|Thur. + 2| 6 |b|Sun. || 2| 4 |e|Wed. || 2| 4 |g|Fri. + 3| 5 |c|Mon. || 3| 3 |f|Thur.|| 3| 3 |a|Sat. + 4| 4 |d|Tues.|| 4| 2 |g|Fri. || 4| 2 |b|Sun. + 5| 3 |e|Wed. || 5|_Non._ |a|Sat. || 5|_Non._ |c|Mon. + 6| 2 |f|Thur.|| 6| 8 |b|Sun. || 6| 8 |d|Tues. + 7|_Non._ |g|Fri. || 7| 7 |c|Mon. || 7| 7 |e|Wed. + 8| 8 |a|Sat. || 8| 6 |d|Tues.|| 8| 6 |f|Thur. + 9| 7 |b|Sun. || 9| 5 |e|Wed. || 9| 5 |g|Fri. + 10| 6 |c|Mon. ||10| 4 |f|Thur.||10| 4 |a|Sat. + 11| 5 |d|Tues.||11| 3 |g|Fri. ||11| 3 |b|Sun. + 12| 4 |e|Wed. ||12| 2 |a|Sat. ||12| 2 |c|Mon. + 13| 3 |f|Thur.||13|_Ides._|b|Sun. ||13|_Ides._|d|Tues. + 14| 2 |g|Fri. ||14| 18 |c|Mon. ||14| 19 |e|Wed. + 15|_Ides._|a|Sat. ||15| 17 |d|Tues.||15| 18 |f|Thur. + 16| 17 |b|Sun. ||16| 16 |e|Wed. ||16| 17 |g|Fri. + 17| 16 |c|Mon. ||17| 15 |f|Thur.||17| 16 |a|Sat. + 18| 15 |d|Tues.||18| 14 |g|Fri. ||18| 15 |b|Sun. + 19| 14 |e|Wed. ||19| 13 |a|Sat. ||19| 14 |c|Mon. + 20| 13 |f|Thur.||20| 12 |b|Sun. ||20| 13 |d|Tues. + 21| 12 |g|Fri. ||21| 11 |c|Mon. ||21| 12 |e|Wed. + 22| 11 |a|Sat. ||22| 10 |d|Tues.||22| 11 |f|Thur. + 23| 10 |b|Sun. ||23| 9 |e|Wed. ||23| 10 |g|Fri. + 24| 9 |c|Mon. ||24| 8 |f|Thur.||24| 9 |a|Sat. + 25| 8 |d|Tues.||25| 7 |g|Fri. ||25| 8 |b|Sun. + 26| 7 |e|Wed. ||26| 6 |a|Sat. ||26| 7 |c|Mon. + 27| 6 |f|Thur.||27| 5 |b|Sun. ||27| 6 |d|Tues. + 28| 5 |g|Fri. ||28| 4 |c|Mon. ||28| 5 |e|Wed. + 29| 4 |a|Sat. ||29| 3 |d|Tues.||29| 4 |f|Thur. + 30| 3 |b|Sun. ||30| 2 |e|Wed. ||30| 3 |g|Fri. + 31| 2 |c|Mon. || | | | ||31| 2 |a|Sat. + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + + --------------++----------------++---------------- + JANUARY. || FEBRUARY. || MARCH. + --------------++----------------++---------------- + _Cal._ 1 || _Cal._ 1 || _Cal._ 1 + 6 - 4 = 2 || 6 - 4 = 2 || 8 - 6 = 2 + 6 - 3 = 3 || 6 - 3 = 3 || 8 - 5 = 3 + 6 - 2 = 4 || 6 - 2 = 4 || 8 - 4 = 4 + _Nones_ 5 || _Nones_ 5 || 8 - 3 = 5 + 14 - 8 = 6 || 14 - 8 = 6 || 8 - 2 = 6 + 14 - 7 = 7 || 14 - 7 = 7 || _Nones_ 7 + 14 - 6 = 8 || 14 - 6 = 8 || 16 - 8 = 8 + 14 - 5 = 9 || 14 - 5 = 9 || 16 - 7 = 9 + 14 - 4 = 10 || 14 - 4 = 10 || 16 - 6 = 10 + 14 - 3 = 11 || 14 - 3 = 11 || 16 - 5 = 11 + 14 - 2 = 12 || 14 - 2 = 12 || 16 - 4 = 12 + _Ides_ 13 || _Ides_ 13 || 16 - 3 = 13 + 33 - 19 = 14 || 30 - 16 = 14 || 16 - 2 = 14 + 33 - 18 = 15 || 30 - 15 = 15 || _Ides_ 15 + 33 - 17 = 16 || 30 - 14 = 16 || 33 - 17 = 16 + 33 - 16 = 17 || 30 - 13 = 17 || 33 - 16 = 17 + 33 - 15 = 18 || 30 - 12 = 18 || 33 - 15 = 18 + 33 - 14 = 19 || 30 - 11 = 19 || 33 - 14 = 19 + 33 - 13 = 20 || 30 - 10 = 20 || 33 - 13 = 20 + 33 - 12 = 21 || 30 - 9 = 21 || 33 - 12 = 21 + 33 - 11 = 22 || 30 - 8 = 22 || 33 - 11 = 22 + 33 - 10 = 23 || 30 - 7 = 23 || 33 - 10 = 23 + 33 - 9 = 24 || 30 - 6 = 24 || 33 - 9 = 24 + 33 - 8 = 25 || 31 - 6 = 25 || 33 - 8 = 25 + 33 - 7 = 26 || 31 - 5 = 26 || 33 - 7 = 26 + 33 - 6 = 27 || 31 - 4 = 27 || 33 - 6 = 27 + 33 - 5 = 28 || 31 - 3 = 28 || 33 - 5 = 28 + 33 - 4 = 29 || 31 - 2 = 29 || 33 - 4 = 29 + 33 - 3 = 30 || || 33 - 3 = 30 + 33 - 2 = 31 || || 33 - 2 = 31 + --------------++----------------++---------------- + + + + +PART SECOND. + +MATHEMATICAL. + + + + +CHAPTER I. + +ERRORS OF THE JULIAN CALENDAR. + + +It will be necessary in the first place to understand the difference +between the Julian and Gregorian rule of intercalation. If the number of +any year be exactly divisible by four it is leap year; if the remainder be +1, it is the first year after leap-year; if 2, the second; if 3, the +third; thus: + + 1888 ÷ 4 = 472, no remainder. + 1889 ÷ 4 = 472, remainder, 1. + 1890 ÷ 4 = 472, remainder, 2. + 1891 ÷ 4 = 472, remainder, 3. + 1892 ÷ 4 = 473, no remainder. + +And so on, every fourth year being leap-year of 366 days. + +This is the Julian rule of intercalation, which is corrected by the +Gregorian by making every centurial year, or the year that completes the +century, a common year, if not exactly divisible by 400; so that only +every fourth centurial year is leap-year; thus, 1,700, 1,800, and 1,900 +are common years, but 2,000, the fourth centurial year, is leap year, and +so on. + +By the Julian rule three-fourths of a day is gained every century, which +in 400 years amounts to three days. This is corrected by the Gregorian, by +making three consecutive centurial years common years, thus suppressing +three days in 400 years. + + +RULE. + +Multiply the difference between the Julian and the solar year by 100, and +we have the error in 100 years. Multiply this product by 4 and we have the +error in 400 years. Now, 400 is the tenth of 4,000; therefore, multiply +the last product by 10, and we have the error in 4,000 years. Now, as the +discrepancy between the Julian and Gregorian year is three days in 400 +years, making 3-400 of a day every year, so by dividing 365-1/4, the +number of days in a year, by 3-400, we have the time it would take to make +a revolution of the seasons. + + +SOLUTION. + +(365 d, 6 h.) - (365 d, 5 h, 48 m, 49.62 s.) = (11 m, 10.38 s.) Now, (11 +m, 10.38 s.) × 100 = 18 h, 37.3 m, the gain in 100 years. This is, +reckoned in round numbers, 18 hours, or three-fourths of a day. Now, (3/4 +× 4) = (1 × 3) = 3: the Julian rule gaining three days, the Gregorian +suppressing three days in 400 years. (3 × 10) = 30, the number of days +gained by the Julian rule in 4,000 years. 365-1/4 ÷ 3 400 = 48,700, so +that in this long period of time, this falling back 3/4 of a day every +century would amount to 365-1/4 days; therefore, 48,699 Julian years are +equal to 48,700 Gregorian years. + + + + +CHAPTER II. + +ERRORS OF THE GREGORIAN CALENDAR. + + +By reference to the preceding chapter it will be seen that there is an +error of 37.3 minutes in every 100 years not corrected by the Gregorian +calendar; this amounts to only .373 of a minute a year, or one day in +3,861 years, and one day and fifty-two minutes in 4,000 years. + + +RULE. + +To find how long it would take to gain one day: Divide the number of +minutes in a day by the decimal .373, that being the fraction of a minute +gained every year. To find how much time would be gained in 4,000 years, +multiply the decimal .373 by 4,000, and you will have the answer in +minutes, which must be reduced to hours. + + +SOLUTION. + +(24 × 60) ÷ .373 = 3,861, nearly; hence the error would amount to only one +day in 3,861 years. + +(.373 × 4,000) ÷ 60 = (24 h, 52 m,) = (1 d, 0 h, 52 m), the error in 4,000 +years. + +This trifling error in the Gregorian calendar may be corrected by +suppressing the intercalations in the year 4,000, and its multiples, +8,000, 12,000, 16,000, etc., so that it will not amount to a day in +100,000 years. + + +RULE. + +Divide 100,000 by 4,000 and you will have the number of intercalations +suppressed in 100,000 years. Multiply 1 d, 52 m, (that being the error in +4,000 years) by this quotient, and you will have the discrepancy between +the Gregorian and solar year for 100,000 years. By this improved method we +suppress 25 days, so that the error will only amount to 25 times 52 +minutes. + + +SOLUTION. + +100,000 ÷ 4,000 × (1 d, 52 m,) = (25d, 21 h, 40 m.) Now, (25d, 21 h, 40 +m,) - 25 d = (21 h, 40 m,) the error in 100,000. + + + + +CHAPTER III. + +DOMINICAL LETTER. + + +Dominical (from the Latin _Dominus_, Lord,) indicating the Lord's day or +Sunday. Dominical letter, one of the first seven letters of the alphabet +used to denote the Sabbath or Lord's day. + +For the sake of greater generality, the days of the week are denoted by +the first seven letters of the alphabet, A, B, C, D, E, F, G, which are +placed in the calendar beside the days of the year, so that A stands +opposite the first day of January, B opposite the second, C opposite the +third, and so on to G, which stands opposite the seventh; after which A +returns to the eighth, and so on through the 365 days of the year. + +Now, if one of the days of the week, Sunday for example, is represented by +F, Monday will be represented by G, Tuesday by A, Wednesday by B, Thursday +by C, Friday by D, and Saturday by E; and every Sunday throughout the year +will have the same character, F, every Monday G, every Tuesday A, and so +with regard to the rest. + +The letter which denotes Sunday is called the Dominical or Sunday letter +for that year; and when the dominical letter of the year is known, the +letters which respectively correspond to the other days of the week become +known also. Did the year consist of 364 days, or 52 weeks invariably, the +first day of the year and the first day of the month, and in fact any day +of any year, or any month, would always commence on the same day of the +week. But every common year consists of 365 days, or 52 weeks and 1 day, +so that the following year will begin one day later in the week than the +year preceding. Thus the year 1837 commenced on Sunday, the following +year, 1838, on Monday, 1839 on Tuesday, and so on. + +As the year consists of 52 weeks and 1 day, it is evident that the day +which begins and ends the year must occur 53 times; thus the year 1837 +begins on Sunday and ends on Sunday; so the following year, 1838, must +begin on Monday. As A represented all the Sundays in 1837 and as A always +stands for the first day of January, so in 1838 it will represent all the +Mondays, and the dominical letter goes back from A to G; so that G +represents all the Sundays in 1838, A all the Mondays, B all the Tuesdays, +and so on, the dominical letter going back one place in every year of 365 +days. + +While the following year commences one day later in the week than the year +preceding, the dominical letter goes back one place from the preceding +year; thus while the year 1865 commenced on Sunday, 1866 on Monday, 1867 +on Tuesday, the dominical letters are A, G and F, respectively. Therefore, +if every year consisted of 365 days, the dominical cycle would be +completed in seven years, so that after seven years the first day of the +year would again occur on the same day of the week. + +But this order is interrupted every four years by giving February 29 days, +thereby making the year to consist of 366 days, which is 52 weeks and two +days, so that the following year would commence two days later in the week +than the year preceding, thus the year 1888 being leap-year, had two +dominical letters, A and G; A for January and February, and G for the rest +of the year. The year commenced on Sunday and ended on Monday, making 53 +Sundays and 53 Mondays, and the following year, 1889, to commence on +Tuesday. It now becomes evident that if the years all consisted of 364 +days, or 52 weeks, they would all commence on the same day of the week; if +they all consisted of 365 days, or 52 weeks and one day, they would all +commence one day later in the week than the year preceding; if they all +consisted of 366 days, or 52 weeks and two days, they would commence two +days later in the week; if 367 days or 52 weeks and three days, then three +days later, and so on, one day later for every additional day. It is also +evident that every additional day causes the dominical letter to go back +one place. Now in leap-year the 29th day of February is the additional or +intercalary day. So one letter for January and February, and another for +the rest of the year. If the number of years in the intercalary period +were two, and seven being the number of days in the week, their product +would be 2 × 7 = 14; fourteen, then, would be the number of years in the +cycle. Again, if the number of years in the intercalary period were three, +and the number of days in the week being seven, their product would be 3 × +7 = 21; twenty-one would then be the number of years in the cycle. But the +number of years in the intercalary period is four, and the number of days +in the week is seven, therefore their product is 4 × 7 = 28; twenty-eight +is then the number of years in the cycle. + +This period is called the dominical or solar cycle, and restores the first +day of the year to the same day of the week. At the end of the cycle the +dominical letters return again in the same order, on the same days of the +month. Thus, for the year 1801, the dominical letter is D; 1802, C; 1803, +B; 1804, A and G; and so on, going back five places every four years for +twenty-eight years, when the cycle, being ended, D is again dominical +letter for 1829, C for 1830, and so on every 28 years forever, according +to the Julian rule of intercalation. + +But this order is interrupted in the Gregorian calendar at the end of the +century by the secular suppression of the leap-year. It is not +interrupted, however, at the end of every century, for the leap-year is +not suppressed in every fourth centurial year; consequently the cycle will +then be continued for two hundred years. It should be here stated that +this order continued without interruption from the commencement of the era +until the reformation of the calendar in 1582, during which time the +Julian calendar, or Old Style was used. + +It has already been shown that if the number of years in the intercalary +period be multiplied by seven, the number of days in the week, their +product will be the number of years in the cycle. Now, in the Gregorian +calendar, the intercalary period is 400 years; this number being +multiplied by seven, their product would be 2,800 years, as the interval +in which the coincidence is restored between the days of the year and the +days of the week. + +This long period, however, may be reduced to 400 years; for since the +dominical letter goes back five places every four years, in 400 years it +will go back 500 places in the Julian and 497 in the Gregorian calendar, +three intercalations being suppressed in the Gregorian every 400 years. +Now 497 is exactly divisible by seven, the number of days in the week, +therefore, after 400 years the cycle will be completed, and the dominical +letters will return again in the same order, on the same days of the +month. + +In answer to the question, "Why two dominical letters for leap-year?" we +reply, because of the additional or intercalary day after the 28th of +February. It has already been shown that every additional day causes the +dominical letter to go back one place. As there are 366 days in leap-year, +the letter must go back two places, one being used for January and +February, and the other for the rest of the year. Did we continue one +letter through the year and then go back two places, it would cause +confusion in computation, unless the intercalation be made at the end of +the year. Whenever the intercalation is made there must necessarily be a +change in the dominical letter. Had it been so arranged that the +additional day was placed after the 30th of June or September, then the +first letter would be used until the intercalation is made in June or +September, and the second to the end of the year. Or suppose that the end +of the year had been fixed as the time and place for the intercalation, +(which would have been much more convenient for computation,) then there +would have been no use whatever for the second dominical letter, but at +the end of the year we would go back two places; thus, in the year 1888, +instead of A being dominical letter for two months merely, it would be +continued through the year, and then passing back to F, no use whatever +being made of G, and so on at the end of every leap-year. Hence it is +evident that this arrangement would have been much more convenient, but we +have this order of the months, and the number of days in the months as +Augustus Cæsar left them eight years before Christ. The dominical letter +probably was not known until the Council of Nice, in the year of our Lord +325, where, in all probability, it had its origin. + + + + +CHAPTER IV. + +RULE FOR FINDING THE DOMINICAL LETTER. + + +Divide the number of the given year by 4, neglecting the remainders, and +add the quotient to the given number. Divide this amount by 7, and if the +remainder be less than three, take it from 3; but if it be 3 or more than +3, take it from 10 and the remainder will be the number of the letter +calling A, 1; B, 2; C, 3, etc. + +By this rule the dominical letter is found from the commencement of the +era to October 5th, 1582. O. S. From October 15th, 1582, till the year +1700, take the remainder as found by the rule from 6, if it be less than +6, but if the remainder be 6, take it from 13, and so on according to +instructions given in the table on 49th page. It should be understood +here, that in leap-years the letter found by the preceding rule will be +the dominical letter for that part of the year that follows the 29th of +February, while the letter which follows it will be the one for January +and February. + + +EXAMPLES. + +To find the dominical letter for 1365, we have 1365 ÷ 4 = 341 +; 1365 + +341 = 1706; 1706 ÷ 7 = 243, remainder 5. Then 10 - 5 = 5; therefore E +being the fifth letter is the dominical letter for 1365. + +To find the dominical letter for 1620, we have 1620 ÷ 4 = 405; 1620 + 405 += 2025; 2025 ÷ 7 = 289, remainder 2. Then 6 - 2 = 4; therefore, D and E +are the dominical letters for 1620; E for January and February, and D for +the rest of the year. The process of finding the dominical letter is very +simple and easily understood, if we observe the following order: + +1st. Divide by 4. + +2d. Add to the given number. + +3d. Divide by 7. + +4th. Take the remainder from 3 or 10, from the commencement of the era to +October 5th, 1582. From October 15th, 1582 to 1700, from 6 or 13. From +1700 to 1800, from 7, and so on. See table on 49th page. + +We divide by 4 because the intercalary period is four years; and as every +fourth year contains the divisor 4 once more than any of the three +preceding years, so there is one more added to the fourth year than there +is to any of the three preceding years; and as every year consists of 52 +weeks and one day, this additional year gives an additional day to the +remainder after dividing by 7. For example, the year + + 1 of the era consists of 52 w. 1 d. + 2 years consist of 104 w. 2 d. + 3 years consist of 156 w. 3 d. + (4 ÷ 4) + 4 = 5 years consist of 260 w. 5 d. + +Hence the numbers thus formed will be 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, +15, and so on. + +We divide by 7, because there are seven days in the week, and the +remainders show how many days more than an even number of weeks there are +in the given year. Take, for example, the first twelve years of the era +after being increased by one-fourth, and we have + + 1 ÷ 7 = 0 remainder 1 Then 3 - 1 = 2 = B + 2 ÷ 7 = 0 " 2 " 3 - 2 = 1 = A + 3 ÷ 7 = 0 " 3 " 10 - 3 = 7 = G + 5 ÷ 7 = 0 " 5 " 10 - 5 = 5 = F E + 6 ÷ 7 = 0 " 6 " 10 - 6 = 4 = D + 7 ÷ 7 = 1 " 0 " 3 - 0 = 3 = C + 8 ÷ 7 = 1 " 1 " 3 - 1 = 2 = B + 10 ÷ 7 = 1 " 3 " 10 - 3 = 7 = A G + 11 ÷ 7 = 1 " 4 " 10 - 4 = 6 = F + 12 ÷ 7 = 1 " 5 " 10 - 5 = 5 = E + 13 ÷ 7 = 1 " 6 " 10 - 6 = 4 = D + 15 ÷ 7 = 2 " 1 " 3 - 1 = 2 = C B + +From this table it may be seen that it is these remainders representing +the number of days more than an even number of weeks in the given year, +that we have to deal with in finding the dominical letter. + +Did the year consist of 364 days, or 52 weeks, invariably, there would be +no change in the dominical letter from year to year, but the letter that +represents Sunday in any given year would represent Sunday in every year. +Did the year consist of only 363 days, thus wanting one day of an even +number of weeks, then these remainders, instead of being taken from a +given remainder, would be added to that number, thus removing the +dominical letter forward one place, and the beginning of the year, instead +of being one day later, would be one day earlier in the week than in the +preceding year. + +Thus, if the year 1 of the era be taken from 3, we would have 3 - 1 = 2; +therefore, B being the second letter, is dominical letter for the year 1. +But if the year consist of only 363 days, then the 1 instead of being +taken from 3 would be added to 3; then we would have 3 + 1 = 4; therefore, +D being the fourth letter would be dominical letter for the year 1. The +former going back from C to B, the latter forward from C to D; or which +amounts to the same thing, make the year to consist of 51 weeks and 6 +days; then 10 - 6 = 4, making D the dominical letter as before. + +As seven is the number of days in the week, and the object of these +subtractions is to remove the dominical letter back one place every common +year, and two in leap-year, why not take these remainders from 7? We +answer, all depends upon the day of the week on which the era commenced. +Had G, the seventh letter been dominical letter for the year preceding the +era, then these remainders would be taken from 7; and 7 would be used +until change of style in 1582. But we know from computation that C, the +third letter, is dominical letter for the year preceding the era; so we +commence with three, and take the smaller remainders, 1 and 2 from 3; that +brings us to A. We take the larger remainders, from 3 to 6, from 3 + 7 = +10. We add the 7 because there are seven days in the week. We use the +number 10 until we get back to C, the third letter, the place from whence +we started. For example, we have + + 3 - 1 = 2 = B + 3 - 2 = 1 = A + 10 - 3 = 7 = G + 10 - 4 = 6 = F + 10 - 5 = 5 = E + 10 - 6 = 4 = D + 3 - 0 = 3 = C + +The cycle of seven days being completed, we commence with the number three +again, and so on until 1582, when on account of the errors of the Julian +calendar, ten days were suppressed to restore the coincidence of the solar +and civil year. Now every day suppressed removes the dominical letter +forward one place; so counting from C to C again is seven, D is eight, E +is nine, and F is ten. As F is the sixth letter, we take the remainders +from 1 to 5, from 6; if the remainder be 6, take it from 6 + 7 = 13. Then +6 or 13 is used till 1700, when, another day being suppressed, the number +is increased to 7. And again in 1800, for the same reason, a change is +made to 1 or 8; in 1900 to 2 or 9, and so on. It will be seen by the table +on the 49th page that the smaller numbers run from 1 to 7; the larger ones +from 8 to 13. + +From the commencement of the Christian era to October 5th, 1582, take the +remainders, after dividing by 7, from 3 or 10; from October 15th, + + 1582 to 1700 from 6 or 13 + 1700 to 1800 " 7 + 1800 to 1900 " 1 or 8 + 1900 to 2100 " 2 or 9 + 2100 to 2200 " 3 or 10 + 2200 to 2300 " 4 or 11 + 2300 to 2500 " 5 or 12 + 2500 to 2600 " 6 or 13 + 2600 to 2700 " 7 + 2700 to 2900 " 1 or 8 + 2900 to 3000 " 2 or 9 + 3000 to 3100 " 3 or 10 + 3100 to 3300 " 4 or 11 + 3300 to 3400 " 5 or 12 + 3400 to 3500 " 6 or 13 + 3500 to 3700 " 7 + 3700 to 3800 " 1 or 8 + 3800 to 3900 " 2 or 9 + 3900 to 4000 " 3 or 10 + 4000 to 4100 " 4 or 11 + 4100 to 4200 " 5 or 12 + 4200 to 4300 " 6 or 13 + 4300 to 4500 " 7 + 4500 to 4600 " 1 or 8 + 4600 to 4700 " 2 or 9 + 4700 to 4900 " 3 or 10 + 4900 to 5000 " 4 or 11 + 5000 to 5100 " 5 or 12 + + + + +CHAPTER V. + +RULE FOR FINDING THE DAY OF THE WEEK OF ANY GIVEN DATE, FOR BOTH OLD AND +NEW STYLES. + + +By arranging the dominical letters in the order in which the different +months commence, the day of the week on which any month of any year, or +day of the month has fallen or will fall, from the commencement of the +Christian era to the year of our Lord 4000, may be calculated. (Appendix +G.) They have been arranged thus in the following couplet, in which At +stands for January, Dover for February, Dwells for March, etc. + + At Dover Dwells George Brown, Esquire, + Good Carlos Finch, and David Fryer. + +Now if A be dominical or Sunday letter for a given year, then January and +October being represented by the same letter, begin on Sunday; February, +March and November, for the same reason, begin on Wednesday; April and +July on Saturday; May on Monday, June on Thursday, August on Tuesday, +September and December on Friday. It is evident that every month in the +year must commence on some one day of the week represented by one of the +first seven letters of the alphabet. Now let + + January 1st be represented by A, Sun. + Feb. 1st (4 w. 3 d. from the preceding date) by D, Wed. + Mar. 1st 4 w. 0 d. " " " by D, Wed. + Apr. 1st 4 w. 3 d. " " " by G, Sat. + May 1st 4 w. 2 d. " " " by B, Mon. + June 1st 4 w. 3 d. " " " by E, Thur. + July 1st 4 w. 2 d. " " " by G, Sat. + Aug. 1st 4 w. 3 d. " " " by C, Tues. + Sept. 1st 4 w. 3 d. " " " by F, Fri. + Oct. 1st 4 w. 2 d. " " " by A, Sun. + Nov. 1st 4 w. 3 d. " " " by D, Wed. + Dec. 1st 4 w. 2 d. " " " by F, Fri. + +Now each of these letters placed opposite the months respectively +represents the day of the week on which the month commences, and they are +the first letters of each word in the preceding couplet. + +To find the day of the week on which a given day of any year will occur, +we have the following + + +RULE. + +Find the dominical letter for the year. Read from this to the letter which +begins the given month, always reading from A toward G, calling the +dominical letter Sunday, the next Monday, etc. This will show on what day +of the week the month commenced; then reckoning the number of days from +this will give the day required. + + +EXAMPLES. + +History records the fall of Constantinople on May 29th, 1453. On what day +of the week did it occur? We have then 1453 ÷ 4 = 363 +; 1453 + 363 = +1816; 1816 ÷ 7 = 259, remainder 3. Then 10 - 3 = 7; therefore, G being the +seventh letter is dominical letter for 1453. Now reading from G to B, the +letter for May, we have G Sunday, A Monday, and B Tuesday; hence May +commenced on Tuesday and the 29th was Tuesday. + +The change from Old to New Style was made by Pope Gregory XIII, October +5th, 1582. On what day of the week did it occur? We have then 1582 ÷ 4 = +395+; 1582 + 395 = 1977; 1977 ÷ 7 = 282, remainder 3. Then 10 - 3 = 7; +therefore, G being the seventh letter, is dominical letter for 1582. Now +reading from G to A, the letter for October, we have G Sunday, A Monday, +etc. Hence October commenced on Monday, and the 5th was Friday. + +On what day of the week did the 15th of the same month fall in 1582? We +have then 1582 ÷ 4 = 395+; 1582 + 395 = 1977; 1977 ÷ 7 = 282, remainder 3. +Then 6 - 3 = 3; therefore, C being the third letter, is the dominical +letter for 1582. Now reading from C to A, the letter for October, we have +C Sunday, D Monday, E Tuesday, etc. Hence October commenced on Friday, and +the 15th was Friday. + +How is this, says one? You have just shown by computation that October, +1582, commenced on Monday, you now say that it occurred on Friday. You +also stated that the 5th was Friday; you now say that the 15th was Friday. +This is absurd; ten is not a multiple of seven. There is nothing absurd +about it. The former computation was Old Style, the latter New Style, the +Old being ten days behind the new. + +As regards an interval of ten days between the two Fridays, there was +none; Friday, the 5th, and Friday, the 15th, was one and the same day; +there was no interval, nothing ever occurred, there was no time for +anything to occur; the edict of the Pope decided it; he said the 5th +should be called the 15th, and it was so. + +Hence to October the 5th, 1582, the computation should be Old Style; from +the 15th to the end of the year New Style. + +On what day of the week did the years 1, 2 and 3, of the era commence? +None of these numbers can be divided by 4; neither are they divisible by +7; but they may be treated as remainders after dividing by 7. Now each of +these numbers of years consists of an even number of weeks with remainders +of 1, 2 and 3 days respectively. Hence we have then for the year 1, 3 - 1 += 2; therefore, B being the second letter, is the dominical letter for the +year 1. Now reading from B to A, the letter for January, we have B Sunday, +C Monday, D Tuesday, etc. Hence January commenced on Saturday. + +Then we have for the year 2, 3 - 2 = 1; therefore A being the first +letter, is dominical letter for the year 2; hence it is evident that +January commenced on Sunday. Again we have for the year 3, 10 - 3 = 7; +therefore, G being the seventh letter, is dominical letter for the year 3. +Now reading from G to A, the letter for January, we have G Sunday, A +Monday; hence January commenced on Monday. + +On what day of the week did the year 4 commence? Now we have a number that +is divisible by 4, it being the first leap-year in the era, so we have 4 ÷ +4 = 1; 4 + 1 = 5; 5 ÷ 7 = 0, remainder 5. Then 10 - 5 = 5; therefore, E +being the 5th letter, is dominical letter for that part of the year which +follows the 29th of February, while F, the letter that follows it, is +dominical letter for January and February. Now reading from F to A, the +letter for January, we have F Sunday, G Monday, A Tuesday; hence January +commenced on Tuesday. + +Now we have disposed of the first four years of the era; the dominical +letters being B, A, G, and F, E. Hence it is evident, while one year +consists of an even number of weeks and one day, two years of an even +number of weeks and two days, three years of an even number of weeks and +three days, that every fourth year, by intercalation, is made to consist +of 366 days; so that four years consist of an even number of weeks and +five days; for we have (4 ÷ 4) + 4 = 5, the dominical letter going back +from G in the year 3, to F, for January and February in the year 4, and +from F to E for the rest of the year, causing the following year to +commence two days later in the week than the year preceding. + +The year 1 had 53 Saturdays; the year 2, 53 Sundays; the year 3, 53 +Mondays, and the year 4, 53 Tuesdays and 53 Wednesdays, causing the year 5 +to commence on Thursday, two days later in the week than the preceding +year. Now what is true concerning the first four years of the era, is true +concerning all the future years, and the reason for the divisions, +additions and subtractions in finding the dominical letter is evident. + +The Declaration of Independence was signed July 4, 1776. On what day of +the week did it occur? We have then 1776 ÷ 4 = 444; 1776 + 444 = 2220; +2220 ÷ 7 = 317, remainder 1. Then 7 - 1 = 6, therefore F and G are the +dominical letters for 1776, G for January and February, and F for the rest +of the year. Now reading from F to G, the letter for July, we have F +Sunday, G Monday; hence July commenced on Monday, and the fourth was +Thursday. On what day of the week did Lee surrender to Grant, which +occurred on April 9th, 1865? We have then 1865 ÷ 4 = 466+; 1865 + 466 = +2331; 2331 ÷ 7 = 333, remainder 0. Then 1 - 0 = 1; therefore, A being the +first letter, is dominical letter for 1865. Now reading from A to G, the +letter for April, we have A Sunday, B Monday, C Tuesday, etc. Hence April +commenced on Saturday, and the 9th was Sunday. + +Benjamin Harrison was inaugurated President of the United States on +Monday, March 4, 1889. On what day of the week will the 4th of March fall +in 1989? We have then 1989 ÷ 4 = 497+; 1989 + 497 = 2486; 2486 ÷ 7 = 355, +remainder 1. Then 2 - 1 = 1; therefore, A being the first letter, is +dominical letter for 1989. Now, reading from A to D, the letter for March, +we have A Sunday, B Monday, C Tuesday, and D Wednesday; hence March will +commence on Wednesday, and the 4th will fall on Saturday. Columbus landed +on the island of San Salvador on Friday, October 12, 1492. On what day of +the month and on what day of the week will the four hundredth anniversary +fall in 1892? + +The day of the month on which Columbus landed is, of course, the day to be +observed in commemoration of that event. The Julian calendar, which was +then in use throughout Europe, and the very best that had ever been given +to the world, made the year too long by more than eleven minutes. Those +eleven minutes a year had accumulated, from the council of Nice, in 325, +to the discovery of America, in 1492, to nine days, so that the civil year +was nine days behind the true or solar time; that is, when the Earth, in +her annual revolution, had arrived at that point of the ecliptic +coinciding with the 21st of October, the civil year, according to the +Julian calendar, was the 12th. + +Now, to restore the coincidence, the nine days must be dropped, or +suppressed, calling what was erroneously called the 12th of October, the +21st. Since the Julian calendar was corrected by Gregory, in 1582, we have +so intercalated as to retain, very nearly, the coincidence of the solar +and the civil year. It has already been shown in Chapter III, (q. v.) that +in the Gregorian calendar, the cycle which restores the coincidence of the +day of the month and the day of the week, is completed in 400 years; so +that after 400 years, events will again transpire in the same order, on +the same day of the week. Now, as Columbus landed on Friday, October 21st, +1492, so Friday, October 21st, 1892, is the day of the month and also the +day of the week to be observed in commemoration of that event. We have +then 1892 ÷ 4 = 473; 1892 + 473 = 2365; 2365 ÷ 7 = 337, remainder 6. Then +8 - 6 = 2; therefore, B and C are dominical letters for 1892, C for +January and February, and B for the rest of the year. Now, reading from B +to A, the letter for October, we have B Sunday, C Monday, etc. Hence +October will commence on Saturday and the 21st will be Friday. + +Although there was an error of thirteen days in the Julian calendar when +it was reformed by Gregory, in 1582, there was a correction made of only +ten days. There was still an error of three days from the time of Julius +Cæsar to the Council of Nice, which remained uncorrected. Gregory restored +the vernal equinox to the 21st of March, its date at the meeting of that +council, not to the place it occupied in the time of Cæsar, namely, the +24th of March. Had he done so it would now fall on the 24th, by adopting +the Gregorian rule of intercalation. Appendix H. + +If desirable calculations may be made in both Old and New Styles from the +year of our Lord 300. There is no perceptible discrepancy in the +calendars, however, until the close of the 4th century, when it amounts to +nearly one day, reckoned in round numbers one day. Now in order to make +the calculation, proceed according to rule already given for finding the +dominical letter, and for New Style take the remainders after dividing by +seven from the numbers in the following table: + + From 400 to 500 From 4 or 11 + " 500 " 600 " 5 " 12 + " 600 " 700 " 6 " 13 + " 700 " 900 " 7 + " 900 " 1000 " 1 " 8 + " 1000 " 1100 " 2 " 9 + " 1100 " 1300 " 3 " 10 + " 1300 " 1400 " 4 " 11 + " 1400 " 1500 " 5 " 12 + " 1500 " 1700 " 6 " 13 + +It will be found by calculation that from the year + + 400 to 500 the discrepancy is 1 day + 500 " 600 " " " 2 " + 600 " 700 " " " 3 " + 700 " 900 " " " 4 " + 900 " 1000 " " " 5 " + 1000 " 1100 " " " 6 " + 1100 " 1300 " " " 7 " + 1300 " 1400 " " " 8 " + 1400 " 1500 " " " 9 " + 1500 " 1700 " " " 10 " + +Hence the necessity, in reforming the calendar in 1582, of suppressing ten +days. (See table on 59th page.) On what day of the week did January +commence in 450? We have then 450 ÷ 4 = 112+; 450 + 112 = 562; 562 ÷ 7 = +80, remainder 2. Then 3 - 2 = 1; therefore, A being the first letter, is +dominical letter for 450, Old Style, and January commenced on Sunday. For +New Style we have 4 - 2 = 2; therefore, B being the second letter, is +dominical letter for the year 450. Now reading from B to A, the letter for +January, we have B Sunday, C Monday, D Tuesday, etc. + +Hence, January commenced on Saturday. Old Style makes Sunday the first +day; New Style makes Saturday the first and Sunday the second. On what day +of the week did January commence in the year 1250? We have then 1250 ÷ 4 = +312+; 1250 + 312 = 1562; 1562 ÷ 7 = 223, remainder 1. Then 3 - 1 = 2; +therefore, B being the second letter, is dominical letter for the year +1250, Old Style. Now, reading from B to A, the letter for January, we have +B Sunday, C Monday, etc. Hence January commenced on Saturday. B is also +dominical letter, New Style; for we take the remainder after dividing by +7, from the same number. + +As both Old and New Styles have the same dominical letter, so both make +January to commence on the same day of the week; but Old Style, during +this century, is seven days behind the true time, so that when it is the +first day of January by the Old, it is the eighth by the New. + + Vernal equinox in the time of Numa, about 700 B. C. + + It is here seen by the errors of the Julian Calendar + the Vernal Equinox is made to occur + three days earlier every 400 years, so + that in 1582 it fell on the + 11th instead of the + 21st of March. 18 + + 17 + + 16 + + 15 + + 14 + + 13 + + 12 + + 11 By suppressing 10 d + + Hou + + " + + " + + + + Hou + + " + + " + + + + By the Gregorian rule of intercalation the coincidence of + years. + + + March 24, 46 B. C. + + 23 | | 1 A. D. + | Restored | + 22 | | 100 " " + | by | + 21 | | 300 " " + | | | | Julius | + 20 | | | | | 400 " " + | | | | Cæsar, | + 19 | Vernal | | | 500 " " + | equinox | | 46 B. C., | + | at the | | | 600 " " + | Council | | to the | + | of | | | 800 " " + | Nice, | | place it | + | 325 | | | 900 " " + | A. D. | | occupied | + | | | | | 1000 " " + | | | | in the | + | | | | | 1200 " " + | | | | time of | + | | | | | 1300 " " + | | | | Numa. | + | | | | | 1400 " " + | | | | | + ays, Coincidence 0 Restored in | | 1600 " " + | | | + rs behind time, 18 | 6 in advance. | | 1700 " " + | | | + " " 12 | 12 " " | | 1800 " " + | | | + " " 6 | 18 " " | | 1900 " " + | | | + Coincidence 0 Restored. | | 2000 " " + | | | + rs behind time, 18 | 6 in advance. | | 2100 " " + | | | + " " 12 | 12 " " | | 2200 " " + | | | + " " 6 | 18 " " | | 2300 " " + | | | + Coincidence 0 Restored. | | 2400 " " + + the solar and civil year is restored very nearly every 400 + +Appendix I. + + + + +CHAPTER VI. + +A SIMPLE METHOD FOR FINDING THE DAY OF THE WEEK OF EVENTS WHICH OCCUR +QUADRENNIALLY. + + +The inaugural of the Presidents. The day of the week on which they have +occurred, and on which they will occur for the next one hundred years: + + April 30th, 1789, Thursday, George Washington. + March 4th, 1793, Monday, " " + " " 1797, Saturday, John Adams + " " 1801, Wednesday, Thomas Jefferson. + " " 1805, Monday, " " + " " 1809, Saturday, James Madison. + " " 1813, Thursday, " " + " " 1817, Tuesday, James Monroe. + " " 1821, Sunday, " " + " " 1825, Friday, John Q. Adams. + " " 1829, Wednesday, Andrew Jackson. + " " 1833, Monday, " " + " " 1837, Saturday, Martin Van Buren. + " " 1841, Thursday, Wm. H. Harrison. + " " 1845, Tuesday, James K. Polk. + " " 1849, Sunday, Zachary Taylor. + " " 1853, Friday, Franklin Pierce. + " " 1857, Wednesday, James Buchanan. + " " 1861, Monday, Abraham Lincoln. + " " 1865, Saturday, " " + " " 1869, Thursday, Ulysses S. Grant. + " " 1873, Tuesday, " " + " " 1877, Sunday, Rutherford B. Hays. + " " 1881, Friday, James A. Garfield. + " " 1885, Wednesday, Grover Cleveland. + " " 1889, Monday, Benjamin Harrison. + " " 1893, Saturday, Grover Cleveland. + " " 1897, Thursday, + " " 1901, Monday, + " " 1905, Saturday, + " " 1909, Thursday, + " " 1913, Tuesday, + " " 1917, Sunday, + " " 1921, Friday, + " " 1925, Wednesday, + " " 1929, Monday, + " " 1933, Saturday, + " " 1937, Thursday, + " " 1941, Tuesday, + " " 1945, Sunday, + " " 1949, Friday, + " " 1953, Wednesday, + " " 1957, Monday, + " " 1961, Saturday, + " " 1965, Thursday, + " " 1969, Tuesday, + " " 1973, Sunday, + " " 1977, Friday, + " " 1981, Wednesday, + " " 1985, Monday, + " " 1989, Saturday, + " " 1993, Thursday. + +Any one understanding what has been said in a preceding chapter concerning +the dominical letter, can very easily make out such a table without going +through the process of making calculations for every year. As every +succeeding year, or any day of the year, commences one day later in the +week than the year preceding, and two days later in leap-year, which makes +five days every four years, and as the Presidential term is four years, so +every inaugural occurs five days later in the week than it did in the +preceding term. + +Now, as counting forward five days is equivalent to counting back two, it +will be much more convenient to count back two days every term. There is +one exception, however, to this rule; the year which completes the century +is reckoned as a common year (that is, three centuries out of four), +consequently we count forward only four days or back three. + +Commencing, then, with the second inaugural of Washington, which occurred +on Monday, March 4, 1793, and counting back two days to Saturday in 1797, +three days to Wednesday in 1801 and two days to 1805, and so on two days +every term till 1901, when, for reasons already given, we count back three +days again for one term only, after which it will be two days for the next +two hundred years; hence anyone can make his calculations as he writes, +and as fast as he can write. See table on 61st page. + + +SOME PECULIARITIES CONCERNING EVENTS WHICH FALL ON THE TWENTY-NINTH DAY OF +FEBRUARY. + +The civil year and the day must be regarded as commencing at the same +instant. We cannot well reckon a fraction of a day, giving to February 28 +days and 6 hours, making the following month to commence six hours later +every year; if so, then March, for example, in + + 1888 would commence at 12 m. night. + 1889 " " " 6 a. m. + 1890 " " " 12 m. + 1891 " " " 6 p. m. + 1892 " " " 12 m. night, + +again, and so on. + +Instead of doing so, we wait until the fraction accumulates to a whole +day; then give to February 29 days, and the year 366. Therefore, events +which fall on the 29th of February cannot be celebrated annually, but only +quadrennially; and at the close of those centuries in which the +intercalations are suppressed only octennially. For example: From the year +1696 to 1704, 1796 to 1804, and 1896 to 1904, there is no 29th day of +February; consequently no day of the month in the civil year on which an +event falling on the 29th of February could be celebrated. Therefore, a +person born on the 29th of February, 1896, could celebrate no birthday +till 1904, a period of eight years. + +In every common year February has 28 days, each day of the week being +contained in the number of days in the month four times; but in leap-year, +when February has 29 days, the day which begins and ends the month is +contained five times. Let us suppose that in a certain year, when February +has 29 days, the month comes in on Friday; it also must necessarily end on +Friday. + +After four years it will commence on Wednesday, and end on Wednesday, and +so on, going back two days in the week every four years, until after 28 +years we come back to Friday again. This, as has already been explained, +is the dominical or solar cycle. For example: February in + + The year 4 has five Fridays. + " " 8 " " Wednesdays. + " " 12 " " Mondays. + " " 16 " " Saturdays. + " " 20 " " Thursdays. + " " 24 " " Tuesdays. + " " 28 " " Sundays. + " " 32 " " Fridays. + +So that after 28 years we come back to Friday again; and so on every 28 +years, until change of style in 1582, when the Gregorian rule of +intercalation being adopted by suppressing the intercalations in three +centurial years out of four interrupts this order at the close of these +three centuries. For example--1700, 1800 and 1900, after which the cycle +of 28 years will be continued until 2100, and so on. The cycle being +interrupted by the Gregorian rule of intercalation, causes all events +which occur between 28 and 12 years of the close of the centuries to fall +on the same day of the week again in 40 years; and those events that fall +within 12 years of the close of these centuries, to fall on the same day +of the week again in 12 years; after which the cycle of 28 years will be +continued during the century. See following table: + + 1804 February has five Wednesdays. + 1808 " " " Mondays. + 1812 " " " Saturdays. + 1816 " " " Thursdays. + 1820 " " " Tuesdays. + 1824 " " " Sundays. + 1828 " " " Fridays. + 1832 " " " Wednesdays. + 1836 " " " Mondays. + 1840 " " " Saturdays. + 1844 " " " Thursdays. + 1848 " " " Tuesdays. + 1852 " " " Sundays. + 1856 " " " Fridays. + 1860 " " " Wednesdays. + 1864 " " " Mondays. + 1868 " " " Saturdays. + 1872 " " " Thursdays. + 1876 " " " Tuesdays. + 1880 " " " Sundays. + 1884 " " " Fridays. + 1888 " " " Wednesdays. + 1892 " " " Mondays. + 1896 " " " Saturdays. + 1900 + 1904 " " " Mondays. + 1908 " " " Saturdays. + 1912 " " " Thursdays. + 1916 " " " Tuesdays. + 1920 " " " Sundays. + 1924 " " " Fridays. + 1928 " " " Wednesdays. + +It will be seen from this table that in 1804 February had five Wednesdays; +and then again in 1832, 1860 and 1888; then suppressing the intercalation +in the year 1900 suppresses the 29th of February; so opposite 1900 in the +table is blank, and the 29th of February does not occur again till 1904, +and the five Wednesdays do not occur again till 1928--that is, 40 years +from 1888, when it last occurred. + +Again taking the five Mondays which occurred first in this century, in +1808, and then again in 1836, 1864 and in 1892, you will see, for reasons +already given, that it will occur again in 12 years, that is, in 1904; and +so on with all the days of the week, when it will be seen what is peculiar +concerning the 29th of February. + +But attention is particularly called to the five Thursdays, which occur +first in this century 1816, and then again in 1844 and 1872, the last date +being within 28 years of the close of the century. Suppressing the +intercalation suppresses the 29th of February; consequently the five +Thursdays do not occur again till 1912, that is 40 years from the +preceding date, after which the cycle will be continued for two hundred +years. + +Hence it may be seen that the dominical or solar cycle of 28 years is so +interrupted at the close of these centuries by the suppression of the +leap-year, that certain events do not occur again on the same day of the +week under 40 years, while others are repeated again on the same day of +the week in 12 years; also the number of years in the cycle, that is 28 + +12 = 40. + +And again the change of style in 1582, causes all events which occur +between 28 and 8 years of that change, to fall again on the same day of +the week in 36 years, and all that occur within 8 years of that change to +be repeated again on the same day of the week in 8 years, after which the +cycle of 28 years is continued for 100 years; also that the number of +years in the cycle, that is, 28 + 8 = 36. + + + + +CHAPTER VII. + +RULES FOR FINDING THE DAY OF THE WEEK OF EVENTS THAT TRANSPIRED PRIOR TO +THE CHRISTIAN ERA. + + +First, it should be understood that the year 4 is the first leap year in +our era, reckoning from the year 1 B. C., which must necessarily be leap +year; so that the odd numbers 1, 5, 9, 13, etc., are leap years. Hence +every year that is divisible by four and one remainder, is leap year; if +no remainder, it is the first year after leap-year; if 3, the second; if +2, the third, thus: + + 45 ÷ 4 = 11, remainder, 1, + 44 ÷ 4 = 11, no remainder, + 43 ÷ 4 = 10, remainder, 3, + 42 ÷ 4 = 10, remainder, 2, + 41 ÷ 4 = 10, remainder, 1, + +and so on, every year being divided by four and 1 remainder is leap-year +of 366 days. It should be borne in mind that the same calendar was in use +without any correction from the days of Julius Cæsar 46 B. C. to Pope +Gregory XIII in 1582; consequently the method of finding the dominical +letter is, in some respects, similar to the one already given on the 44th +page. But in some respects the one is the reverse of the other, for we +reckon backward and forward from a fixed point--the era; that is the +numbers increase each way from the era. Also the dominical letters occur +in the natural order of the letters in reckoning backward, but exactly the +reverse in reckoning forward. See table on the 73d page, where the +dominical letter is placed opposite each year from 45 B. C. to 45 A. D. +Now we use the same number 3, because C, the third letter is dominical +letter for the year 1 B. C., the point from which we reckon. But instead +of taking the remainder, after dividing by 7, _from_ 3 or 10, to find the +number of the letter, as in Part Second, Chapter IV, (q. v.) we add the +remainder _to_ 3; hence we have the following: + + +RULE. + +Divide the number of the given year by 4, neglecting the remainders, and +add the quotient to the given number, divide this amount by 7, and add the +remainder to 3, and that amount will give the number of the letter, +calling A, 1; B, 2; C, 3, etc.; except the first year after leap-year, +(which is the year exactly divisible by 4), the number of the letter is +one less than is indicated by the rule. + +This rule gives the dominical letter for January and February only, in +leap-year, while the letter that precedes it, is the letter for the rest +of the year. If the amount be greater than seven, we should reckon from A +to A or B again. + +It has already been stated in Part First, Chapter III, (q. v.), that a +change was made by Augustus Cæsar about 8 B. C., in the number of days in +the month; and, as this change effects the day of the week on which +certain events fall, it becomes necessary that they should be presented as +they were arranged by Julius Cæsar, and as corrected by Augustus. Julius +Cæsar gave to February 29 days in common years, and in leap-year 30. This +arrangement was the very best that could possibly be made, but, as has +already been shown, it was interrupted to gratify the vanity of Augustus. + +The left hand column in the table on the 72d page represents the number of +days in each month from the days of Julius Cæsar to Augustus, a period of +37 years. The right hand column represents the number of days in the +months as they now are, and have been since the change was made by +Augustus, 8 B. C. Consequently the rule for finding the day of the week on +which events have fallen for the 37 years prior to the last mentioned +date, is not perfectly exact, and needs a little explanation here. + +The rule itself is given, and fully explained in Part Second, Chapter V, +(q. v.) but cannot be applied to the 37 years without some correction. In +all the months marked with a star, events fall one day later in the week +than that which is indicated by the rule. This should be borne in mind, +and make the event one day later in the week than that which is found by +the rule. For example, Julius Cæsar was assassinated on the 15th of March, +44 B. C. By giving to February 28 days the first day of March would fall +on Wednesday, and, of course, the 15th would be Wednesday. But Cæsar gave +to February 29 days, so that the first day of March fell on Thursday, and +the 15th was Thursday. + +Hence, every event from March to September will fall one day later in the +week than the rule indicates. But the rule is applicable to September, for +it will make no difference whether there are 29 days in February or 31 in +August, there are the same number of days from February to September. But +the 31 days in September will cause all events to fall one day later in +the week during the month of October, but they coincide again during the +month of November. The order is interrupted again in December by giving 31 +days to November. See following table: + + _As Arranged by Julius_ | _As Corrected by Augustus,_ + _Cæsar._ | _8 B. C._ + | + January, 31 | January, 31 + February, 29 | February, 28 + March, 31* | March, 31 + April, 30* | April, 30 + May, 31* | May, 31 + June, 30* | June, 30 + July, 31* | July, 31 + August, 30* | August, 31 + September, 31 | September, 30 + October, 30* | October, 31 + November, 31 | November, 30 + December, 30* | December, 31 + + + ---------+-----+---------+-----+---------+-----+---------+----- + Dominical|Year.|Dominical|Year.|Dominical|Year.|Dominical|Year. + Letter. | | Letter. | | Letter. | | Letter. | + ---------+-----+---------+-----+---------+-----+---------+----- + |B. C.| |B. C.| |A. D.| |A. D. + cb | 45 | b | 22 | b | 1 | c | 23 + a | 44 | ag | 21 | a | 2 | ba | 24 + g | 43 | f | 20 | g | 3 | g | 25 + f | 42 | e | 19 | fe | 4 | f | 26 + ed | 41 | d | 18 | d | 5 | e | 27 + c | 40 | cb | 17 | c | 6 | dc | 28 + b | 39 | a | 16 | b | 7 | b | 29 + a | 38 | g | 15 | ag | 8 | a | 30 + gf | 37 | f | 14 | f | 9 | g | 31 + e | 36 | ed | 13 | e | 10 | fe | 32 + d | 35 | c | 12 | d | 11 | d | 33 + c | 34 | b | 11 | cb | 12 | c | 34 + ba | 33 | a | 10 | a | 13 | b | 35 + g | 32 | gf | 9 | g | 14 | ag | 36 + f | 31 | e | 8 | f | 15 | f | 37 + e | 30 | d | 7 | ed | 16 | e | 38 + dc | 29 | c | 6 | c | 17 | d | 39 + b | 28 | ba | 5 | b | 18 | cb | 40 + a | 27 | g | 4 | a | 19 | a | 41 + g | 26 | f | 3 | gf | 20 | g | 42 + fe | 25 | e | 2 | e | 21 | f | 43 + d | 24 | dc | 1 | d | 22 | ed | 44 + c | 23 | | | | | c | 45 + ---------+-----+---------+-----+---------+-----+---------+----- + + + + +PART THIRD. + +CYCLES--JULIAN PERIOD--EASTER. + +HEBREW CALENDAR. + + + + +CHAPTER I. + +THE SOLAR CYCLE. + + +Cycle, (Latin _Cyclus_, ring or circle). The revolution of a certain +period of time which finishes and re-commences perpetually. Cycles were +invented for the purpose of chronology, and for marking the intervals in +which two or more periods of unequal length are each completed a certain +number of times, so that both begin exactly in the same circumstance as at +first. Cycles used in chronology are three: The solar cycle, the lunar +cycle, and the cycle of indiction. + +The solar cycle is a period of time after which the same days of the year +recur on the same days of the week. If every year contained 365 days, then +every year would commence one day later in the week than the year +preceding, and the cycle would be completed in seven years. For if the +first day of January, in any given year, fall on Sunday, then the +following year on Monday, the third on Tuesday, and so on to Sunday again +in seven years. + +But this order is interrupted in the Julian calendar every four years by +giving to February 29 days, and consequently the year 366. Now the number +of years in the intercalary period being four and the days of the week +being seven, their product is 4 × 7 = 28; twenty-eight years then is a +period after which the first day of the year and the first day of every +month recur again in the same order on the same day of the week. This +period is called the solar cycle or the cycle of the sun, the origin of +which is unknown; but is supposed to have been invented about the time of +the Council of Nice, in the year of our Lord 325; but the first year of +the cycle is placed by chronologists nine years before the commencement of +the Christian era. + +Hence the year of the cycle corresponding to any given year in the Julian +calendar is found by the following rule: Add nine to the date and divide +the sum by twenty-eight; the quotient is the number of cycles elapsed, and +the remainder is the year of the cycle. Should there be no remainder, the +proposed year is the twenty-eighth, or last of the cycle. Thus, for the +year 1892, we have (1892 + 9) ÷ 28 = 67, remainder 25. Therefore, 67 is +the number of cycles, and 25 the number in the cycle. + + + + +CHAPTER II. + +THE LUNAR CYCLE. + + +The Lunar cycle, or the cycle of the moon, is a period of nineteen years, +after which the new and full moons fall on the same days of the year as +they did nineteen years before. This cycle was invented by Meton, a +celebrated astronomer of Athens, and may be regarded as the masterpiece of +ancient astronomy. In nineteen solar years there are 235 lunations, a +number which, on being divided by nineteen, gives twelve lunations, with +seven of a remainder, to be distributed among the years of the period. + +The period of Meton, therefore, consisted of twelve years containing +twelve months each, and seven years containing thirteen mouths each, and +these last formed the third, fifth, eighth, eleventh, thirteenth, +sixteenth, and nineteenth years of the cycle. As it had now been +discovered that the exact length of the lunation is a little more than +twenty-nine and a half days, it became necessary to abandon the alternate +succession of full and deficient months; and, in order to preserve a more +accurate correspondence between the civil month and the lunation, Meton +divided the cycle into 125 full months of 30 days, and 110 deficient +months of 29 days each. The number of days in the period was, therefore, +6940; for (125 × 30) + (110 × 29) = 6940. + +In order to distribute the deficient months through the period in the most +equable manner, the whole period may be regarded as consisting of 235 full +months of thirty days, or 7050 days, from which 110 days are to be +deducted; for (235 × 30) = 7050; 7050 - 110 = 6940, as before. This gives +one day to be suppressed in sixty-four, so that if we suppose the months +to contain each thirty days, and then omit every sixty-fourth day in +reckoning from the beginning of the period, those months in which the +omission takes place will, of course, be the deficient months. + +The number of days in the period being known, it is easy to ascertain its +accuracy both in respect of the solar and lunar motions. The exact length +of nineteen solar years is (365d, 5h, 48m, 49.62s.) × 19 = 6939d, 14h, +27m, 42.78s.; hence, the period, which is exactly 6940 days, exceeds +nineteen annual revolutions of the earth by a little more than nine and a +half hours. On the other hand, the exact time of the synodic revolution of +the moon is 29d, 12h, 44m, 2.87s.; 235 lunations, therefore, contain 235 × +(29d, 12h, 44m, 2.87s.) = (6939d, 16h, 31m, 14.45s.), so that the period +exceeds 235 lunations by nearly seven and a half hours. + +At the end of four cycles, or seventy-six years, the accumulation of the +seven and a half hours of difference between the cycle and 235 lunations +amounts to thirty hours, or one whole day and six hours. Calippus, +therefore, in order to make a correction of the Metonic cycle, proposed to +quadruple the period of Meton, and deduct one day at the end of that time +by changing one of the full months into a deficient month. The period of +Calippus, therefore, consisted of three Metonic cycles of 6940 days each, +and a period of 6939 days; and its error in respect to the moon, +consequently, amounted to only six hours, or to one day in 304 years. +This period exceeds seventy-six true solar years by 14h, 9m, 8.88s., but +coincides exactly with seventy-six Julian years; and in the time of +Calippus the length of the solar year was almost universally supposed to +be exactly 365-1/4 days. + + + + +CHAPTER III. + +THE LUNAR CYCLE AND GOLDEN NUMBER. + + +In connecting the lunar month with the solar year, the framers of the +ecclesiastical calendar adopted the period of Meton, or lunar cycle, which +they supposed to be exact. A different arrangement has, however, been +followed with respect to the distribution of the months. The lunations are +supposed to consist of twenty-nine and thirty days alternately, or the +lunar year of 354 days; and in order to make up nineteen solar years, six +embolismic or intercalary months, of thirty days each, are introduced in +the course of the cycle, and one of twenty-nine days is added at the end. +This gives (19 × 354) + (6 × 30) + 29 = 6935 days, to be distributed among +235 lunar months. + +But every leap-year one day must be added to the lunar month in which the +29th of February is included. Now if leap-year happened on the first, +second or third year of the period, there will be five leap-years in the +period, but only four when the first leap-year falls on the fourth. In the +former case the number of days in the period becomes 6940, and in the +latter 6939. The mean length of the cycle is, therefore, 6939-3/4 days, +agreeing exactly with nineteen Julian years. By means of the lunar cycle +the new moons of the calendar were indicated before the reformation in +1582. As the cycle restores these phenomena to the same days of the civil +month, they will fall on the same days in any two years which occupy the +same place in the cycle; consequently a table of the moon's phases for +nineteen years will serve for any year whatever when we know its number in +the cycle. + +The number of the year in the cycle is called the Golden Number; either +because it was so termed by the Greeks, who, on account of its utility, +ordered it to be inscribed in letters of gold in their temples, or more +probably because it was usual to distinguish it by red letters in the +calendar. The Golden Numbers were introduced into the calendar about the +year 530, but disposed as they would have been if they had been inserted +at the time of the Council of Nice. The cycle is supposed to commence with +the year in which the new moon falls on the first day of January, which +took place the year preceding the commencement of our era. + +Hence to find the Golden Number for any year, we have the following rule: +Add one to the date, divide the sum by nineteen; the quotient is the +number of cycles elapsed, and the remainder is the Golden Number. Should +there be no remainder, the proposed year is, of course, the last or +nineteenth of the cycle. Thus, for the year 1892, we have (1892 + 1) ÷ 19 += 99, remainder 12; therefore, 99 is the number of cycles, and 12 the +number in the cycle, or the Golden number. + +It ought to be remarked that the new moons determined in this manner, may +differ from the astronomical new moons sometimes as much as two days. The +reason is, that the sum of the solar and lunar inequalities which are +compensated in the whole period, may amount in certain cases to 10 degrees +and thereby cause the new moon to arrive on the second day before or after +its mean time. + +The cycle of the sun brings back the days of the month to the same day of +the week; the cycle of the moon restores the new moons to the same day of +the month; therefore, 28 × 19 = 532 years, includes all the variations in +respect of the new moons and the dominical letter, and is consequently a +period after which the new moons again occur on the same day of the month +and the same day of the week. This is called the Dionysian or Great +Paschal Period, from its having been employed by Dionysius Exiguus in +determining Easter Sunday. + + + + +CHAPTER IV. + +CYCLE OF INDICTION, AND THE JULIAN PERIOD. + + +The cycle of Indiction or Roman Indiction, is a period of fifteen years; +not astronomical like the two former, but entirely arbitrary. Its origin +and the purpose for which it was established are alike uncertain; but it +is conjectured that it was introduced by Constantine the Great, about the +year 312 of the common era, and had reference to certain judicial acts +that took place under the Greek emperors at stated intervals of fifteen +years. In chronological reckoning, it is considered as having commenced on +the first day of January of the year 313. + +By extending it backward, it will be found that the cycle commenced three +years before the beginning of our era. In order, therefore, to find the +number of any year in the cycle of indiction, we have this rule: Add three +to the date, divide the number by fifteen; and the remainder is the year +of the indiction. Should there be no remainder, the proposed year is the +fifteenth or last of the cycle. Thus, for the year 1892, we have (1892 + +3) ÷ 15 = 126, remainder 5. Therefore, 5 is the number in the cycle. + +The Julian period, proposed by the celebrated Joseph Scaliger, as an +universal measure of chronology, is a period of 7980 years, and is formed +by the continual multiplication of the three numbers, 28, 19 and 15; that +is, of the cycle of the sun, the cycle of the moon, and the cycle of +indiction. Thus, (28 × 19 × 15) = 7980. In the course of this long period +no two years can be expressed by the same numbers in all the three cycles. + +The first year of the Christian era had 10 for its number in the cycle of +the sun, 2 in the cycle of the moon, and 4 in the cycle of the indiction. +Now, it is found by actual calculation, that the only number less than +7980 which, on being divided successively by 28, 19, and 15, leaves the +respective remainders 10, 2 and 4, is 4714. Hence, the first year of the +Christian era corresponded with the year 4714 of the Julian period, which +period coincides with the 710th before the common mundane era 4004 B. C.; +for 4004 + 710 = 4714. Hence, also, the year of our era corresponding to +any other year of the period, or _vice versa_, is found by the following +rule: + +When the given year is anterior to the commencement of the era, subtract +the number of the year of the Julian period from 4714, and the remainder +is the year before Christ; or, subtract the year before Christ from 4714, +and the remainder is the corresponding year in the Julian period. Thus, +Rome was founded in the year 3960 of the Julian period. What was the year +before Christ? We have then 4714 - 3960 = 754. Julius Cæsar was +assassinated 44 years before Christ, what was the corresponding year of +the Julian period? We have then, 4714 - 44 = 4670. + +When the given year is after Christ, subtract 4713 from the year of the +period, and the remainder is the year of the era; or add 4713 to the year +of the era, and the sum is the corresponding year in the Julian period. +Thus, the Council of Nice was convened in the year 5038 of the Julian +period, what was the year of our era? We have then, 5038 - 4713 = 325. +What year of the Julian period corresponds with the present year, 1892? We +have then, 4713 + 1892 = 6605. + + + + +CHAPTER V. + +EASTER. + + +Easter (Germ. _Ostern_, Old Saxon _Oster_, from _Osten_, signifying +rising). The English name is probably derived from Ostera or Eostre, the +Teutonic goddess of spring, whose festival occurred about the same time of +the year as the celebration of Easter. The Hebrew-Greek word Pascha has +passed into the name given to this feast by most Christian nations. This +festival is held in commemoration of our Lord's resurrection. + +The Jews celebrated their passover, in conformity with the directions +given them by Moses, on the 14th day of the month Nisan, being the lunar +month of which the 14th day either falls on or next follows the day of the +vernal equinox. In the year of our Lord's crucifixion this fell on a +Friday; the resurrection, therefore, took place on the first day of the +week, which from thence is denominated the Lord's Day. + +The primitive Christians, in celebrating this anniversary, fell into two +different systems. The Western churches observed the nearest Sunday to the +full moon of Nisan, taking no account of the day on which the passover +would be celebrated. The Asiatics, on the other hand, following the Jewish +calendar, adopted the 14th of Nisan upon which to commemorate the +crucifixion, and observed the festival of Easter on the third day +following, upon whatever day of the week that might fall, hence they +obtained the name of Quartodecimans, (from quarto, four, and decem, ten,) +the fourteenth day men. The former appealed to the authority of St. Peter +and St. Paul, the latter to that of St. John. + +The dispute which took place upon this point in the second and third +centuries of our era is remarkable, as connected with perhaps the first +event which can be brought to bear upon the question of the primacy of the +Roman bishop; and it is the more interesting as both parties are +accustomed to claim it as a testimony in favor of their own views. Victor, +bishop of Rome, wrote an imperious letter to the Asiatic bishops, +requiring their conformity to the Western rule; which was answered by +Polycrates, bishop of Ephesus, in the name of the rest, expressing their +resolution to maintain the custom handed down to them by their ancestors. +The Roman bishop thereupon broke off communion with them; but he was +rebuked by Irenaeus, of Lyons, and it was agreed by his mediation that +each party should retain its customs. Such continued to be the practice +till the time of Constantine, when the Council of Nice determined the +matter by the following Canons: + +_a_--Easter must be celebrated on a Sunday. + +_b_--This Sunday must follow the 14th day of the paschal moon, so that if +the 14th day of the paschal moon fall on a Sunday, then Easter must be +celebrated on the Sunday following. + +_c_--The paschal moon is that moon of which the 14th day either falls on +or next follows the day of the vernal equinox. + +_d_--The 21st of March is to be accounted the day of the vernal equinox. +(Appendix L.) + +Sometimes a misunderstanding has arisen from not observing that this +regulation is to be construed according to the tabular full moon as +determined from the epact, and not by the true full moon, which in +general, occurs one or two days earlier. From these conditions it follows, +that if the paschal full moon fall on Saturday, the 21st of March, then +Easter will happen on the 22d, its earliest possible date. For if the full +moon arrive on the 20th, it would not be the paschal full moon, which +cannot happen before the 21st, consequently the following moon is the +paschal full moon, which happens 30 days after the 20th of March, which is +the 19th of April. Now, if in this case the 19th of April is Sunday, then +Easter must be celebrated the following Sunday, or the 26th of April. +Hence, Easter Sunday cannot happen earlier than the 22d of March, or later +than the 26th of April. + +The observance of these rules renders it necessary to reconcile three +periods which have no common measure, namely, the week, the lunar month, +and the solar year; and as this can be done only approximately, and within +certain limits, the determination of Easter is an affair of considerable +nicety and complication. It has already been shown that the lunar cycle +contained 6939 days and 18 hours; also, that the exact time of 235 +lunations is 6939d, 16h, 31m, 14.45s. The difference, which is 1h, 28m, +45.55s., amounts to a day in 308 years, so that at the end of this time +the new moons occur one day earlier than they are indicated by the Golden +Numbers. During the 1257 years that elapsed between the Council of Nice +and the reformation, the error had accumulated to four days, so that the +new moons, which were marked in the calendar as happening, for example, on +the 5th of the month, actually fell on the 1st. + +It would have been easy to correct this error by placing the Golden +Numbers four lines higher in the new calendar, but the suppression of ten +days had already rendered it necessary to place them ten lines lower, and +to carry those which belonged, for example, to the 5th and 6th of the +month, to the 15th and 16th. But supposing this correction to have been +made, it would have become necessary, at the end of 308 years, to place +them one line higher, in consequence of the accumulation of the error of +the cycle to a whole day. On the other hand, as the Golden Numbers were +only adapted to the Julian calendar, every omission of the centenary +intercalation would require them to be placed one line lower, opposite the +6th, for example, instead of the 5th of the month, so that, generally +speaking, the places of the Golden Numbers would have to be changed every +century. On this account Lilius thought fit to reject the Golden Numbers +from the Calendar, and supply their places by another set of numbers +called Epacts, the use of which we shall now proceed to explain. + +Epact, (Greek _epaktos_, added or introduced). The excess of the solar +year beyond the lunar, employed in the calendar to signify the moon's age +at the beginning of the year. The common solar year consisted of 365 days +and the lunar year only 354 days, the difference is eleven; whence, if a +new moon fall on the first day of January in any year, the moon will be +eleven days old on the first day of the following year, and twenty-two +days old on the first of the third year. The numbers eleven and twenty-two +are therefore the epacts of those years respectively. Another addition of +eleven gives thirty-three for the epact of the fourth year; but in +consequence of the insertion of the intercalary month in each third year +of the lunar cycle, this epact is reduced to three; for 33 - 30 = 3. In +like manner the epacts of all the following years of the cycle are +obtained by successively adding eleven to the epact of the former year, +and rejecting thirty as often as the sum exceeds or equals that number. + +In order to show how the epacts are connected with the Golden Numbers, let +a cypher represent the new moon on the first day of January in any year, +then the epacts and Golden Numbers for a whole lunar cycle would be +represented thus: + + 1 2 3 4 5 6 7 8 9 + 0 11 22 3 14 25 6 17 28 + + 10 11 12 13 14 15 16 17 18 19 + 9 20 1 12 23 4 15 26 7 18 + +But the order is interrupted at the end of the cycle; for the epact of the +following year found in the same manner would be 18 + 11 = 29, whereas it +ought to be a cipher to correspond with the moon's age and the Golden +Number 1. The reason for this is, that the intercalary month, inserted at +the end of the cycle, contains only twenty-nine days instead of thirty; +whence, after 11 has been added to the epact of the year corresponding to +the Golden Number 19, we must reject twenty-nine instead of thirty, in +order to have the epact of the succeeding year; or, which comes to the +same thing, we must add twelve to the epact of the last year of the cycle, +and then reject thirty as before. Thus, 18 + 12 = 30; 30 - 30 = 0; the +cipher corresponding with the Golden Number 1. + +This method of forming the epacts might have been continued indefinitely +if the Julian intercalation had been followed without correction and the +cycle had been perfectly exact; but as neither of these suppositions is +true, two equations or corrections must be applied, one depending on the +error of the Julian year, which is called the solar equation; the other on +the errors of the lunar cycle, which is called the lunar equation. The +solar equation occurs three times in 400 years, namely, in every secular +year which is not a leap-year; for in this case the omission of the +intercalary day causes the new moons to arrive one day later in all the +following months, so that the moon's age at the end of the month is one +day less than it would have been if the intercalation had been made, and +the epacts must accordingly be all diminished by unity. Thus, the epacts +11, 22, 3, 14, etc., become 10, 21, 2, 13, etc. + +On the other hand, when the time by which the new moons anticipate the +lunar cycle amounts to a whole day, which, as we have seen, it does in 308 +years, the new moons will arrive one day earlier and the epacts must, +consequently, be increased by unity. Thus, the epacts 11, 22, 3, 14, etc., +in consequence of the lunar equation, becomes 12, 23, 4, 15, etc. In order +to preserve the uniformity of the calendar, the epacts are changed only at +the commencement of the century; the correction of the error of the lunar +cycle is therefore made at the end of 300 years. In the Gregorian calendar +this error is assumed to amount to a day in 312-1/2 years, or eight days +in 2500 years, an assumption which requires the line of epacts to be +changed seven times successively at the end of each period of 300 years, +and once at the end of 400 years; and from the manner in which the epacts +were disposed at the reformation, it was found most correct to suppose one +of the periods of 2500 years to terminate with the year 1800. + +The years in which the solar equation occurs, counting from the +reformation, are 1700, 1800, 1900, 2100, 2200, 2300, 2500, etc. Those in +which the lunar equation occurs are 1800, 2100, 2400, 2700, 3000, 3300, +3600, 3900, after which 4300, 4600, and so on. When the solar equation +occurs, the epacts are diminished by unity; when the lunar equation +occurs, the epacts are augmented by unity; and when both equations occur +together, as in 1800, 2100, 2700, etc., they compensate each other, and +the epacts are not changed. + + + + +CHAPTER VI. + +A NEW AND EASY METHOD OF FIXING THE DATE OF EASTER. + + +In determining the date of Easter, we make use of the numbers called +epacts; and, as these numbers have already been explained in the preceding +chapter, (q. v.) it will be necessary to give them only a brief notice +here. Epact, as has already been defined, is the excess of the solar year +beyond the lunar, employed in the calendar to signify the moon's age at +the beginning of the year; that is, if a new moon fall on the first day +of January in any year, it will be eleven days old on the first day of +the following year, and twenty-two days old on the first day of the third +year, and so on. + +Now, in this work, in fixing the date of Easter, we abandon the use of the +new moons altogether, and make calculations wholly from the paschal full +moons, which cannot happen earlier than the 21st of March, nor later than +the 19th of April. Appendix J. The epacts are here used to show the day of +the month on which the paschal full moons fall; that is, if the paschal +moon fall on a given day of the month in any year, it will happen eleven +days earlier the following year, and twenty-two days earlier the third +year, and so on. To illustrate, suppose the paschal moon fall on the 18th +of April in any given year, on the following year it would fall on the +7th, in the third year on the 27th of March; and in the fourth year the +moon would full on the 16th of March, but that would not be the paschal +moon, which cannot happen earlier than the 21st; so the following moon +would be the paschal moon, which happens thirty days later, or the 15th of +April; then the fifth year it would fall on the 4th of April, and so on. + +The solar and lunar equations or corrections are not made by change of +epacts, for only one line of epacts is used in this work, but these +corrections are made by a change of the day of the month on which the +cycle commences. This change is made at the beginning of a century, and, +of course, does not occur but once in a hundred years, and frequently no +change is made for two, and even three hundred years. The reason for +making these changes has been given in the preceding chapter, (q. v.), +and will again be noticed in the proper place. The line of epacts used are +thus represented, commencing with a cipher as the point of departure: 0, +11, 22, 3, 14, 25, 6, 17, 28, 9, 20, 1, 12, 23, 4, 15, 26, 7, 18. It +should be borne in mind that the epacts are obtained by successively +adding eleven to the epact of the former year, and rejecting thirty as +often as the sum exceeds or equals that number. But, as the intercalary +month inserted at the end of the cycle contains only 29 days, add twelve +instead of eleven, to eighteen, the last of the cycle, and then reject +thirty as before; thus, 18 + 12 = 30; then 30 - 30 = 0. The cycle being +completed, we again commence with the cipher as the point of departure. + +After having found the paschal full moons for one lunar cycle, a period of +nineteen years, then the paschal moons again occur in the same order, on +the same days of the month, as they did nineteen years before. Now, as has +also been shown in the preceding chapter, this cycle might have been +continued indefinitely had the Julian intercalation been followed without +correction, and the cycle been perfectly exact; but neither of these being +true, two equations or corrections must be made, one depending on the +error of the Julian calendar, which is called the solar-equation; the +other on the error of the lunar cycle, which is called the lunar equation. + +Every omission of the intercalary day, which occurs three times in 400 +years, will cause the full moons to fall one day later; for example, on +the 13th of the month instead of the 12th. On the other hand, as has also +been shown in the preceding chapter, the error of the lunar cycle is one +day in 300 years; so that at the end of every 300 years the full moons +will fall one day earlier, for example, on the 11th of the month instead +of the 12th. Now, when both equations occur together, they compensate each +other; that is, while the solar equation would cause the full moon to fall +on the 13th, the lunar equation would make it fall on the 11th; therefore, +no correction is to be made--there is nothing to correct. Had they +occurred singly, the full moon, at the beginning of the cycle, would have +fallen either on the 13th or the 11th; but as they occur together, no +change is made; and the full moons of the calendar will remain as they are +for the next one hundred years. + +Hence, the date of Easter may very easily be determined, as indicated in +the following tables (q. v.). It is known by actual calculation that the +paschal full moon fell on the 12th of April in the year 1596, which moon +was the first of a cycle after the reformation of the calendar by Gregory. +Now, by taking the epact of the following years of the cycle, which are +11, 22, 3, 14, 25, etc., from 12, the date of the first paschal moon, and +you will have all the moons of the cycle. Of course, the epacts 22, 25, +etc., cannot be taken from 12, but being carried back from the 12th of +April, they will show on what day in March the full moons fall. When the +epacts are greater than 12, it would be more convenient to take them from +43, as the number of days in March being 31, so 12 + 31 = 43. + +To find the paschal moons of the cycle, we have then this rule: If the +epact is less than 12, take it from 12; if greater, take it from 43, and +the remainder will be the date of the paschal moon; unless the full moon +fall before the 21st of March, in which case the following moon will be +the paschal moon, which happens thirty days later. But when the solar +equation occurs in 1710, causing the cycle to commence with the 13th of +April, then the epacts must be taken from 13, or 13 + 31 = 44. And again +in 1900, the correction makes the cycle commence on the 14th of April; so +the number from which the epacts are taken is 14, or 14 + 31 = 45, and so +on. Whenever there is a change of date of the paschal moon in the +beginning of the cycle, as there is again in 2204, 2318 and 2413, etc., as +may be seen in the following tables, then the epacts must be taken from +that date, or that date plus 31, the number of days in March. + +Or the date of the paschal moons may very easily be determined by taking +eleven successively from the date of every preceding full moon, and that +will give the date of the paschal moons; only it should be borne in mind +that, whenever the full moon falls before the 21st of March, the following +moon is the paschal moon, which happens thirty days later. + +As Easter Sunday is the first Sunday after the paschal full moon, so all +that remains to be done in fixing the date of Easter, is to find the day +of the month on which that Sunday falls; and as this can easily be done by +the use of the dominical letter, which letter and its use in fixing dates +having been fully explained in Part Second, Chapters IV and V, (q. v.), a +repetition seems to be unnecessary here. + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + gf | 1596 | April 12 | 14 | 0 | 1 + e | 1597 | " 1 | 6 | 11 | 2 + d | 1598 | March 21 | 22 | 22 | 3 + c | 1599 | April 9 | 11 | 3 | 4 + ba | 1600 | March 29 | 2 | 14 | 5 + g | 1601 | April 17 | 22 | 25 | 6 + f | 1602 | " 6 | 7 | 6 | 7 + e | 1603 | March 26 | 30 | 17 | 8 + dc | 1604 | April 14 | 18 | 28 | 9 + b | 1605 | " 3 | 10 | 9 | 10 + a | 1606 | March 23 | 26 | 20 | 11 + g | 1607 | April 11 | 15 | 1 | 12 + fe | 1608 | March 31 | 6 | 12 | 13 + d | 1609 | April 19 | 26 | 23 | 14 + c | 1610 | " 8 | 11 | 4 | 15 + b | 1611 | March 28 | 3 | 15 | 16 + ag | 1612 | April 16 | 22 | 26 | 17 + f | 1613 | " 5 | 7 | 7 | 18 + e | 1614 | March 25 | 30 | 18 | 19 + d | 1615 | April 12 | 19 | 0 | 1 + cb | 1616 | " 1 | 3 | 11 | 2 + a | 1617 | March 21 | 26 | 22 | 3 + g | 1618 | April 9 | 15 | 3 | 4 + f | 1619 | March 29 | 31 | 14 | 5 + ed | 1620 | April 17 | 19 | 25 | 6 + c | 1621 | " 6 | 11 | 6 | 7 + b | 1622 | March 26 | 27 | 17 | 8 + a | 1623 | April 14 | 16 | 28 | 9 + gf | 1624 | " 3 | 7 | 9 | 10 + e | 1625 | March 23 | 30 | 20 | 11 + d | 1626 | April 11 | 12 | 1 | 12 + c | 1627 | March 31 | 4 | 12 | 13 + ba | 1628 | April 19 | 23 | 23 | 14 + g | 1629 | " 8 | 15 | 4 | 15 + f | 1630 | March 28 | 31 | 15 | 16 + e | 1631 | April 16 | 20 | 26 | 17 + dc | 1632 | " 5 | 11 | 7 | 18 + b | 1633 | March 25 | 27 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +By close examination of the above tables, it will be seen that there is +just eleven days difference in the date of these paschal moons, from year +to year, through the whole lunar cycle, and through all lunar cycles. In +determining the date of Easter, it will also be seen, that whenever the +full moon falls before the 21st of March, then the following moon, which +happens thirty days later, is the paschal moon, as the 21st of March is +its earliest possible date. Also when the cycle is + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + a | 1634 | April 12 | 16 | 0 | 1 + g | 1635 | " 1 | 8 | 11 | 2 + fe | 1636 | March 21 | 23 | 22 | 3 + d | 1637 | April 9 | 12 | 3 | 4 + c | 1638 | March 29 | 4 | 14 | 5 + b | 1639 | April 17 | 24 | 25 | 6 + ag | 1640 | " 6 | 8 | 6 | 7 + f | 1641 | March 26 | 31 | 17 | 8 + e | 1642 | April 24 | 20 | 28 | 9 + d | 1643 | " 3 | 5 | 9 | 10 + cb | 1644 | March 23 | 27 | 20 | 11 + a | 1645 | April 11 | 16 | 1 | 12 + g | 1646 | March 31 | 1 | 12 | 13 + f | 1647 | April 19 | 21 | 23 | 14 + ed | 1648 | " 8 | 12 | 4 | 15 + c | 1649 | March 28 | 4 | 15 | 16 + b | 1650 | April 16 | 17 | 26 | 17 + a | 1651 | " 5 | 9 | 7 | 18 + gf | 1652 | March 25 | 31 | 18 | 19 + e | 1653 | April 12 | 13 | 0 | 1 + d | 1654 | " 1 | 5 | 11 | 2 + c | 1655 | March 21 | 28 | 22 | 3 + ba | 1656 | April 9 | 16 | 3 | 4 + g | 1657 | March 29 | 1 | 14 | 5 + f | 1658 | April 17 | 21 | 25 | 6 + e | 1659 | " 6 | 13 | 6 | 7 + dc | 1660 | March 26 | 28 | 17 | 8 + b | 1661 | April 14 | 17 | 28 | 9 + a | 1662 | " 3 | 9 | 9 | 10 + g | 1663 | March 23 | 25 | 20 | 11 + fe | 1664 | April 11 | 13 | 1 | 12 + d | 1665 | March 31 | 5 | 12 | 13 + c | 1666 | April 19 | 25 | 23 | 14 + b | 1667 | " 8 | 10 | 4 | 15 + ag | 1668 | March 28 | 1 | 15 | 16 + f | 1669 | April 16 | 21 | 26 | 17 + e | 1670 | " 5 | 6 | 7 | 18 + d | 1671 | March 25 | 29 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +completed, then the paschal moons again occur in the same order, on the +same day of the month as they did nineteen years before. Now this cycle is +six times repeated in a period of 114 years, when the intercalary day +being suppressed in 1700, causes the first paschal moon of the cycle to +fall on the 13th of April instead of the 12th, and all the moons of the +cycle to fall one day later than they would had the correction not been +made. The cycle is now repeated ten times without + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + cb | 1672 | April 12 | 17 | 0 | 1 + a | 1673 | " 1 | 2 | 11 | 2 + g | 1674 | March 21 | 25 | 22 | 3 + f | 1675 | April 9 | 14 | 3 | 4 + ed | 1676 | March 29 | 5 | 14 | 5 + c | 1677 | April 17 | 18 | 25 | 6 + b | 1678 | " 6 | 10 | 6 | 7 + a | 1679 | March 26 | 2 | 17 | 8 + gf | 1680 | April 24 | 21 | 28 | 9 + e | 1681 | " 3 | 6 | 9 | 10 + d | 1682 | March 23 | 29 | 20 | 11 + c | 1683 | April 11 | 18 | 1 | 12 + ba | 1684 | March 31 | 2 | 12 | 13 + g | 1685 | April 19 | 22 | 23 | 14 + f | 1686 | " 8 | 14 | 4 | 15 + e | 1687 | March 28 | 30 | 15 | 16 + dc | 1688 | April 16 | 18 | 26 | 17 + b | 1689 | " 5 | 10 | 7 | 18 + a | 1690 | March 25 | 26 | 18 | 19 + g | 1691 | April 12 | 15 | 0 | 1 + fe | 1692 | " 1 | 6 | 11 | 2 + d | 1693 | March 21 | 22 | 22 | 3 + c | 1694 | April 9 | 11 | 3 | 4 + b | 1695 | March 29 | 3 | 14 | 5 + ag | 1696 | April 17 | 22 | 25 | 6 + f | 1697 | " 6 | 7 | 6 | 7 + e | 1698 | March 26 | 30 | 17 | 8 + d | 1699 | April 14 | 19 | 28 | 9 + c | 1700 | " 3 | 4 | 9 | 10 + b | 1701 | March 23 | 27 | 20 | 11 + a | 1702 | April 11 | 16 | 1 | 12 + g | 1703 | March 31 | 1 | 12 | 13 + fe | 1704 | April 19 | 20 | 23 | 14 + d | 1705 | " 8 | 12 | 4 | 15 + c | 1706 | March 28 | 4 | 15 | 16 + b | 1707 | April 16 | 17 | 26 | 17 + ag | 1708 | " 5 | 8 | 7 | 18 + f | 1709 | March 25 | 31 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +correction, that is, till the year 1900, a period of 190 years, when the +intercalation being again suppressed, causes the first paschal moon of the +cycle to fall on the 14th of April, and, of course, all the other moons of +the cycle to fall one day later. The reason the correction is not made the +first year of the century is, the lunar cycle must first be completed, and +that did not occur until 1710. As 100 is not a multiple of 19, the number +of years in the cycle, and, as the corrections + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + e | 1710 | April 13 | 20 | 0 | 1 + d | 1711 | " 2 | 5 | 11 | 2 + cb | 1712 | March 22 | 27 | 22 | 3 + a | 1713 | April 10 | 16 | 3 | 4 + g | 1714 | March 30 | 1 | 14 | 5 + f | 1715 | April 18 | 21 | 25 | 6 + ed | 1716 | " 7 | 12 | 6 | 7 + c | 1717 | March 27 | 28 | 17 | 8 + b | 1718 | April 15 | 17 | 28 | 9 + a | 1719 | " 4 | 9 | 9 | 10 + gf | 1720 | March 24 | 31 | 20 | 11 + e | 1721 | April 12 | 13 | 1 | 12 + d | 1722 | " 1 | 5 | 12 | 13 + c | 1723 | March 21 | 28 | 23 | 14 + ba | 1724 | April 9 | 16 | 4 | 15 + g | 1725 | March 29 | 1 | 15 | 16 + f | 1726 | April 17 | 21 | 26 | 17 + e | 1727 | " 6 | 13 | 7 | 18 + dc | 1728 | March 26 | 28 | 18 | 19 + b | 1729 | April 13 | 17 | 0 | 1 + a | 1730 | " 2 | 9 | 11 | 2 + g | 1731 | March 22 | 25 | 22 | 3 + fe | 1732 | April 10 | 13 | 3 | 4 + d | 1733 | March 30 | 5 | 14 | 5 + c | 1734 | April 18 | 25 | 25 | 6 + b | 1735 | " 7 | 10 | 6 | 7 + ag | 1736 | March 27 | 1 | 17 | 8 + f | 1737 | April 15 | 21 | 28 | 9 + e | 1738 | " 4 | 6 | 9 | 10 + d | 1739 | March 24 | 29 | 20 | 11 + cb | 1740 | April 12 | 17 | 1 | 12 + a | 1741 | " 1 | 2 | 12 | 13 + g | 1742 | March 21 | 25 | 23 | 14 + f | 1743 | April 9 | 14 | 4 | 15 + ed | 1744 | March 29 | 5 | 15 | 16 + c | 1745 | April 17 | 18 | 26 | 17 + b | 1746 | " 6 | 10 | 7 | 18 + a | 1747 | March 26 | 2 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +cannot be made only at the beginning of the cycle, so they cannot be made +the first year of the century only once in 1900 years. It may be seen from +one of the above tables that the correction is made in the year 1900, for +the reason that that is the first century which is a multiple of 19. The +next centurial year that is exactly divisible by 19, is 3800. Therefore, +none of the corrections for the next 1900 years, will occur on the first +year of the century. It may also be seen from + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + gf | 1748 | April 13 | 14 | 0 | 1 + e | 1749 | " 2 | 6 | 11 | 2 + d | 1750 | March 22 | 29 | 22 | 3 + c | 1751 | April 10 | 11 | 3 | 4 + ba | 1752 | March 30 | 2 | 14 | 5 + g | 1753 | April 18 | 22 | 25 | 6 + f | 1754 | " 7 | 14 | 6 | 7 + e | 1755 | March 27 | 30 | 17 | 8 + dc | 1756 | April 15 | 18 | 28 | 9 + b | 1757 | " 4 | 10 | 9 | 10 + a | 1758 | March 24 | 26 | 20 | 11 + g | 1759 | April 12 | 15 | 1 | 12 + fe | 1760 | " 1 | 6 | 12 | 13 + d | 1761 | March 21 | 22 | 23 | 14 + c | 1762 | April 9 | 11 | 4 | 15 + b | 1763 | March 29 | 3 | 15 | 16 + ag | 1764 | April 17 | 22 | 26 | 17 + f | 1765 | " 6 | 7 | 7 | 18 + e | 1766 | March 26 | 30 | 18 | 19 + d | 1767 | April 13 | 19 | 0 | 1 + cb | 1768 | " 2 | 3 | 11 | 2 + a | 1769 | March 22 | 26 | 22 | 3 + g | 1770 | April 10 | 15 | 3 | 4 + f | 1771 | March 30 | 31 | 14 | 5 + ed | 1772 | April 18 | 19 | 25 | 6 + c | 1773 | " 7 | 11 | 6 | 7 + b | 1774 | March 27 | 3 | 17 | 8 + a | 1775 | April 15 | 16 | 28 | 9 + gf | 1776 | " 4 | 7 | 9 | 10 + e | 1777 | March 24 | 30 | 20 | 11 + d | 1778 | April 12 | 19 | 1 | 12 + c | 1779 | " 1 | 4 | 12 | 13 + ba | 1780 | March 21 | 26 | 23 | 14 + g | 1781 | April 9 | 15 | 4 | 15 + f | 1782 | March 29 | 31 | 15 | 16 + e | 1783 | April 17 | 20 | 26 | 17 + dc | 1784 | " 6 | 11 | 7 | 18 + b | 1785 | March 26 | 27 | 18 | 19 + ----------+-------+----------+---------+--------+---------- + +the above tables, that, though the intercalary day was suppressed in the +year 1800, no change is made in the date of the paschal moon. The reason +is, the lunar equation also occurred; while the former correction would +cause the paschal moon to fall one day later, that is on the 14th day of +April, the latter would make it fall one day earlier, that is on the 12th; +so they compensate each other, and there is no correction to be made until +the year 1900, when the solar equation + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + a | 1786 | April 13 | 16 | 0 | 1 + g | 1787 | " 2 | 8 | 11 | 2 + fe | 1788 | March 22 | 23 | 22 | 3 + d | 1789 | April 10 | 12 | 3 | 4 + c | 1790 | March 30 | 4 | 14 | 5 + b | 1791 | April 18 | 24 | 25 | 6 + ag | 1792 | " 7 | 8 | 6 | 7 + f | 1793 | March 27 | 31 | 17 | 8 + e | 1794 | April 15 | 20 | 28 | 9 + d | 1795 | " 4 | 5 | 9 | 10 + cb | 1796 | March 24 | 27 | 20 | 11 + a | 1797 | April 12 | 16 | 1 | 12 + g | 1798 | " 1 | 8 | 12 | 13 + f | 1799 | March 21 | 24 | 23 | 14 + e | 1800 | April 9 | 13 | 4 | 15 + d | 1801 | March 29 | 5 | 15 | 16 + c | 1802 | April 17 | 18 | 26 | 17 + b | 1803 | " 6 | 10 | 7 | 18 + ag | 1804 | March 26 | 1 | 18 | 19 + f | 1805 | April 13 | 14 | 0 | 1 + e | 1806 | " 2 | 6 | 11 | 2 + d | 1807 | March 22 | 29 | 22 | 3 + cb | 1808 | April 10 | 17 | 3 | 4 + a | 1809 | March 30 | 2 | 14 | 5 + g | 1810 | April 18 | 22 | 25 | 6 + f | 1811 | " 7 | 14 | 6 | 7 + ed | 1812 | March 27 | 29 | 17 | 8 + c | 1813 | April 15 | 18 | 28 | 9 + b | 1814 | " 4 | 10 | 9 | 10 + a | 1815 | March 24 | 26 | 20 | 11 + gf | 1816 | April 12 | 14 | 1 | 12 + e | 1817 | " 1 | 6 | 12 | 13 + d | 1818 | March 21 | 22 | 23 | 14 + c | 1819 | April 9 | 11 | 4 | 15 + ba | 1820 | March 29 | 2 | 15 | 16 + g | 1821 | April 17 | 22 | 26 | 17 + f | 1822 | " 6 | 7 | 7 | 18 + e | 1823 | March 26 | 30 | 18 | 19 + ----------+-------+----------+---------+--------+---------- + +again occurs, and the first paschal moon of the cycle falls on the 14th; +which cycle is repeated sixteen times in a period of 304 years, after +which, in 2204, the date of the first paschal moon is the 15th of April. +The reason there is no correction to make in this long period is, first, +the year 2000 is a common year in the Gregorian calendar; second, in the +year 2100 both the solar and the lunar equations again occur, and +occurring together, they compensate each other; consequently + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + dc | 1824 | April 13 | 17 | 0 | 1 + b | 1825 | " 2 | 2 | 11 | 2 + a | 1826 | March 22 | 25 | 22 | 3 + g | 1827 | April 10 | 14 | 3 | 4 + fe | 1828 | March 30 | 5 | 14 | 5 + d | 1829 | April 18 | 18 | 25 | 6 + c | 1830 | " 7 | 10 | 6 | 7 + b | 1831 | March 27 | 2 | 17 | 8 + ag | 1832 | April 15 | 21 | 28 | 9 + f | 1833 | " 4 | 6 | 9 | 10 + e | 1834 | March 24 | 29 | 20 | 11 + d | 1835 | April 12 | 18 | 1 | 12 + cb | 1836 | " 1 | 2 | 12 | 13 + a | 1837 | March 21 | 22 | 23 | 14 + g | 1838 | " 9 | 14 | 4 | 15 + f | 1839 | March 29 | 30 | 15 | 16 + ed | 1840 | April 17 | 18 | 26 | 17 + c | 1841 | " 6 | 10 | 7 | 18 + b | 1842 | March 26 | 26 | 18 | 19 + a | 1843 | April 13 | 15 | 0 | 1 + gf | 1844 | " 2 | 6 | 11 | 2 + e | 1845 | March 22 | 22 | 22 | 3 + d | 1846 | April 10 | 11 | 3 | 4 + c | 1847 | March 30 | 3 | 14 | 5 + ba | 1848 | April 18 | 22 | 25 | 6 + g | 1849 | " 7 | 7 | 6 | 7 + f | 1850 | March 27 | 30 | 17 | 8 + e | 1851 | April 15 | 19 | 28 | 9 + dc | 1852 | " 4 | 4 | 9 | 10 + b | 1853 | March 24 | 27 | 20 | 11 + a | 1854 | April 12 | 16 | 1 | 12 + g | 1855 | " 1 | 1 | 12 | 13 + fe | 1856 | March 21 | 20 | 23 | 14 + d | 1857 | " 9 | 12 | 4 | 15 + c | 1858 | March 29 | 4 | 15 | 16 + b | 1859 | April 17 | 17 | 26 | 17 + ag | 1860 | " 6 | 8 | 7 | 18 + f | 1861 | March 26 | 31 | 18 | 19 + ----------+-------+----------+---------+--------+---------- + +the cycle is continued until 2204, after which, as has already been +stated, the date of the first paschal moon is the 15th of April. This +cycle is repeated six times in a period of 114 years, when in 2318, for +reasons already given, the date of the first paschal moon of the next +cycle falls on the 16th, and is repeated five times in a period of 95 +years, when, in 2413, the lunar equation occurs alone, and the date of the +first paschal moon for the next 95 years, that is till the year 2508, + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + e | 1862 | April 13 | 20 | 0 | 1 + d | 1863 | " 2 | 5 | 11 | 2 + cb | 1864 | March 22 | 27 | 22 | 3 + a | 1865 | April 10 | 16 | 3 | 4 + g | 1866 | March 30 | 1 | 14 | 5 + f | 1867 | April 18 | 21 | 25 | 6 + ed | 1868 | " 7 | 12 | 6 | 7 + c | 1869 | March 27 | 28 | 17 | 8 + b | 1870 | April 15 | 17 | 28 | 9 + a | 1871 | " 4 | 9 | 9 | 10 + gf | 1872 | March 24 | 31 | 20 | 11 + e | 1873 | April 12 | 13 | 1 | 12 + d | 1874 | " 1 | 5 | 12 | 13 + c | 1875 | March 21 | 28 | 23 | 14 + ba | 1876 | April 9 | 16 | 4 | 15 + g | 1877 | March 29 | 1 | 15 | 16 + f | 1878 | April 17 | 21 | 26 | 17 + e | 1879 | " 6 | 13 | 7 | 18 + dc | 1880 | March 26 | 28 | 18 | 19 + b | 1881 | April 13 | 17 | 0 | 1 + a | 1882 | " 2 | 9 | 11 | 2 + g | 1883 | March 22 | 25 | 22 | 3 + fe | 1884 | April 10 | 13 | 3 | 4 + d | 1885 | March 30 | 5 | 14 | 5 + c | 1886 | April 18 | 25 | 25 | 6 + b | 1887 | " 7 | 10 | 6 | 7 + ag | 1888 | March 27 | 1 | 17 | 8 + f | 1889 | April 15 | 21 | 28 | 9 + e | 1890 | " 4 | 6 | 9 | 10 + d | 1891 | March 24 | 29 | 20 | 11 + cb | 1892 | April 12 | 17 | 1 | 12 + a | 1893 | " 1 | 2 | 12 | 13 + g | 1894 | March 21 | 25 | 23 | 14 + f | 1895 | April 9 | 14 | 4 | 15 + ed | 1896 | March 29 | 5 | 15 | 16 + c | 1897 | April 17 | 18 | 26 | 17 + b | 1898 | " 6 | 10 | 7 | 18 + a | 1899 | March 26 | 2 | 18 | 19 + ----------+-------+----------+---------+--------+---------- + +falls back to the 15th of April. After which the 16th, on account of the +solar equation, is again the date of the first paschal moon of the cycle +for another period of 95 years; that is till the year 2603, when the solar +equation causes the first paschal moon to fall on the 17th, which cycle is +repeated sixteen times during another period of 304 years, after which, in +2907, the correction makes the date of the first paschal moon of the + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + g | 1900 | April 14 | 15 | 0 | 1 + f | 1901 | " 3 | 7 | 11 | 2 + e | 1902 | March 23 | 30 | 22 | 3 + d | 1903 | April 11 | 12 | 3 | 4 + cb | 1904 | March 31 | 3 | 14 | 5 + a | 1905 | April 19 | 23 | 25 | 6 + g | 1906 | " 8 | 15 | 6 | 7 + f | 1907 | March 28 | 31 | 17 | 8 + ed | 1908 | April 16 | 19 | 28 | 9 + c | 1909 | " 5 | 11 | 9 | 10 + b | 1910 | March 25 | 27 | 20 | 11 + a | 1911 | April 13 | 16 | 1 | 12 + gf | 1912 | " 2 | 7 | 12 | 13 + e | 1913 | March 22 | 23 | 23 | 14 + d | 1914 | April 10 | 12 | 4 | 15 + c | 1915 | March 30 | 4 | 15 | 16 + ba | 1916 | April 18 | 23 | 26 | 17 + g | 1917 | " 7 | 8 | 7 | 18 + f | 1918 | March 27 | 31 | 18 | 19 + e | 1919 | April 14 | 20 | 0 | 1 + dc | 1920 | " 3 | 4 | 11 | 2 + b | 1921 | March 23 | 27 | 22 | 3 + a | 1922 | April 11 | 16 | 3 | 4 + g | 1923 | March 31 | 1 | 14 | 5 + fe | 1924 | April 19 | 20 | 25 | 6 + d | 1925 | " 8 | 12 | 6 | 7 + c | 1926 | March 28 | 4 | 17 | 8 + b | 1927 | April 16 | 17 | 28 | 9 + ag | 1928 | " 5 | 8 | 9 | 10 + f | 1929 | March 25 | 31 | 20 | 11 + e | 1930 | April 13 | 20 | 1 | 12 + d | 1931 | " 2 | 5 | 12 | 13 + cb | 1932 | March 22 | 27 | 23 | 14 + a | 1933 | April 10 | 16 | 4 | 15 + g | 1934 | March 30 | 1 | 15 | 16 + f | 1935 | April 18 | 21 | 26 | 17 + ed | 1936 | " 7 | 12 | 7 | 18 + c | 1937 | March 27 | 28 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +cycle, the 18th of April, which cycle is continued without correction till +the year 3116, a period of 209 years. By reference to the above tables, it +will be seen that the solar and lunar equations occur together in the year +2700 and compensate each other; also, that the year 2800 is a common year +in the Gregorian calendar; consequently there is no correction to make +from 2603 to 2907; also the two equations occur together + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + b | 1938 | April 14 | 17 | 0 | 1 + a | 1939 | " 3 | 9 | 11 | 2 + gf | 1940 | March 23 | 24 | 22 | 3 + e | 1941 | April 11 | 13 | 3 | 4 + d | 1942 | March 31 | 5 | 14 | 5 + c | 1943 | April 19 | 25 | 25 | 6 + ba | 1944 | " 8 | 9 | 6 | 7 + g | 1945 | March 28 | 1 | 17 | 8 + f | 1946 | April 16 | 21 | 28 | 9 + e | 1947 | " 5 | 6 | 9 | 10 + dc | 1948 | March 25 | 28 | 20 | 11 + b | 1949 | April 13 | 17 | 1 | 12 + a | 1950 | " 2 | 9 | 12 | 13 + g | 1951 | March 22 | 25 | 23 | 14 + fe | 1952 | April 10 | 13 | 4 | 15 + d | 1953 | March 30 | 5 | 15 | 16 + c | 1954 | April 18 | 25 | 26 | 17 + b | 1955 | " 7 | 10 | 7 | 18 + ag | 1956 | March 27 | 1 | 18 | 19 + f | 1957 | April 14 | 21 | 0 | 1 + e | 1958 | " 3 | 6 | 11 | 2 + d | 1959 | March 23 | 29 | 22 | 3 + cb | 1960 | April 11 | 17 | 3 | 4 + a | 1961 | March 31 | 2 | 14 | 5 + g | 1962 | April 19 | 22 | 25 | 6 + f | 1963 | " 8 | 14 | 6 | 7 + ed | 1964 | March 28 | 29 | 17 | 8 + c | 1965 | April 16 | 18 | 28 | 9 + b | 1966 | " 5 | 10 | 9 | 10 + a | 1967 | March 25 | 26 | 20 | 11 + gf | 1968 | April 13 | 14 | 1 | 12 + e | 1969 | " 2 | 6 | 12 | 13 + d | 1970 | March 22 | 29 | 23 | 14 + c | 1971 | April 10 | 11 | 4 | 15 + ba | 1972 | March 30 | 2 | 15 | 16 + g | 1973 | April 18 | 22 | 26 | 17 + f | 1974 | " 7 | 14 | 7 | 18 + e | 1975 | March 27 | 30 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +again in the year 3000 and compensate each other, is the reason there is +no correction to make from 2907 to 3116, after which the first paschal +moon falls on the 19th, and is repeated fifteen times in a period of 285 +years, that is till the year 3401, when the correction makes the 20th of +April, the date of the full moon, but that cannot be the paschal moon, +which cannot happen later than the 19th; consequently the + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + dc | 1976 | April 14 | 18 | 0 | 1 + b | 1977 | " 3 | 10 | 11 | 2 + a | 1978 | March 23 | 26 | 22 | 3 + g | 1979 | April 11 | 15 | 3 | 4 + fe | 1980 | March 31 | 6 | 14 | 5 + d | 1981 | April 19 | 26 | 25 | 6 + c | 1982 | " 8 | 11 | 6 | 7 + b | 1983 | March 28 | 3 | 17 | 8 + ag | 1984 | April 16 | 22 | 28 | 9 + f | 1985 | " 5 | 7 | 9 | 10 + e | 1986 | March 25 | 30 | 20 | 11 + d | 1987 | April 13 | 19 | 1 | 12 + cb | 1988 | " 2 | 3 | 12 | 13 + a | 1989 | March 22 | 26 | 23 | 14 + g | 1990 | April 10 | 15 | 4 | 15 + f | 1991 | March 30 | 31 | 15 | 16 + ed | 1992 | April 18 | 19 | 26 | 17 + c | 1993 | " 7 | 11 | 7 | 18 + b | 1994 | March 27 | 3 | 18 | 19 + a | 1995 | April 14 | 16 | 0 | 1 + gf | 1996 | " 3 | 7 | 11 | 2 + e | 1997 | March 23 | 30 | 22 | 3 + d | 1998 | April 11 | 12 | 3 | 4 + c | 1999 | March 31 | 4 | 14 | 5 + ba | 2000 | April 19 | 23 | 25 | 6 + g | 2001 | " 8 | 15 | 6 | 7 + f | 2002 | March 28 | 31 | 17 | 8 + e | 2003 | April 16 | 20 | 28 | 9 + dc | 2004 | " 5 | 11 | 9 | 10 + b | 2005 | March 25 | 27 | 20 | 11 + a | 2006 | April 13 | 16 | 1 | 12 + g | 2007 | " 2 | 8 | 12 | 13 + fe | 2008 | March 22 | 23 | 23 | 14 + d | 2009 | April 10 | 12 | 4 | 15 + c | 2010 | March 30 | 4 | 15 | 16 + b | 2011 | April 18 | 24 | 26 | 17 + ag | 2012 | " 7 | 8 | 7 | 18 + f | 2013 | March 27 | 31 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +moon that precedes it by thirty days, and which falls on the 21st of +March, is the date of the first paschal moon of the cycle which commences +with the year 3401. The day of the month on which Easter Sunday has fallen +or will fall, from the year 1596 to 2013, is already determined, and may +be seen by reference to the above tables. From 2013 to 3401, the date of +Easter is determined for one lunar cycle only, at the + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + ag | 2204 | April 15 | 22 | 0 | 1 + f | 2205 | " 4 | 7 | 11 | 2 + e | 2206 | March 24 | 30 | 22 | 3 + d | 2207 | April 12 | 19 | 3 | 4 + cb | 2208 | " 1 | 3 | 14 | 5 + a | 2209 | March 21 | 26 | 25 | 6 + g | 2210 | April 9 | 15 | 6 | 7 + f | 2211 | March 29 | 31 | 17 | 8 + ed | 2212 | April 17 | 19 | 28 | 9 + c | 2213 | " 6 | 11 | 9 | 10 + b | 2214 | March 26 | 27 | 20 | 11 + a | 2215 | April 14 | 16 | 1 | 12 + gf | 2216 | " 3 | 7 | 12 | 13 + e | 2217 | March 23 | 30 | 23 | 14 + d | 2218 | April 11 | 12 | 4 | 15 + c | 2219 | March 31 | 4 | 15 | 16 + ba | 2220 | April 19 | 23 | 26 | 17 + g | 2221 | " 8 | 15 | 7 | 18 + f | 2222 | March 28 | 31 | 18 | 19 + f | 2318 | April 16 | 21 | 0 | 1 + e | 2319 | " 5 | 6 | 11 | 2 + dc | 2320 | March 25 | 28 | 22 | 3 + b | 2321 | April 13 | 17 | 3 | 4 + a | 2322 | " 2 | 9 | 14 | 5 + g | 2323 | March 22 | 25 | 25 | 6 + fe | 2324 | April 10 | 13 | 6 | 7 + d | 2325 | March 30 | 5 | 17 | 8 + c | 2326 | April 18 | 25 | 28 | 9 + b | 2327 | " 7 | 10 | 9 | 10 + ag | 2328 | March 27 | 1 | 20 | 11 + f | 2329 | April 15 | 21 | 1 | 12 + e | 2330 | " 4 | 6 | 12 | 13 + d | 2331 | March 24 | 29 | 23 | 14 + cb | 2332 | April 12 | 17 | 4 | 15 + a | 2333 | " 1 | 2 | 15 | 16 + g | 2334 | March 21 | 25 | 26 | 17 + f | 2335 | April 9 | 14 | 7 | 18 + ed | 2336 | March 29 | 5 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +beginning of each period; for the reason that it was deemed unnecessary, +because the paschal moons, the epacts, and the Golden Numbers are the same +for every cycle in the period. Therefore, all that remains to be done is +to find the day of the month on which the first Sunday, after the paschal +moon, falls. The dominical letters for any period may very easily be found +by counting backwards one letter each year for every common + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + f | 2413 | April 15 | 21 | 0 | 1 + e | 2414 | " 4 | 6 | 11 | 2 + d | 2415 | March 24 | 29 | 22 | 3 + cb | 2416 | April 12 | 17 | 3 | 4 + a | 2417 | " 1 | 2 | 14 | 5 + g | 2418 | March 21 | 25 | 25 | 6 + f | 2419 | April 9 | 14 | 6 | 7 + ed | 2420 | March 29 | 5 | 17 | 8 + c | 2421 | April 17 | 18 | 28 | 9 + b | 2422 | " 6 | 10 | 9 | 10 + a | 2423 | March 26 | 2 | 20 | 11 + gf | 2424 | April 14 | 21 | 1 | 12 + e | 2425 | " 3 | 6 | 12 | 13 + d | 2426 | March 23 | 29 | 23 | 14 + c | 2427 | April 11 | 18 | 4 | 15 + ba | 2428 | March 31 | 2 | 15 | 16 + g | 2429 | April 19 | 22 | 26 | 17 + f | 2430 | " 8 | 14 | 7 | 18 + e | 2431 | March 28 | 30 | 18 | 19 + ag | 2508 | April 16 | 22 | 0 | 1 + f | 2509 | " 5 | 7 | 11 | 2 + e | 2510 | March 25 | 30 | 22 | 3 + d | 2511 | April 13 | 19 | 3 | 4 + cb | 2512 | " 2 | 3 | 14 | 5 + a | 2513 | March 22 | 26 | 25 | 6 + g | 2514 | April 10 | 15 | 6 | 7 + f | 2515 | March 30 | 31 | 17 | 8 + ed | 2516 | April 18 | 19 | 28 | 9 + c | 2617 | " 7 | 11 | 9 | 10 + b | 2518 | March 27 | 3 | 20 | 11 + a | 2519 | April 15 | 16 | 1 | 12 + gf | 2520 | " 4 | 7 | 12 | 13 + e | 2521 | March 24 | 30 | 23 | 14 + d | 2522 | April 12 | 19 | 4 | 15 + c | 2523 | " 1 | 4 | 15 | 16 + ba | 2524 | March 21 | 26 | 26 | 17 + g | 2525 | April 9 | 15 | 7 | 18 + f | 2526 | March 29 | 31 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +year, and two for leap-year, the fourth letter being dominical letter for +January and February and the fifth for the rest of the year; thus, if G be +dominical letter for any given year, we would have then, G, F, E, DC; B, +A, G, FE; D, C, B, AG; F, E, D, CB, etc. By counting these letters +backwards, or in the tables, from the bottom of the column upwards, they +will occur in alphabetical order. Again it may be seen by reference + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + b | 2603 | April 17 | 24 | 0 | 1 + ag | 2604 | " 6 | 8 | 11 | 2 + f | 2605 | March 26 | 31 | 22 | 3 + e | 2606 | April 14 | 20 | 3 | 4 + d | 2607 | " 3 | 5 | 14 | 5 + cb | 2608 | March 23 | 27 | 25 | 6 + a | 2609 | April 11 | 16 | 6 | 7 + g | 2610 | March 31 | 1 | 17 | 8 + f | 2611 | April 19 | 21 | 28 | 9 + ed | 2612 | " 8 | 12 | 9 | 10 + c | 2613 | March 28 | 4 | 20 | 11 + b | 2614 | April 16 | 17 | 1 | 12 + a | 2615 | " 5 | 9 | 12 | 13 + gf | 2616 | March 25 | 31 | 23 | 14 + e | 2617 | April 13 | 20 | 4 | 15 + d | 2618 | " 2 | 5 | 15 | 16 + c | 2619 | March 22 | 28 | 26 | 17 + ba | 2620 | April 10 | 16 | 7 | 18 + g | 2621 | March 30 | 1 | 18 | 19 + b | 2907 | April 18 | 24 | 0 | 1 + ag | 2908 | " 7 | 8 | 11 | 2 + f | 2909 | March 27 | 31 | 22 | 3 + e | 2910 | April 15 | 20 | 3 | 4 + d | 2911 | " 4 | 5 | 14 | 5 + cb | 2912 | March 24 | 27 | 25 | 6 + a | 2913 | April 12 | 16 | 6 | 7 + g | 2914 | " 1 | 8 | 17 | 8 + f | 2915 | March 21 | 24 | 28 | 9 + ed | 2916 | April 9 | 12 | 9 | 10 + c | 2917 | March 29 | 4 | 20 | 11 + b | 2918 | April 17 | 24 | 1 | 12 + a | 2919 | " 6 | 9 | 12 | 13 + gf | 2920 | March 26 | 31 | 23 | 14 + e | 2921 | April 14 | 20 | 4 | 15 + d | 2922 | " 3 | 5 | 15 | 16 + c | 2923 | March 23 | 28 | 26 | 17 + ba | 2924 | April 11 | 16 | 7 | 18 + g | 2925 | March 31 | 1 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +to these tables, that Easter occurs less frequently on the 22d of March, +its earliest possible date, and the 25th of April, which has hitherto been +considered its latest possible date, than any of the days intervening. It +cannot happen on the 22d, only when the paschal moon falls on the 21st, +and that day must be Saturday. It fell on the 22d, first, after the +reformation of the calendar by Gregory in 1598; again in 1693, 1761, + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + ba | 3116 | April 19 | 23 | 0 | 1 + g | 3117 | " 8 | 15 | 11 | 2 + f | 3118 | March 28 | 31 | 22 | 3 + e | 3119 | April 16 | 20 | 3 | 4 + dc | 3120 | " 5 | 11 | 14 | 5 + b | 3121 | March 25 | 27 | 25 | 6 + a | 3122 | April 13 | 16 | 6 | 7 + g | 3123 | " 2 | 8 | 17 | 8 + fe | 3124 | March 22 | 23 | 28 | 9 + d | 3125 | April 10 | 12 | 9 | 10 + c | 3126 | March 30 | 4 | 20 | 11 + b | 3127 | April 18 | 24 | 1 | 12 + ag | 3128 | " 7 | 8 | 12 | 13 + f | 3129 | March 27 | 31 | 23 | 14 + e | 3130 | April 15 | 20 | 4 | 15 + d | 3131 | " 4 | 5 | 15 | 16 + cb | 3132 | March 24 | 27 | 26 | 17 + a | 3133 | April 12 | 16 | 7 | 18 + g | 3134 | " 1 | 8 | 18 | 19 + d | 3401 | March 21 | 22 | 0 | 1 + c | 3402 | April 9 | 11 | 11 | 2 + b | 3403 | March 29 | 3 | 22 | 3 + ag | 3404 | April 17 | 22 | 3 | 4 + f | 3405 | " 6 | 7 | 14 | 5 + e | 3406 | March 26 | 30 | 25 | 6 + d | 3407 | April 14 | 19 | 6 | 7 + cb | 3408 | " 3 | 10 | 17 | 8 + a | 3409 | March 23 | 26 | 28 | 9 + g | 3410 | April 11 | 15 | 9 | 10 + f | 3411 | March 31 | 7 | 20 | 11 + ed | 3412 | April 19 | 26 | 1 | 12 + c | 3413 | " 8 | 11 | 12 | 13 + b | 3414 | March 28 | 3 | 23 | 14 + a | 3415 | April 16 | 23 | 4 | 15 + gf | 3416 | " 5 | 7 | 15 | 16 + e | 3417 | March 25 | 30 | 26 | 17 + d | 3418 | April 13 | 19 | 7 | 18 + c | 3419 | " 2 | 4 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +and in 1818. It has not occurred since, nor will not again till 2285, a +period of 467 years. The reason that it does not occur on the 22d of March +in this long period is, the paschal moon does not fall on the 21st, from +the year 1900 to 2204, a period of 304 years. We refer to the tabular +moon, not to the true or astronomical moon, which may occur on the 21st +more than once in this long period. + + + + +CHAPTER VII. + +CHURCH FEASTS AND FASTS WHOSE DATE DEPEND ON THE DATE OF EASTER. + + +Feasts, or Festivals, are days set apart by the church, either for the +grateful memorial of the most remarkable events connected with the plan of +redemption, or upon which to commemorate the actions and sufferings of +such persons as have been most instrumental in carrying forward the +designs of God for the salvation of mankind. + +The ecclesiastical year is divided into eight seasons, namely: +Advent-tide, Christmas-tide, Epiphany-tide, Lenten-tide, Easter-tide, +Ascension-tide, Whitsun-tide, and Trinity-tide. The first day of each of +these seasons has been, and is now observed by the church in commemoration +of some of the most remarkable events connected with the plan of +redemption. All these will be noticed in the order in which they occur in +the ecclesiastical year, while many other days intervening, which are +observed as feasts or fasts, will be given a passing notice. + +_a_--Advent Sunday, which is the day nearest St. Andrew's Day (Nov. 30), +or the first Sunday after the 26th of November, has been recognized since +the sixth century as the first day of the ecclesiastical year. + +Advent (Latin _Adventus_, the coming,) signifies the coming of our +Saviour, the period of the approach of the nativity. As Advent-tide lasts +from Advent Sunday to Christmas, the length of the season depends upon +the day of the month on which Advent Sunday falls. As it may happen as +early as the 27th of November or as late as the 3d of December, so +Advent-tide will contain no more than twenty-eight days nor less than +twenty-two. It should be borne in mind that, though this festival is +classed among the movable feasts, it does not depend upon the date of +Easter, but upon the day of the month on which Advent Sunday falls. The +four Sundays before Christmas were made preparation days for the festival +of Christmas, and were called the first, second, third, and fourth Sundays +in Advent. + +Ember days and Ember weeks are the four seasons set apart by the Western +church for special prayer and fasting, and the ordination of clergy; known +in the church as _quatuor tempora_, (the four seasons.) The Ember weeks +are the weeks next following St. Lucy's Day (Dec. 13th), the first Sunday +in Lent, Whitsun Day, and Holy Cross Day (Sept. 14th). The Wednesdays, +Fridays and Saturdays of these weeks are the Ember days distinctively. The +name by some is supposed to be derived from a German word signifying +Abstinence; by others it is supposed to signify Ashes. + +_b_--Christmas (from Christ and the Saxon _maess_, signifying the mass and +a feast), is a festival held in commemoration of the nativity of our +Saviour throughout nearly the whole of Christendom. It is occupied, +therefore, with the event (the incarnation) which forms the center and +turning point of the history of the world. Though the day of Christ's +birth cannot be ascertained from the New Testament, nor from any other +source, yet the whole Christian world for more than 1300 years have +concurred in celebrating the nativity on the 25th of December. This is +the first of the four great feasts in the ecclesiastical year; the other +three are Easter, Ascension, and Whitsun Day. The length of Christmas-tide +or season is twelve days, lasting from the 25th of December to Epiphany. + +_c_--Epiphany (Greek _Epiphania_, _Theophania_ or _Christophania_,) is a +festival in commemoration of the manifestation of Jesus Christ to the +world as the Son of God, and referring to the appearance of the star which +announced our Saviour's birth to the Gentiles, and the visit of the Magi, +or wise Men of the East to the infant Jesus. This festival is held on the +6th of January invariably, consequently is not a movable feast, though the +length of Epiphany-tide depends upon the date of Easter. As Easter may +happen as early as the 22d of March or as late as the 26th of April (a +variation of thirty-five days), so Epiphany-tide may consist of no less +than twelve days nor more than forty-seven, as the season always ends the +day before Septuagesima Sunday. (See tables at the close of this chapter.) + +Septuagesima, Sexagesima, Quinquagesima. There being exactly fifty days +between the Sunday next before Lent and Easter Day, inclusive, that Sunday +was termed Quinquagesima, i. e., the fiftieth; and the two immediately +preceding Sundays were called from the next round numbers Sexagesima, the +sixtieth; and Septuagesima, the seventieth. + +The Paschal Season extends from Septuagesima Sunday to Low Sunday, a +period of seventy days. It takes its name from the Paschal festival or +Easter, whose services end with Low Sunday, the octave, or eighth day, of +Easter. It begins with Septuagesima Sunday because the church services +then begin to prepare the minds of the faithful for the services of Lent, +which are themselves the preparation for Easter. May not Septuagesima +Sunday be so called because there are just seventy days in the Paschal +Season? + +Shrove-tide literally means confession-time, and is the name given to the +days immediately preceding Ash Wednesday. These days were so called +because on them, and especially on the last of them (Shrove Tuesday) +people were accustomed to confess their sins as a preparation for Lent. In +most Roman Catholic countries it begins with Quinquagesima Sunday, the +Sunday before Lent. + +Ash Wednesday, the first day of Lent, (Latin _dies cinerum_, the day of +Ashes), was so called because it was customary on that day for penitents +to appear in sackcloth, upon which occasion ashes were sprinkled upon +them. + +_d_--Lent, (Anglo-Saxon _lengten_. Perhaps from _lenegan_, to lengthen, +because at this season the days lengthen) the forty days fast, is the +preparation for Easter, and is observed in commemoration of our Lord's +fast in the wilderness. In most languages the name given to this fast +signifies the number of days--forty; but our word Lent signifies the +Spring Fast, for Lenten-tide in the Anglo-Saxon language was the Season of +Spring, in German, Lenz. + +The six Sundays in the Lenten-tide of forty-six days are not counted in +the fast, as all Sundays in the year are reckoned as feast days, because +our Saviour arose from the dead on the first day of the week. + +Quadragesima Sunday, the first Sunday in Lent, is so called by analogy +with the three Sundays which precede Lent, and which (as has already been +stated) are called respectively Septuagesima, seventieth; Sexagesima, +sixtieth; Quinquagesima, fiftieth; and then Quadragesima, fortieth; in +round numbers forty days before Easter. + +Holy Week, the last week in Lent, called also Passion Week, because within +it is commemorated our Lord's sufferings. The days specially solemnized +are Palm Sunday, Spy Wednesday, Holy, or Maundy Thursday, and Good Friday. + +Palm Sunday (Latin _Dominica Palmarium_, or _Dominica_ in _Palmis_) is the +name usually given the Sunday before Easter; a day celebrated in +commemoration of Christ's triumphal entry into Jerusalem, so called +because the people who had come to the feast, when they heard that Jesus +was coming, took branches of palm trees and went forth to meet him, and +cried, "Hosanna; blessed is the King of Israel that cometh in the name of +the Lord." + +Spy Wednesday, so called in allusion to the betrayal of Christ by Judas, +or the day on which he made the bargain to deliver him into the hands of +his enemies for thirty pieces of silver. + +Maundy Thursday (from _Dies mandati_, mandate Thursday), so called either +from the command given his disciples to love one another, or to +commemorate the sacrament of His supper. + +Good Friday, so called in acknowledgment of the benefit derived from the +death of Christ. + +The closing scenes in the life of Christ, the events of Wednesday, +Thursday and Friday of Holy Week, are events of much more importance than +were ever before crowded into any one week in the history of the world. +The betrayal on Wednesday, the institution of the sacrament on Thursday +night, also the words of our Saviour as recorded in John's gospel, from +the 14th to the 17th chapters inclusive, the agony and the bloody sweat in +the garden, the arrest and trial during Thursday night and Friday morning, +the crucifixion at the third hour, the darkness that was over all the land +from the sixth to the ninth hour, and the last words of the blessed Jesus, +"It is finished," (tasted death for every man); these we say, are events +of more importance to man than were ever before crowded into any one week +in the world's history. + +The prophets who prophesied of these things, inquired and searched +diligently, "searching what, or what manner of time the Spirit of Christ +which was in them did signify, when it testified beforehand the sufferings +of Christ and the glory that should follow." And about an hour before this +prophecy began to be fulfilled our Saviour uttered these words: "Verily, +verily, I say unto you, that ye shall weep and lament, but the world shall +rejoice; and ye shall be sorrowful, but your sorrow shall be turned into +joy." It was probably not more than an hour from the time these words fell +from the Saviour's lips, that he was arrested and led away to undergo a +trial; cruel mocking and scourging, crucifixion and death upon the cross. + +Then cometh Joseph of Arimathea, bringing fine linen, and Nicodemus with +his hundred pounds of myrrh and aloes, and they two took the body of the +Lord Jesus and wrapped it in the linen with the spices, and laid it in +Joseph's own new tomb, which he had hewn out in a rock, wherein never man +before was laid, and rolled a great stone against the door of the +sepulcher and departed. Thus endeth Passion Week. While the body of Jesus +is in the sepulcher the world is rejoicing, and the disciples are weeping +and lamenting, according to the words of the Saviour, "Ye shall weep and +lament, but the world shall rejoice." + + He dies! the friend of sinners dies! + Lo! Salem's daughters weep around; + A solemn darkness veils the skies, + A sudden trembling shakes the ground. + +_e_--Easter (German, _Ostern_, Old Saxon _Oster_, from _osten_, signifying +rising,) is a church festival in commemoration of the resurrection of our +Lord from the dead. But the apparent victory which the enemies of Christ +had gained was of short duration, the rejoicing of the world did not long +continue, the remaining words of our Saviour must needs be fulfilled: "But +your sorrow shall be turned into joy." Now, upon the first day of the +week, very early in the morning, (Easter morning) the two Marys came to +the sepulcher bringing the sweet spices and ointments which they had +prepared for the purpose of anointing the body of the Lord Jesus, but were +greatly astonished when they saw that the great stone, which they had seen +rolled against the door of the sepulcher on Friday afternoon, was rolled +away, and an angel sitting upon it whose countenance was like lightning, +and for fear of whom the keepers did shake and become as dead men. But to +the women he said, "Fear not ye; for I know that ye seek Jesus which was +crucified, He is not here, for He is risen." That you may know for a +certainty that He is risen, come and see the place where you saw Him laid +only a few hours ago. Now go quickly and tell His disciples that He is +risen from the dead, and behold He goeth before you into Galilee, there +shall ye see Him. And they departed quickly from the sepulcher with fear +and great joy, and did run to carry the good news to the disciples. But +how much greater their joy soon after their departure when Jesus himself +met them with the comforting words, "Be not afraid, but go tell my +brethren that they go into Galilee, and there shall they see Me." + +The subject for conversation for the past two days had been Jesus and the +crucifixion, but now Jesus and the resurrection. Some believed, but some +doubted. Others ran to the sepulcher and found it even as the women had +said. While the chief priests and elders hired the soldiers to say that +the disciples came by night and stole him away while we slept. But how +should they know what had become of Him if they were sleeping? The truth +was they were so overcome with fear by the brightness of the angels' +countenance that they became as dead men, not knowing what was transpiring +around them. But it was truly good tidings and great joy to the disciples +of Christ on that Easter morning. + + The rising God forsakes the tomb; + In vain the tomb forbids His rise; + Vain the stone, the watch, the seal, + Christ has burst the gates of hell; + Death in vain forbids His rise; + Christ hath opened Paradise. + +The spirit of Christ in the prophets had testified beforehand the +suffering of Christ and the glory that should follow. That morning and +that day was not only joyful to the disciples of Christ, but _glorious_; +it was "joy unspeakable and _full_ of glory." Although 1863 years have +rolled around since that Easter morning, yet we are as much interested in +what then and there transpired as were the Marys, and Peter, and John, who +were the first at the sepulcher, and who were permitted the same day to +see their risen Lord, whom having not seen, we love; in whom, though now +we see Him not, yet believing, we [as well as they] rejoice "with joy +unspeakable and full of glory." + +Low Sunday. The first Sunday after Easter is so called because it was +customary to repeat on this day some part of the solemnity which was used +on Easter day, whence it took the name of Low Sunday, being celebrated as +a feast, but of a lower degree than Easter day itself. The next Sunday +after Easter has been popularly, so called in England, perhaps by +corruption for close, (_Pascha Clausum_) close of Easter. _Dominica_ in +_Albis_, (the Sunday of white garments) a title anciently given to the +first Sunday after Easter, because on this day those persons who had been +baptized at Easter appear for the last time in the chrysomes, or white +robes which they received at baptism. These were laid up in the church as +evidences of their baptismal profession. + +Rogation Days, (Latin _rogare_, to beseech,) are the Monday, Tuesday and +Wednesday after Rogation Sunday and before Ascension Day, (Holy Thursday.) +About the middle of the fifth century Mamertus, bishop of Vienna, upon the +prospect of a great fire that threatened his diocese, appointed that +extraordinary prayer and supplication should be offered up to God, with +fasting, for averting the impending evils upon the above mentioned days; +from which supplications (called by the Latins _rogationes_) these days +have ever since been called Rogation Days. As retained in our present +calendar, they are simply private fasts. + +_f_--Ascension Day, or Holy Thursday, one of the great religious festivals +of the Roman Catholic and Episcopal churches, is held on the fortieth day +after Easter, and ten days before Whitsun Day, to commemorate the +Ascension of our Lord into heaven. Ascension Day has been observed at +least since the year of our Lord 64, and perhaps earlier. Saint Augustine +believed it to have been instituted either by the apostles themselves, or +the bishops immediately succeeding them. + +Expectation Week is the whole of the interval between Ascension Day and +Whitsun Day, so called because at this time the apostles, according to the +command of our Saviour, continued at Jerusalem, in earnest prayer and +expectation of the Holy Comforter which was to abide with them forever. +The Sunday between Ascension Day and Whitsun Day is called Expectation +Sunday. + +Pentecost, (Greek, _Pentecostos_, fiftieth), a Jewish festival; so called +because it was observed on the fiftieth day after the feast of unleavened +bread, called also the feast of weeks, being celebrated seven weeks from +the feast of the Passover. It also commemorated the giving of the law on +Mount Sinai upon that day. The origin of the Anglo-Saxon name of White +Sunday, which also occurs in Icelandic, is somewhat obscure, for in the +Roman churches the _Dominica_ in _Albis_, (Low Sunday, q. v.) so called +from the white robes then worn by the persons baptized at Easter, has +always been the Sunday immediately following Easter. It hardly seems +probable that there should be another Sunday of White Garments within six +weeks. In German it is known by the name _Pfingsten_, old German +_Wingsten_, old English _Whitsun_, hence, probably, our word Whitsun Day, +not White Sunday. + +_g_--Whitsun Day, or Pentecost, is the last of the four _great_ festivals +in the ecclesiastical year, held in commemoration of the outpouring of the +Holy Spirit on the infant church ten days after the Ascension. Among the +last words of our Saviour to the apostles on the very day that He was +taken up, were "Behold I send the promise of my Father upon you, but tarry +ye in the city of Jerusalem until ye be endowed with power from on high." +After ten days of earnest, believing prayer, and expectation, suddenly, +but not unexpectedly, there came a sound from heaven as a rushing, mighty +wind, and it filled all the house where they were sitting, and there +appeared unto them cloven tongues like as of fire, and it sat upon each of +them; and they were all filled with the Holy Ghost, and began to speak +with other tongues as the Spirit gave them utterance; and the multitude +came together, and were amazed, saying one to the other what meaneth this? +Others mocking said, these men are full of new wine. But Peter lifted up +his voice and said, these are not drunken as ye suppose, seeing it is but +the third hour of the day, (nine o'clock in the morning,) men are not +usually drunk so early in the morning; but this is that which the prophet +Joel eight hundred years ago said should come to pass in these last days; +the promise of the Father, the baptism of the Holy Ghost for which they +had been waiting for the past ten days; something of that _glory_ that +should follow the crucifixion, death, resurrection and ascension of the +Lord Jesus into Heaven, the glory of the Christian church, of the +Christian dispensation, and which is destined to fill the whole earth. + + "Waft, Waft, ye winds his story, + And you, ye waters, roll, + Till like a sea of glory, + It spreads from pole to pole." + +_h_--Trinity Sunday, the octave, or eighth day of the feast of Pentecost, +is a church festival held in commemoration of the doctrine of the Trinity. +The introduction of this day into the calendar is of comparatively recent +date, it being established by Pope Benedict XI, in the year of our Lord +1305. It is probable that the zeal of many Christians against the use of +images in the eighth and ninth centuries may have been the first cause of +the appointment of a distinct day for meditating upon the nature of the +Holy Trinity in unity, or the one true God as distinguished from idols. +The reason for its late introduction is that in the creed of the church, +and in its psalms, hymns, and doxologies, great prominence was given to +this doctrine, and it was thought that there was no need to set apart a +particular day for that which was done every day. This is the last of the +movable feasts in the ecclesiastical year, being held eight weeks after +Easter; so it may happen as early as the 17th of May or as late as the +20th of June. The length of both Epiphany and Trinity-tide depend upon the +date of Easter. As Epiphany-tide is shortened by the early date of +Easter, so Trinity-tide is lengthened proportionately, and as +Epiphany-tide is lengthened by the later date of Easter so Trinity-tide is +shortened proportionately; so Trinity-tide may contain no more than 196 +days nor less than 161. (See tables at the close of this chapter.) + +All Saints Day, or All hallowmass (Anglo-Saxon _all_, and _halig_, holy) a +festival celebrated by the Roman Catholic and Episcopal churches on the +first day of November, in honor of all Saints and martyrs. It was +introduced into the Western church in the beginning of the seventh century +by Boniface. The number of saints being exceedingly multiplied, it was +found too burdensome to dedicate a feast day to each, there being, indeed, +scarcely hours enough in the year to distribute among them all. It was +therefore resolved to commemorate on one day all who had no particular +day. By order of Gregory IV, it was celebrated on the first of November, +834; formerly the first of May was the day appointed. It was introduced +into England about 870, and is still observed in the English and Lutheran +churches, as well as the Church of Rome on the first of November. + +All-Souls' Day, a festival held by Roman Catholics on the 2d of November, +for special prayer in behalf of all the faithful dead. It was first +introduced in 998, by Odilon, Abbot of Clugni, who enjoined it on his own +order. It was soon after adopted by neighboring churches. It is the day on +which, in the Romish church, extraordinary masses are repeated for the +relief of souls said to be in purgatory. Formerly on this day persons +dressed in black perambulated the towns and cities, each provided with a +bell of dismal tone, which was rung in public places by way of exhortation +to the people to remember the souls in purgatory. In some parts of the +west of England it is still the custom for the village children to go +around to all their neighbors souling, as they call it, collecting small +contributions, and singing the following verses, taken down from two of +the children themselves: + + Soul! Soul! for a soul-cake, + Pray good mistress, for a soul-cake, + One for Peter, two for Paul, + Three for Him that made us all. + + Soul! soul! for an apple or two; + If you've got no apples, pears will do, + Up with your kettle, and down with your pan, + Give me a good big one and I'll be gone. + +The soul cake referred to in the verses is a sort of bun which the people +used to make, and to give to one another on the 2d of November. + +In the following tables there is presented at one view the day of the +month on which the principal feasts and fasts fall in the ecclesiastical +year 1817-18 and 1885-86. In the former Easter happens at its earliest +possible date, in the latter at its latest date in this century: + + ------------------------------------------+--------------+-------------- + _YEAR 1817-18._ | _Days in_ | _Sundays in_ + |_Each Season._|_Each Season._ + ------------------------------------------+--------------+-------------- + | | + _a_--Advent Sunday, November 30th; | | + Advent-tide, | 25 | 4 + | | + _1st_ Ember Week, after December 13th; | | + Ember Days, Wednesday, Friday and | | + Saturday. | | + | | + _b_--Christmas, December 25th; | | + Christmas-tide, | 12 | 2 + | | + _c_--Epiphany, January 6th; Epiphany-tide,| 12 | 1 + Septuagesima Sunday, January 18th, | 7 | 1 + Paschal season from Jan. 18th to | | + March 29th, 70 days | | + Sexagesima Sunday, January 25th, | 7 | 1 + Quinquagesima Sunday, February 1st, | 3 | 1 + Shrove-tide, (confession time) Shrove| | + Tues., Feb. 3d. | | + | | + _d_--Ash Wednesday, Feb 4th, Lent begins; | | + Lenten-tide, | 46 | 6 + First Sunday in Lent (Quadragesima) | | + February 8th. | | + | | + _2d_ Ember Week after first Sunday in | | + Lent; Ember Days, Wednesday, Friday| | + and Saturday. | | + Holy Week, the week before Easter; | | + Special Days, Palm Sunday, Spy | | + Wednesday, Maundy Thursday, and | | + Good Friday, March 15th, 18th, | | + 19th and 20th. | | + | | + _e_--Easter Sunday, March 22d; | | + Easter-tide, | 39 | 6 + Low Sunday, March 29th; Paschal | | + Season ends. | | + Rogation Sunday, April 26th; Rogation| | + Days, the Monday, Tuesday and | | + Wednesday after Rogation Sunday. | | + | | + _f_--Ascension Day (Holy Thursday), April | | + 30th; Ascension-tide, | 10 | 1 + Expectation Sunday, First Sunday | | + after Ascension, May 3d. | | + | | + _g_--Whitsun Day, (Pentecost) May 10th; | | + Whitsun-tide, | 7 | 1 + | | + _3d_ Ember Week, after Whitsun Day; Ember | | + Days, Wednesday, Friday and | | + Saturday. | | + | | + _h_--Trinity Sunday, May 17th; | 196 | 28 + Trinity-tide, | | + | | + _4th_ Ember Week, after September 14th; | | + Ember Days, Wednesday, Friday and | | + Saturday. | | + | | + All Saints' Day, November 1st. | | + | | + All Souls' Day, November 2d. | | + +--------------+-------------- + Appendix K. | 364 | 52 + ------------------------------------------+--------------+-------------- + + ------------------------------------------+--------------+-------------- + _YEAR 1885-86._ | _Days in_ | _Sundays in_ + |_Each Season._|_Each Season._ + ------------------------------------------+--------------+-------------- + | | + _a_--Advent Sunday, November 29th, | | + Advent-tide, | 26 | 4 + | | + _1st_ Ember Week, after December 13th; | | + Ember Days, Wednesday, Friday and | | + Saturday. | | + | | + _b_--Christmas, December 25th; | | + Christmas-tide, | 12 | 2 + | | + _c_--Epiphany, January 6th; Epiphany-tide,| 46 | 6 + Septuagesima Sunday, February 21st, | 7 | 1 + Paschal season, from Feb. 21st to May| | + 2d, 70 days. | | + Sexagesima Sunday, February 28th, | 7 | 1 + Quinquagesima Sunday, March 7th, | 3 | 1 + Shrove-tide, (confession time) Shrove| | + Tues., Mar. 9th. | | + | | + _d_--Ash Wednesday, March 10th, Lent | | + begins; Lenten-tide | 46 | 6 + First Sunday in Lent (Quadragesima) | | + March 14th. | | + | | + _2d_ Ember Week after first Sunday in | | + Lent; Ember Days, Wednesday, Friday| | + and Saturday. | | + Holy Week, the week before Easter; | | + Special Days, Palm Sunday, Spy | | + Wednesday, Maundy Thursday and Good| | + Friday, April 18th, 21st, 22d and | | + 23d. | | + | | + _e_--Easter Sunday, April 25th; | | + Easter-tide, | 39 | 6 + Low Sunday, May 2d, Paschal Season | | + ends. | | + Rogation Sunday, May 30th; Rogation | | + Days, the Monday, Tuesday and | | + Wednesday after Rogation Sunday. | | + | | + _f_--Ascension Day (Holy Thursday), June | | + 3d; Ascension-tide, | 10 | 1 + Expectation Sunday, first Sunday | | + after Ascension, June 6th. | | + | | + _g_--Whitsun Day, (Pentecost) June 13th; | | + Whitsun-tide, | 7 | 1 + | | + _3d_ Ember Week, after Whitsun Day; Ember | | + Days, Wednesday, Friday and | | + Saturday. | | + | | + _h_--Trinity Sunday, June 20th; | | + Trinity-tide, | 161 | 23 + | | + _4th_ Ember Week, after September 14th; | | + Ember Days, Wednesday, Friday and | | + Saturday. | | + | | + All Saints' Day, November 1st. | | + | | + All Souls' Day, November 2d | | + +--------------+-------------- + Appendix K. | 364 | 52 + ------------------------------------------+--------------+-------------- + + + + +CHAPTER VIII. + +HEBREW CALENDAR. + + +To the Bible student a knowledge of the Hebrew calendar is indispensable, +if he would know how the date of events recorded in the Bible are made to +correspond with our present English calendar. From the exodus (1491 B. C.) +downward, the Hebrew month was lunar, and commenced invariably with the +new moon. + +Dr. Smith, author of Bible Dictionary, says that the terms for month and +moon have the same close connection in the Hebrew language as in our own, +only the Hebrew Codesh (that is new moon) is, perhaps, more distinctive +than the corresponding term in our language; for it expresses not simply +the idea of a lunation, but the recurrence of a period commencing +definitely with the new moon. Though the identification of the Jewish +month with our own cannot be effected with precision on account of the +variations that must necessarily exist between the lunar and the solar +month, each of the former ranging over portions of two of the latter, +still it can be shown how they may be made to coincide very nearly by a +systematic method of intercalation. + +Now from new moon to new moon again, is about 29-1/2 days; therefore, the +Hebrew year consisted of 354 days, for 29-1/2 × 12 = 354; so that the +epact, (which is the excess of the solar year beyond the lunar) is eleven +days. Hence, had they no method of intercalation, the commencement of +their year would go back eleven days every year, and consequently make a +revolution of the seasons every thirty-three years, for 365 ÷ 11 = 33 +nearly. + +To illustrate, let us suppose that the new moon of Nisan, which is the +first month in the Sacred year, should on any given year fall on the 10th +of April, then the following year it would fall on the 30th of March, +which is eleven days earlier; the second year it would fall on the 19th of +March or twenty-two days earlier; the third year the new moon would fall +on the 8th of March or thirty-three days earlier, but that would not be +the new moon of Nisan, which cannot happen earlier than the 11th, so the +following moon which happens thirty days later on the 7th of April is the +new moon of Nisan. Hence it may be seen that by intercalating a full month +every three years, or which comes nearer to accuracy seven times in +nineteen years, restores the coincidence of the solar and the lunar year, +and consequently the moons to the same day of the month on which they fell +nineteen years before. + +The method of designating the months previous to the exodus, was by their +numerical order, as the ancient Hebrews had no particular name to express +their month. They said the first, second and third month, and so on. No +names of months appear in the Bible until about the time of the +institution of the passover, when the Lord spake unto Moses and Aaron in +the land of Egypt, saying this month, (Abib, which appears to have had its +origin in Egypt,) shall be unto you the beginning of months; it shall be +the first month of the year to you. + +The names of the months appear to belong to two distinct periods. In the +first place we have those peculiar to the Jews previous to the captivity, +viz: Abib, the first month in commemoration of the exodus; Zif, the +second, Ethanim, the seventh, and Bul, the eighth. These names are of +Hebrew origin, and have reference to the characteristics of the seasons, a +circumstance which clearly shows that the months, by intercalation, were +made to return at the same period of the year. Thus, Abib was the month of +the ears of corn, that is the month in which the ears of corn became full, +or ripe on the 16th day, that is the 2d day of the feast of unleavened +bread. Zif, the month of blossoms or the bloom of flowers. Ethanim, the +month of gifts, that is of fruits, and Bul, the month of rain. These were +superceded after the captivity, by Nisan, Iyar, Tisri and Hesvan, or +Marchesvan. + +Marchesvan, coinciding as it does with the rainy season in Palestine, is +considered a pure Hebrew term. The modern Jews consider it a compound +word, from mar, drop, and Chesvan; the former betokening that it was wet, +and the latter being the proper name of the month. Hence the name +indicates the wet month. In the second place we have the names of six +others which appear in the Bible subsequently to the Babylonian captivity, +viz.: Sivan, the third; Elul, the sixth; Kislev, the ninth; Tebet, the +tenth; Sebat, the eleventh, and Adar, the twelfth. There are two other +months whose names do not appear in the Bible, viz.: Tamuz, the fourth, +and Ab, the fifth. The name of the intercalary month is called Ve-Adar, or +2d Adar because placed in the calendar after Adar and before Nisan. + +Dr. Smith says these names are probably borrowed from the Syrians in whose +regular calendar we find names answering to most of them. He also says it +was the opinion of the Talmudists, that these names were introduced by the +Jews who returned from the Babylonish captivity, and also that they are +certainly used exclusively by writers of the post-Babylonian period. + +Inasmuch as the Hebrew months coincided with the seasons, as we have +already shown, it follows as a matter of course, that an additional month +must have been inserted every third year, which would bring the number up +to thirteen. No notice, however, is taken of this month in the Bible, +neither have we reason to think that it was inserted according to any +exact rule, but it was added whenever it was discovered that the barley +harvest did not coincide with the ordinary return of the month Abib. It +has already been shown that in the modern Jewish calendar the intercalary +month is introduced seven times in nineteen years, according to the +Metonic, or lunar cycle which was adopted by the Jews about 360 A. D. + +The Hebrew calendar is dated from the creation, which is supposed to have +taken place 3761 years before Christ. Hence, to find the number of cycles +elapsed since the creation, also the number in the cycle, we have the +following rule: Add 3761 to the date, divide the sum by nineteen; the +quotient is the number of cycles, and the remainder is the number in the +cycle. Should there be no remainder, the proposed year is, of course, the +last or nineteenth of the cycle. Thus, for the year 1883, we have 1883 + +3761 ÷ 19 = 297, remainder 1; therefore, 297 is the number of cycles, and +1 the number in the cycle. Again, for the year 1893, we have 1893 + 3761 ÷ +19 = 297, remainder 11; therefore 297 is the number of cycles, and 11 the +number in the cycle. Again for the year 1901, we have 1901 + 3761 ÷ 19 = +298, remainder 0; therefore 298 is the number of cycles, and 19 the last +of the cycle. Hence it may be seen that the present cycle commenced with +1883, that 11 is the number in the cycle for the present year 1893, also +that the cycle ends with 1901; so that the next cycle commences with 1902. +If the remainder after dividing by nineteen be 3, 6, 8, 11, 14, 17 or 19 +(0), the year is intercalary or embolismic, consisting of 384 days; if +otherwise it is ordinary, containing only 354 days; so that in a cycle of +nineteen years, we have twelve ordinary years of 354 days each, and seven +embolismic years of 384 days each. But, in either case, the year is +sometimes made a day more, and sometimes a day less, in order that certain +festivals may fall on proper days of the week for their due observance. +Hence the ordinary year may consist of 353, 354 or 355 days, and the +embolismic year of 383, 384 or 385 days. + +In the modern Jewish calendar the New Year commences with the new moon of +Tisri, which may happen as early as the 5th of September or as late as the +5th of October. The new moon of Nisan, which is the first month in the +Sacred year, may happen as early as the 11th of March or as late as the +11th of April. It should be borne in mind that the names of the months +Abib, Zif, Ethanim and Bul were superceded after the captivity, by Nisan, +Iyar, Tisri and Hesvan or Marchesvan; also the name of the third month in +the civil year, Chisleu in the Bible, Kislev in the modern Jewish +calendar. In table No. 1 we have the names of the months in numerical +order, also the number of days in each month. Though the months consist of +30 and 29 days alternately, yet, in the embolismic year, Adar, which in +common years has 29 days, is given 30 days, and 2d Adar 29; so that two +months of 30 days come together. Table No. 2 shows the earliest and the +latest possible date of the new moons of each of the months respectively. + +TABLE 1. HEBREW MONTHS. + + _Sacred Year._ _Civil Year._ + Nisan 30 | Tisri 30 + Iyar 29 | Hesvan 29 + Sivan 30 | Kislev 30 + Tamuz 29 | Tebet 29 + Ab 30 | Sebat 30 + Elul 29 | Adar 30 + Tisri 30 | 2d Adar, Embolismic 29 + Hesvan 29 | Nisan 30 + Kislev 30 | Iyar 29 + Tebet 29 | Sivan 30 + Sebat 30 | Tamuz 29 + Adar 30 | Ab 30 + 2d Adar, Embolismic 29 | Elul 29 + + +TABLE II. HEBREW MONTHS. + + Nisan, March 11th or April 11th + Iyar, April 11th " May 10th + Sivan, May 10th " June 9th + Tamuz, June 9th " July 9th + Ab, July 9th " August 7th + Elul, August 7th " September 5th + Tisri, September 5th " October 5th + Hesvan, October 6th " November 4th + Kislev, November 4th " December 3d + Tebet, December 3d " January 2d + Sebat, January 3d " February 10th + Adar, February 10th " March 12th + +The charts on the three following pages are used to illustrate the +correspondence of the Hebrew months with our own. Each chart represents +the ecliptic, which is the apparent path of the Sun or real path of the +Earth, also the names of the months as they occur in their seasons. The +figures represent the days of the month on which the new moons of the +Hebrew calendar fall. These charts represent the month and the day of the +month on which both the Sacred and the Civil year begins and ends for +three successive years. Hence it may be seen that by intercalating a month +every three years the new moons are restored, very nearly, to the place +they occupied three years before. + + +CHART I. + +[Illustration: This chart represents the day of the month on which all the +new moons fall in the year 1891-92. The sacred year commenced with the new +moon of Nisan on the 9th of April, and the civil year with the new moon of +Tisri on the 3d of October, 1891, and ended respectively with the 28th of +March and the 21st of September, 1892.] + + +CHART II. + +[Illustration: This chart represents the day of the month on which all the +new moons fall in the year 1892-93. It may be here seen that the year +begins and ends about eleven days earlier than the year preceding, also +that all the new moons fall eleven days earlier than they did in the +preceding year.] + + +CHART III. + +[Illustration: This chart represents the year 1893-94. Though the year +begins about eleven days earlier than the preceding, viz.: the 17th of +March, yet it being the year in which a 2d Adar is intercalated, instead +of falling back eleven days, the beginning of the following year is +carried forward 20 days, making a year of 384 days; so that the year +1894-95 will commence with April 5. In 1891 we commenced with April 9. It +will be 19 years before we commence on the 9th of April again.] + + + + +APPENDIX. + + +A.--PAGE 12. + +Authors differ in regard to the length of the solar year. One gives 365 +days, 5 hours, 47 minutes and 51.5 seconds; another, 365 days, 5 hours, 48 +minutes and 46 seconds; and still another, 365 days, 5 hours, 48 minutes +and 49.62 seconds. In this work the last has been accepted as the true +length of the solar year, and all calculations have been made accordingly. + + +B.--PAGE 19. + +There is an apparent discrepancy among authors in regard to the +intercalary day. While one asserts that it was between the 24th and 25th +of February, another equally reliable, says that the 25th was the sexto +calendas and the 24th was the bis-sexto calendas of the Julian calendar. +Now it should be borne in mind that the Julian calendar is the basis of +our own, and is identical with it in the number of months in the year, and +in the number of days in the month. Also when the method of numbering the +days from the beginning of the month was adopted, the intercalation was +made to correspond with the intercalary day in the Julian calendar. + +As in the Julian calendar there were twice the sixth day, so in the +reformed calendar there were twice the 24th day, which was equivalent to +29 days in February. When the calendar was again corrected, making the +29th the intercalary day, then the 24th corresponded with the bis-sexto +calendas of the Julian calendar. This reconciles the apparent +discrepancy. While one author refers to the calendar in which the Julian +rule of intercalation is adopted, another refers to the calendar when so +corrected as to make the 29th of February the intercalary day. See +following table: + + -----------------------------------++----------------------------------- + JULIAN METHOD || MODERN METHOD + OF INTERCALATION. || OF INTERCALATION. + -----------------------------------++----------------------------------- + 1 |_Cal._ | Calendae || 1 |_Cal._ | Calendae + 2 | 4 | Quarto Nonas || 2 | 4 | Quarto Nonas + 3 | 3 | Tertio Nonas || 3 | 3 | Tertio Nonas + 4 | 2 | Pridie Nonas || 4 | 2 | Pridie Nonas + 5 |_Nomes_| Nonae || 5 |_Nomes_| Nonae + 6 | 8 | Octavo Idus || 6 | 8 | Octavo Idus + 7 | 7 | Septimo Idus || 7 | 7 | Septimo Ides + 8 | 6 | Sexto Idus || 8 | 6 | Sexto Idus + 9 | 5 | Quinto Idus || 9 | 5 | Quinto Idus + 10 | 4 | Quarto Idus || 10 | 4 | Quarto Idus + 11 | 3 | Tertio Idus || 11 | 3 | Tertio Idus + 12 | 2 | Pridie Idus || 12 | 2 | Pridie Idus + 13 | _Ides_| Idus || 13 | _Ides_| Idus + 14 | 16 | Sextodecimo Calendas || 14 | 16 | Sextodecimo Calendas + 15 | 15 | Quintodecimo Calendas || 15 | 15 | Quintodecimo Calendas + 16 | 14 | Quartodecimo Calendas || 16 | 14 | Quartodecimo Calendas + 17 | 13 | Tertiodecimo Calendas || 17 | 13 | Tertiodecimo Calendas + 18 | 12 | Duodecimo Calendas || 18 | 12 | Duodecimo Calendas + 19 | 11 | Undecimo Calendas || 19 | 11 | Undecimo Calendas + 20 | 10 | Decimo Calendas || 20 | 10 | Decimo Calendas + 21 | 9 | Nono Calendas || 21 | 9 | Nono Calendas + 22 | 8 | Octavo Calendas || 22 | 8 | Octavo Calendas + 23 | 7 | Septimo Calendas || 23 | 7 | Septimo Calendas + 24 | 6 | Bis-Sexto Calendas || 24 | 6 | Bis-sexto Calendas + 24 | 6 | Sexto Calendas || 25 | 6 | Sexto Calendas + 25 | 5 | Quinto Calendas || 26 | 5 | Quinto Calendas + 26 | 4 | Quarto Calendas || 27 | 4 | Quarto Calendas + 27 | 3 | Tertio Calendas || 28 | 3 | Tertio Calendas + 28 | 2 | Pridie Calendas || 29 | 2 | Pridie Calendas + ---+-------+-----------------------++----+-------+---------------------- + + +C.--PAGE 20. + +The city where the great council was convened in 325 is not in France, as +some have supposed, that being a more modern city of the same orthography, +but pronounced Nees. The city which is so frequently referred to in this +work is in Bythinia, one of the provinces of Asia Minor, situated about 54 +miles southeast of Constantinople, of the same orthography as the former, +but pronounced Ni´ce, and was so named by Lysimachus, a Greek general, +about 300 years before Christ, in honor of his wife Nicea. + + +D.--PAGE 23. + +Between the 23d and 24th of February, 46 years before Christ, there was +intercalated a month of 23 days according to an established method, but +still the civil year was in advance of the solar year by 67 days; so that +when the Earth in her annual revolutions should arrive to that point of +the ecliptic marked the 22d of October, it would be the 1st day of January +in the Roman year. + +Cæsar and his astronomers, knowing this fact and fixing on the 1st day of +January, 45 years before Christ and 709 from the foundation of Rome, for +the reformed calendar to take effect, were under the necessity of +intercalating two months, together consisting of 67 days. Now, as the +civil year would end on the 22d of October, true or solar time, it would +be reckoned in the old calendar the 1st day of January; so they let the +old calendar come to a stand while the Earth performs 67 diurnal +revolutions, and thereby restored the concurrence of the solar and the +civil year. + +As an illustration, let us suppose that in a certain shop where hangs a +regulator are two clocks to be regulated. Both are set with the regulator +at 8 a. m. to see how they will run for ten consecutive hours. It was +found that when it was 6 p. m., by the first clock, it was 5:50 by the +regulator, the clock having gained one minute every hour. + +To rectify this discrepancy we must intercalate 10 minutes by stopping the +clock until it is 6 by the regulator. By this means the coincidence is +restored, and the time lost in the preceding hours is now reckoned in this +last hour, making it to consist of 70 minutes. By this it may be seen how +Cæsar reformed the Roman calendar. The Roman year was too short, by reason +of which the calendar was thrown into confusion, being 90 days in advance +of the true time, so that December, January and February took the place in +the seasons of September, October and November, and September, October and +November the place of June, July and August. To make the correction he +must stop the old Roman clock (the calendar) while the Earth performs 90 +diurnal revolutions to restore the concurrence of the solar and the civil +year, making the year 46 B. C. to consist of 445 days. + +It was also found that when it was 6 p. m., by the regulator, it was only +5:50 by the second clock, it having lost one minute every hour. To rectify +this discrepancy we must suppress 10 minutes, calling it 6 p. m., turning +the hands of the clock to coincide with the regulator, making the last +hour to consist of only 50 minutes, too much time having been reckoned in +the preceding hours. It may be seen by this illustration, how Gregory +corrected the Julian calendar, the Julian year was too long, consequently +behind true or solar time, so that when the correction was made in 1582, +the ten days gained had to be suppressed to restore the coincidence, +making the year to consist of only 355 days. + +As the solar year consists of 365 days and a fraction, Cæsar intended to +retain the concurrence of the solar and the civil year by intercalating a +day every four years; but this made the year a little too long, by reason +of which it became necessary, in 1582, to rectify the error, and by +adopting the Gregorian rule, three intercalations are suppressed every 400 +years; so that by a series of intercalations and suppressions, our +calendar may be preserved in its present state of perfection. + + +E.--PAGE 23. + +As the day and the civil year always commence at the same instance, so +they must end at the same instance; and as the solar year always ends with +a fraction, not only of a day, but of an hour, a minute and even a second; +so there is no rule of intercalation by which the solar and the civil year +can be made to coincide exactly. But the discrepancy is only a few hours +in a hundred years, and that is so corrected by the Gregorian rule of +intercalation that it would amount to a little more than a day in 4,000 +years; and by the improved method less than a day in 100,000 years. + + +F.--PAGE 26. + +It has been stated that by adopting the Julian rule of intercalation, time +was gained; it has also been stated that by the same rule time was lost. +Now both are true. Time is gained in that there is too much time in a +given year, in other words, the year is too long; but what is gained in a +given year is lost to the following year. + +As an illustration let us take the case of the supposed solar year of 365 +days, and the civil year of 366. The civil year would gain one day every +year, or be too long by one day; but the one day gained is lost to the +following years, and if continued 31 years, when the Earth is in that part +of its orbit marked the 1st day of January 32, the civil year would reckon +the 1st day of December 31; so that in the thirty-one years would reckon +thirty-one days too much, and before the civil year is completed, the +Earth will have passed on in its orbit to a point marked the 1st day of +February. + +Now to reform such a calendar, we would have to suppress or drop the +thirty-one days, by calling the 1st day of December the 1st day of +January, and thus the month of December would disappear from the calendar +in the year 31, making a year of only eleven months, consisting of 334 +days. + +If this method be continued 92 years, there would be gained 92 days, to +the loss of 92 days in the year 92. If the calendar be now reformed by +suppressing 92 days, calling the 1st day of October, 92, the 1st day of +January, 93, then October, November and December would disappear from the +calendar in the year 92; and if continued 365 years there would be crowded +into 364 years, 364 days too much; gained to the 364 years to the total +loss of the year 365, passing from 364 to 366; 365 disappearing from the +calendar. + + +G.--PAGE 50. + +An era is a fixed point of time from which a series of years is reckoned. +Among the nations of the Earth there are no less than twenty-five +different eras; but the most of them are not of enough importance to be +mentioned here. Attention is particularly called to the Roman era which +commenced with the building of the city of Rome 753 years before Christ. + +Also the Mahometan era, or the era of the Hegira, employed in Turkey, +Persia and Arabia, which is dated from the flight of Mahomet from Mecca to +Medina, which was Thursday night, the 15th of July, A. D., 622, and it +commenced on Friday, the day following. + +But there is a point from which all computation originally commenced, +namely, the creation of man. Such an era is called the Mundane era. Now +there are different Mundane eras--the common Mundane era 4,004 B. C., the +Grecian Mundane era 5,598 B. C., and the Jewish Mundane era 3,761 B. C. +All these commence computation from the same point, but differ in regard +to the time which has elapsed since their computation commenced. God's +people used the Mundane era, until the Great Creator appeared among us, as +one of us, in the person of our Lord Jesus Christ, to accomplish the great +work of redemption; then His name was introduced as the turning point of +the ages, the starting point of computation. + +This was done by Dionysius Exiguus in the year of our Lord about 540, +known at that time as the Dionysian, as well as the Christian era, and was +first used in historical works by the venerable Bede early in the eighth +century. "It was a great thought of the little monk (whether so called +from his humility or littleness of stature is unknown), to view Christ as +the turning point of the ages, and to introduce this view into +chronology." + +All honor to him who introduced it, and to the nations which have +approved, for thus honoring the Great Redeemer. Dionysius probably did not +know, neither is it now known for a certainty the year of Christ's birth, +but it is evident, however, from the best authorities, that the era +commenced at least five years too late, and probably more. + + +H.--PAGE 57. + +It is recorded that, in the time of Numa, the vernal equinox fell on the +25th of March, and that Julius Cæsar restored it to the 25th, when he +reformed the ancient Roman calendar in the year 46 B. C. It is also +recorded that in less than 400 years from that time, at the meeting of the +Council of Nice in 325, it had fallen back to the 21st--four days in less +than 400 years. + +Now there is an error somewhere, for it is found by actual computation +that the discrepancy between the solar and the Julian year is about three +days in 400 years. It certainly is true that the vernal equinox fell on +the 21st in 325, and was restored to that place by Gregory in 1582; since +which time it has been made to fall on the 21st by the Gregorian rule of +intercalation. Again it is stated by the same author that the +discrepancies in time from Cæsar to Gregory is thirteen days, from the +Council of Nice to Gregory ten days; now 10 + 4 = 14. While our author +states it is thirteen days, he also states it is fourteen days; a +discrepancy of one day. The mistake evidently is in making the 25th +instead of the 24th, the date of the vernal equinox in the time of Cæsar, +consequently a difference of four days instead of three from Cæsar to the +Council of Nice. + + +I.--PAGE 59. + +The concurrence of the solar and the civil year was restored by Gregory in +1582, or 1600 is the same in computation; but the discrepancy between +civil and solar time is 11 minutes and 10.38 seconds every year, which in +100 years will amount to 18 hours, and 37.3 minutes; reckoned in round +numbers 18 hours, and is represented on the chart, hours behind time 18. + +The intercalary day or 24 hours being suppressed in 1700, causes the civil +year to be 6 hours in advance of the solar, and is represented on the +chart 6 hours in advance. + +Now this discrepancy of 18 hours for the next 100 years, will cause the +civil year in 1800 to be 12 hours behind; again suppressing the +intercalation it will be 12 hours in advance. In 1900 it will be 6 hours +behind, but the correction makes 18 hours in advance. The 18 hours gained +the next 100 years restores the coincidence in the year 2000 and so on, +the solar and the civil year being made to coincide very nearly every 400 +years. + +From close examination it will become evident that the solar and the civil +year coincide twice every 400 years, though no account is made of it in +computation. From 6 hours in advance in 1700, the civil year falls back to +12 hours behind the solar in 1800, consequently they must coincide in +1733. + +Again from 12 hours in advance in 1800, it falls back to 6 hours behind +the solar in 1900, consequently they must coincide again in 1867. + +Discrepancy between Julian and solar time in--1 year is (365d. 6h.) +- (365d. 5h. 48m. 49.62s.) = (11m. 10.38s.) + + 100 years is (11m. 10.38s.) × 100 = (18h. 37.3.) + 400 " (18h. 37.3m.) × 4 = (3d. 2h. 29.2m.) + 4,000 " (3d. 2h. 29.2m.) × 10 = (31d. 0h. 52m.) + 100,000 " (31d. 0h. 52m.) × 25 = (773d. 21h. 40m.) + +Discrepancy between Gregorian and solar time in-- + + 1 year is .373m. + 100 years is .373m. × 100 = 37.3m. + 400 years 37.3m. × 4 = 2h. 29.2m. + 4,000 " (2h. 29.2m.) × 10 = 1d. 0h. 52m. + 100,000 " (1d. 0h. 52m.) × 25 = 25d. 21h. 40m. + +Discrepancy between corrected Gregorian and solar time in-- + + 4,000 years is (1d. 0h. 52m.) - 1 day = 52m. + 100,000 " " (52m. × 25) = 21h. 40m. + + +J.--PAGE 89. + +Lilius, author of the "Extended Table of Epacts," says, when the full moon +falls on the 10th of March, the following moon, which happens 29 days +later, is the paschal moon, making the 18th of April its latest possible +date. For, says he, because of the double epact that occurs on the 4th and +5th of April that lunation has only 29 days. It may have been very +convenient for Lilius, in his peculiar method of determining the date of +the paschal moon, to give to that lunation only 29 days; but nevertheless, +when he did so, it was at the expense of accuracy, for he makes a +difference of 12 days in the date of the paschal moon of that year, and +the year preceding, and only 10 days difference between that year and the +succeeding year; whereas the difference is uniformly 11 days from year to +year through the whole cycle of 19 years. + +By referring to the table on the 93d page, it will be seen that, in fixing +the date of the paschal moon, six times in a cycle of 19 years the full +moon falls before the 21st of March, and in every instance except this one +the following moon is reckoned by Lilius 30 days later. By this uniform +method of determining the date of the paschal moon, we make the 19th of +April instead of the 18th, its latest possible date; so it should be borne +in mind that whenever the 19th of April is the date of the paschal moon, +as indicated in the tables commencing with the 93d page, that Lilius, and +probably most, if not all other authors, have the 18th. + +Now it is admitted that notwithstanding the cumbersome apparatus employed +by Lilius in his calculations, the conditions of the problem are not +always satisfied, nor is it possible that they can be always satisfied by +any similar method of proceeding. We admit that none of these calculations +are perfectly exact, but the sum of the solar and lunar inequalities is +compensated in the whole period, or corrections made at the end of certain +periods, not by interrupting the order of a uniform method during the +cycle of 19 years. + +Now the table of epacts was introduced by Lilius himself, making the +excess of the solar year beyond the lunar, in round numbers 11 days. Then +why interrupt this order every 19 years, for a period of 114 years; that +is from 1596 to 1710, by making the epact 12 days for one year, and the +following year only 10? After which, from 1710 to 1900, a period of 190 +years, according to Lilius' own calculations, the epact is uniformly 11 +days, coinciding exactly with the calculations made in this work. + +Then again after the year 1900, he gives to that particular lunation, in +every lunar cycle for a period of 304 years, only 29 days; and having done +so, he is under the necessity of giving only 29 days to another lunation +in the same cycle, and also to all the cycles in the period to avoid the +absurdity of making the paschal moon fall twice on the same day in the +course of a lunar cycle. + +By reference to the 101st page, opposite the year 1905, it will be seen +that the date of the paschal moon is the 19th of April. Lilius, by giving +to that lunation only 29 days, makes its date the 18th; and then again in +the year 1916, lest he should make the paschal moon fall twice on the 18th +of April in the course of a lunar cycle, (a thing which cannot really +occur) he for the first time in more than 400 years, gives only 29 days to +a second lunation in the same cycle and of course to all the cycles in the +period of 304 years. Now the epacts for a lunar cycle of 19 years are +represented thus: + + 26 + -- + 0, 11, 22, 3, 14, 25, 6, 17, 28, 9, 20 + + 27 + -- + 1, 12, 23, 4, 15, 26, 7, 18 + +The number 26 placed over the 25 shows Lilius' first error in giving to +that lunation only 29 days. He thereby makes a difference of 12 days +between the epact 14 and 26, and only 10 between 26 and 6. He now has two +epacts of the same number 26. In order to get out of the dilemma he makes +that 27, by giving to another lunation only 29 days. + + +K.--PAGE 122-3. + +It will probably be noticed that according to the showing in the tables +the ecclesiastical year contains only 364 days. The reason for this is, +that Advent Sunday, which is the first day of the year, happens one day +earlier every year until it occurs on the 27th of November, its earliest +possible date; then the first Sunday after the 26th of November, which is +Advent Sunday, falls on the 3d of December, its latest possible date, so +that the year begins six days later, making a year of 371 days. Then there +is the loss of a day every year until Advent Sunday again falls on the +27th of November and so on. Hence, did the civil year always consist of +365 days, then the ecclesiastical year would always contain either 364 or +371 days. But as every fourth year contains 366 days, this order is so +interrupted that sometimes the first Sunday falls on the 2d instead of the +3d of December; so that the year begins only five days later, making a +year of only 370 days. Hence the ecclesiastical year may consist of either +364, 370 or 371 days. But five times out of six it will contain only 364 +days. + + +L.--PAGE 83. + +But why did the Pope, in correcting the Julian calendar in 1582, not +correct the whole error of thirteen days? Why did he leave the three days +uncorrected? This question has been asked an hundred times, but a correct +answer has never yet been given. Some say that the Pope did according to +his best ability, and would make us believe that neither he nor his +astronomers knew what the error was. This is not true, for history records +the fact of the error, and just what that error was. He simply did not +want to correct the three days, and for good reasons, which we shall +endeavor to show; reasons which every churchman ought to know. + +When Cæsar formed his calendar, 46 B. C., the vernal equinox fell on the +24th of March. At the meeting of the Council of Nice, in 325, it had +fallen back to the 21st, the error being three days in about 400 years. +Now it should be borne in mind that the Julian calendar was the only one +in use at that time, and for the next 1257 years, when in 1582, it was +corrected by Pope Gregory XIII. Easter, and all the movable feasts, had +been unsettled during the 1257 years intervening, from the Council of Nice +to Gregory, on account of the errors of the Julian calendar. The Easter +question had been the cause of a good deal of discussion between the +Eastern and Western churches during the second and third centuries, as +they could not agree on the day of the week on which that event should be +celebrated. + +The Western churches observed the nearest Sunday to the full moon of +Nisan. The Asiatics, on the other hand, adopted the 14th of Nisan upon +which to commemorate the crucifixion, and observed the festival of Easter +on the third day following, upon whatever day of the week that might fall. +Finally, the Council of Nice was convened, and the matter came before that +council, and a reconciliation was accomplished. It was then and there +agreed by the two parties that Easter should be celebrated on the first +Sunday after the full moon that falls upon or next following the day of +the vernal equinox, and that the 21st of March should be accounted the day +of the vernal equinox. + +It has already been shown that the error in the Julian calendar is three +days in 400 years; so that in 400 years from the Council of Nice the +vernal equinox had fallen back to the 18th of March; in 800 years it had +fallen back to the 15th; in 1257 years, that is in 1582, it fell on the +11th. Still the 21st of March, by the only calendar in use at that time, +was accounted the date of the vernal equinox, by which date Easter was +determined, so that, in 1582, when it was the 21st by the calendar, the +correct date was the 31st. Hence, the error had been increasing at the +rate of three days every 400 years until in 1582 it amounted to ten days. + +Again it should be borne in mind that the Pope was a churchman and wished +to abide by the decision of that council in celebrating the festival of +Easter, so he drops the ten days and restores the vernal equinox to the +21st of March, its date at the meeting of the Council of Nice in 325, the +date by which Easter day was determined. He not only made the correction, +but he so reformed the calendar that the solar and the civil year are now +made to coincide very nearly. Had he dropped the thirteen days, the vernal +equinox would have been restored to the 24th of March, its date in the +time of Cæsar, and the 24th would still be its date. But the Council of +Nice decided that the 21st should be the date by which Easter day should +be determined. Hence the reason for dropping the ten days instead of the +thirteen is evident; and it is also evident that the Pope acted +understandingly when he made the correction in 1582. + + + + +ERRATA. + + +On 51st page, ninth line from the bottom of the page, instead of 1453 ÷ 43 += 63+, should be 1453 ÷ 4 = 363+. + +On 76th page, twelfth line from the top of the page, 356 should be 365. + + + + +THE COLUMBUS CELEBRATION. + +THE WELLSBORO MAN WHO BROUGHT ABOUT THE CHANGE IN THE DATE. + +_State Superintendent D. J. Waller, in the School Journal._ + +Who brought about the change in the date? It was down in the books as +October 12th. The Committee of the National Educational Association issued +circulars to the country to observe that day. Congress solemnly resolved +that that day should be celebrated throughout the land. The Commissioners +of the World's Fair fixed upon October 12, as dedication-day, and sent out +invitations to the exercises. Suddenly there was a change. Heralded by no +newspaper discussion, preceded by no exhaustive treatise, without any +authoritative decree, a change was made to October 21. + +The following facts are indisputable. An aged retired minister in the +Methodist Episcopal Church, living in Wellsboro, Tioga County, Pa., author +of a little book entitled "Our Calendar," Rev. George Nichols Packer, saw +the error. He possessed the confidence of Judge Henry W. Williams, of the +Supreme Court of Pennsylvania. After laying the facts before him, he +secured through him the approval by the several Justices composing that +body, of an effort to change to the proper date, October 21st. Equipped +with this approval, he secured the endorsement of his project by Governor +Pattison and some of the heads of the Executive departments at Harrisburg. +He then went to Washington, gained an audience with the President, laid +the subject before the member of Congress from his district, and went +before the Congressional Committee. + +The evidence in support of the proposition was so presented that it could +not be successfully disputed. Congressman W. A. Stone skillfully enlisted +influential collegiates in an effort to correct the error already widely +spread. The correction by the National Legislature was in time to have its +influence upon President Harrison, who named October 21 in his +proclamation, as the day to be observed, and Boston and Chicago fell into +line. + +All honor to Rev. George Nichols Packer, of Wellsboro, Tioga County, +Pennsylvania. + + + + +Transcriber's Notes: + +Passages in italics are indicated by _italics_. + +Punctuation has been corrected without note. + +Corrections noted in the Errata section have been applied to the text. + +The following misprints have been corrected: + "aad" corrected to "and" (page 8) + "leap-year" corrected to "leap-years" (page 45) + missing "the" added (page 45) + "1993" corrected to "1793" (page 63) + "co-incide" standardized to "coincide" (page 71) + "Caesar" standardized to "Cæsar" (page 71) + "conseqently" corrected to "consequently" (page 74) + "1736" corrected to "1737" (page 96) + "countenace" corrected to "countenance" (page 114) + +Other than the corrections listed above, inconsistencies in spelling and +hyphenation have been retained from the original. + +On page 37, "3 400" is presented with a space as in the original text. + + + + + + +End of the Project Gutenberg EBook of Our Calendar, by George Nichols Packer + +*** END OF THIS PROJECT GUTENBERG EBOOK OUR CALENDAR *** + +***** This file should be named 36197-8.txt or 36197-8.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/3/6/1/9/36197/ + +Produced by Bryan Ness and the Online Distributed +Proofreading Team at http://www.pgdp.net (This file was +produced from images generously made available by The +Internet Archive.) + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Our Calendar + +Author: George Nichols Packer + +Release Date: May 23, 2011 [EBook #36197] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK OUR CALENDAR *** + + + + +Produced by Bryan Ness and the Online Distributed +Proofreading Team at http://www.pgdp.net (This file was +produced from images generously made available by The +Internet Archive.) + + + + + + +</pre> + + +<p> </p> +<div class="figcenter"><img src="images/cover.jpg" alt="" /></div> +<p> </p><p> </p> + +<p class="center"><span class="giant">OUR CALENDAR.</span></p> +<p> </p> +<p class="center"><span class="huge">The Julian Calendar and Its Errors.</span></p> +<p class="center">HOW CORRECTED BY THE GREGORIAN.</p> +<p> </p> +<p class="center"><span class="big">Rules For Finding the Dominical Letter,</span></p> +<p class="center"><small>AND THE DAY OF THE WEEK OF ANY EVENT FROM THE<br /> +DAYS OF JULIUS CÆSAR 46 B. C. TO THE YEAR OF<br /> +OUR LORD FOUR THOUSAND—A NEW AND EASY<br /> +METHOD OF FIXING THE DATE OF EASTER.</small></p> +<p> </p> +<p class="center"><span class="big">HEBREW CALENDAR;</span></p> +<p class="center"><small>SHOWING THE CORRESPONDENCE IN THE DATE OF<br /> +EVENTS RECORDED IN THE BIBLE WITH OUR<br /> +PRESENT GREGORIAN CALENDAR.</small></p> +<p> </p> +<p class="center"><span class="smcap">Illustrated by Valuable Tables and Charts.</span></p> +<p> </p> +<p class="center">BY REV. GEORGE NICHOLS PACKER,<br /> +CORNING, N. Y.</p> + +<p> </p><p> </p> +<p><span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span></p> +<p class="center">Entered according to Act of Congress, in 1890, 1892 and 1893,<br /> +<span class="smcap">By Rev. George Nichols Packer</span>,<br /> +In the Office of the Librarian of Congress, Washington, D. C.<br /> +<span class="smcap">All Rights Reserved</span>.</p> +<p class="center">WILLIAMSPORT, PA.:<br /> +FRED R. MILLER BLANK BOOK CO.<br />1893.</p> + +<p> </p><p> </p> +<p><span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span></p> +<p class="center"><small>TO</small><br /> +HON. HENRY W. WILLIAMS,<br /> +<small>JUSTICE OF THE SUPREME COURT OF PENNSYLVANIA<br /> +WHOM<br /> +I HAVE FOUND A TRUE FRIEND IN POVERTY AND IN SICKNESS,<br /> +AND<br /> +FROM WHOM I HAVE RECEIVED WORDS OF ENCOURAGEMENT<br /> +AND COMFORT DURING MANY YEARS OF ADVERSITY,<br /> +AND AT<br /> +WHOSE SUGGESTION THIS LITTLE VOLUME HAS BEEN WRITTEN,<br /> +AND BY<br /> +WHOSE ASSISTANCE IT IS NOW PUBLISHED,<br /> +THIS<br /> +HUMBLE VOLUME IS DEDICATED<br /> +AS A<br /> +TRIBUTE OF RESPECT<br /> +BY THE</small><br /> +AUTHOR.</p> + +<p><span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span></p> + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span></p> +<h2>PREFACE.</h2> + +<p> </p> +<p><span class="dropfig"><img src="images/preface_m.jpg" style="margin-top: -0.5em; margin-bottom: -0.5em;" alt="M" /></span>any years +ago, while engaged in teaching, the writer of this little volume was in the habit of bringing to the attention of his pupils a few +simple rules for finding the dominical letter and the day of the week of +any given event within the past and the present centuries; further than +this he gave the subject no special attention.</p> + +<p>A few years ago, having occasion to learn the day of the week of certain +events that were transpiring at regular intervals on the same day of the +same month, but in different years, he was led to investigate the subject +more thoroughly, so that he is now able to give rules for finding the +dominical letter and the day of the week of any event that has transpired +or will transpire, from the commencement of the Christian era to the year +of our Lord 4,000, and to explain the principles on which these rules +rest. When the investigations were entered upon he had no thought of +writing a book; but having been laid aside from active labor by ill +health, he found relief from the despondency in which sickness and poverty +plunged him by pursuing the study of the calendar, its history, and the +method of disposing of the fraction of a day found in the time<span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span> required +for the revolution of the Earth in its orbit about the Sun.</p> + +<p>He became so much interested in the study of this subject that he +frequently spoke of it to friends and acquaintances whom he met. On one +occasion, while speaking to Hon. H. W. Williams about some of the curious +results of the process by which the coincidence of the solar and the civil +year is preserved, it was suggested to him that he should put the story of +the calendar, its correction by Gregory, and the theory and results of +intercalation, in writing. It was urged that this would give increased +interest to the study, help the writer to forget his pains, and probably +enable him to realize a little money from the sale of his work to meet +pressing wants. Acting upon this suggestion, an effort has been made to +put into this little volume some of the most interesting facts relating to +the origin, condition, and practical operation of the calendar now in use; +together with rules for finding the day of the week on which any given day +of any month has fallen or will fall during four thousand years from the +beginning of our era.</p> + +<p>The writer does not claim absolute originality for all that appears in the +following pages; on the contrary, he has made free use of all the +materials that came within his reach relating to the history of the +calendar and the work of its correction by Gregory. These <span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span>materials, +together with his own calculations, he has arranged in accordance with a +plan of his own devising, so that the outline and the execution of the +work may be truly said to be original. Of its value the world must judge. +It has been prepared in weakness of body and in suffering, which have been +to some extent relieved by the mental occupation thus afforded, but which +may have nevertheless left their impress on the work. But let it be read +before pronouncing judgment upon it. Cicero could infer the littleness of +the Hebrew God from the smallness of the territory he had given his +people. To whom Kitto replies: “The interest and importance of a country +arise, not from its territorial extent, but from the men who form its +living soul; from its institutions bearing the impress of mind and spirit, +and from the events which grow out of the character and condition of its +inhabitants.” So the value of a book does not consist in the size and +number of its pages, but from the knowledge that may be gained by its +perusal.</p> + +<p class="right"><span class="smcap">The Author.</span></p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span></p> +<h2>PREFACE</h2> +<h3>TO THE REVISED EDITION.</h3> + +<p>Soon after the publication of the former edition of this work, it was +suggested that a chapter be added on Easter; rules for fixing its date, +<ins class="correction" title="original: aad">and</ins> also church festivals that depended upon the date of Easter. It was +suggested that this would add very much to the value of the work, if so +presented as to be brought within the comprehension of ordinary minds. +Knowing that the determination of Easter was an affair of considerable +nicety and complication, and had had the attention of our best minds, and +they had failed so to present it, that even among scholarly men, probably +not one in a hundred was able to determine its date without referring to +tables prepared for that purpose the author of this work felt as though he +was hardly competent for the task. Nevertheless it was undertaken, and the +work has been revised and enlarged by a Chapter on the Peculiarities of +the Roman Calendar, another on fixing the date of events prior to the +Christian era, and a third part on Easter, church festivals, and the +Hebrew Calendar. In the opinion of the author, the rules for determining +the date of Easter are so simplified by his new method that any person of +ordinary intelligence may understand them. How well he has succeeded the +public will decide.</p> + +<p class="right">G. N. P.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span></p> +<h2>CONTENTS.</h2> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td colspan="2" align="center"><a href="#PART_FIRST">PART FIRST.</a></td></tr> +<tr><td colspan="2" align="center">DEFINITIONS—HISTORY.</td></tr> +<tr><td colspan="2"> </td><td align="right"><i>Pages.</i></td></tr> +<tr><td align="right"><a href="#CHAPTER_I.1"><span class="smcap">Chapter I.</span></a>—</td><td>Definitions</td><td align="right"><a href="#Page_11">11</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_II.1"><span class="smcap">Chapter II.</span></a>—</td><td>History of the divisions of time, and the old Roman Calendar</td><td align="right"><a href="#Page_12">12</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_III.1"><span class="smcap">Chapter III</span></a>—</td><td>History of the reformation of the Calendar by Julius Cæsar</td><td align="right"><a href="#Page_18">18</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_IV.1"><span class="smcap">Chapter IV.</span></a>—</td><td>History of the reformation of the Julian Calendar by Pope Gregory XIII</td><td align="right"><a href="#Page_20">20</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_V.1"><span class="smcap">Chapter V.</span></a>—</td><td>Peculiarities of the Roman Calendar</td><td align="right"><a href="#Page_26">26</a></td></tr> +<tr><td> </td></tr> +<tr><td colspan="2" align="center"><a href="#PART_SECOND">PART SECOND.</a></td></tr> +<tr><td colspan="2" align="center">MATHEMATICAL.</td></tr> +<tr><td align="right"><a href="#CHAPTER_I.2"><span class="smcap">Chapter I.</span></a>—</td><td>Errors of the Julian Calendar</td><td align="right"><a href="#Page_36">36</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_II.2"><span class="smcap">Chapter II.</span></a>—</td><td>Errors of the Gregorian Calendar</td><td align="right"><a href="#Page_38">38</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_III.2"><span class="smcap">Chapter III.</span></a>—</td><td>Dominical Letter</td><td align="right"><a href="#Page_39">39</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_IV.2"><span class="smcap">Chapter IV.</span></a>—</td><td>Rule for finding the Dominical Letter</td><td align="right"><a href="#Page_44">44</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_V.2"><span class="smcap">Chapter V.</span></a>—</td><td>Rule for finding the day of the week of any given date, for both Old and New Styles</td><td align="right"><a href="#Page_50">50</a></td></tr> +<tr><td valign="top" align="right"><a href="#CHAPTER_VI.2"><span class="smcap">Chapter VI.</span></a>—</td><td>A simple method of finding the day of the week of events, +which occur quadrennially;<br />the inaugural of the Presidents, the day of the week on which they have occurred<br /> +and on which they will occur for the next one hundred years</td><td valign="top" align="right"><a href="#Page_61">61</a></td></tr> +<tr><td> </td><td>Some peculiarities concerning events which fall on the 29th of February</td><td align="right"><a href="#Page_64">64</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_VII.2"><span class="smcap">Chapter VII.</span></a>—</td><td>Rule for finding the day of the week of events prior to the Christian era</td><td align="right"><a href="#Page_68">68</a></td></tr> +<tr><td> <span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span></td></tr> +<tr><td colspan="2" align="center"><a href="#PART_THIRD">PART THIRD.</a></td></tr> +<tr><td colspan="2" align="center">CYCLES—JULIAN PERIOD—EASTER.</td></tr> +<tr><td align="right"><a href="#CHAPTER_I.3"><span class="smcap">Chapter I.</span></a>—</td><td>The Solar Cycle</td><td align="right"><a href="#Page_73">73</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_II.3"><span class="smcap">Chapter II.</span></a>—</td><td>The Lunar Cycle</td><td align="right"><a href="#Page_75">75</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_III.3"><span class="smcap">Chapter III.</span></a>—</td><td>The Lunar Cycle and Golden Number</td><td align="right"><a href="#Page_77">77</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_IV.3"><span class="smcap">Chapter IV.</span></a>—</td><td>Cycle of Indiction, and the Julian Period</td><td align="right"><a href="#Page_79">79</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_V.3"><span class="smcap">Chapter V.</span></a>—</td><td>Easter</td><td align="right"><a href="#Page_82">82</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_VI.3"><span class="smcap">Chapter VI.</span></a>—</td><td>A new and easy method of fixing the date of Easter</td><td align="right"><a href="#Page_88">88</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_VII.3"><span class="smcap">Chapter VII.</span></a>—</td><td>Church feasts and fasts whose date depend on the date of Easter</td><td align="right"><a href="#Page_108">108</a></td></tr> +<tr><td align="right"><a href="#CHAPTER_VIII.3"><span class="smcap">Chapter VIII.</span></a>—</td><td>Hebrew Calendar</td><td align="right"><a href="#Page_124">124</a></td></tr> +<tr><td> </td><td><span class="smcap">Appendix</span></td><td align="right"><a href="#Page_134">134</a></td></tr> +<tr><td> </td><td><span class="smcap">Errata</span></td><td align="right"><a href="#Page_149">149</a></td></tr></table> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span></p> +<p class="center"><span class="giant"><a name="PART_FIRST" id="PART_FIRST"></a>OUR CALENDAR.</span></p> +<p class="center"><span class="huge">PART FIRST.</span></p> +<p class="center"><span class="big">DEFINITIONS. HISTORY.</span></p> +<p> </p> +<h2><a name="CHAPTER_I.1" id="CHAPTER_I.1"></a>CHAPTER I.</h2> +<p class="center"><span class="big">DEFINITIONS.</span></p> + +<p><i>a</i>—A Calendar is a method of distributing time into certain periods +adapted to the purposes of civil life, as hours, days, weeks, months, +years, etc.</p> + +<p><i>b</i>—The only natural divisions of time are the solar day, the solar year, +and the lunar month.</p> + +<p><i>c</i>—An hour is one of the subdivisions of the day into twenty-four equal +parts.</p> + +<p><i>d</i>—The true solar day is the interval of time which elapses between two +consecutive returns of the same terrestrial meridian to the Sun, the mean +length of which is twenty-four hours.</p> + +<p><i>e</i>—The week is a period of seven days, having no reference whatever to +the celestial motions, a circumstance to which it owes its unalterable +uniformity.</p> + +<p><i>f</i>—The lunar month is the time which elapses between two consecutive new +or full moons, and was used in the Roman calendar until the time of Julius +Cæsar, and consists of 29d, 12h, 44m, 2.87s.</p> + +<p><i>g</i>—The calendar month is usually employed to <span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span>denote an arbitrary number +of days approaching a twelfth part of a year, and has now its place in the +calendar of nearly all nations.</p> + +<p><i>h</i>—The year is either astronomical or civil. The solar astronomical year +is the period of time in which the Earth performs a revolution in its +orbit about the sun or passes from any point of the ecliptic to the same +point again, and consists of 365 days, 5 hours, 48 minutes and 49.62 +seconds of mean solar time. <a href="#appena">Appendix A.</a></p> + +<p><i>i</i>—The civil year is that which is employed in chronology, and varies +among different nations, both in respect of the seasons at which it +commences and of its subdivisions.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<h2><a name="CHAPTER_II.1" id="CHAPTER_II.1"></a>CHAPTER II.</h2> +<p class="center"><span class="big">HISTORY OF THE DIVISIONS OF TIME AND THE OLD ROMAN CALENDAR.</span></p> + +<p><i>Day</i>—The subdivision of the day into twenty-four parts or hours has +prevailed since the remotest ages, though different nations have not +agreed either with respect to the epoch of its commencement or the manner +of distributing the hours. Europeans in general, like the ancient +Egyptians, place the commencement of the civil day at midnight; and reckon +twelve morning hours from midnight to midday and twelve evening hours from +midday to midnight. Astronomers, after the example of Ptolemy, regarded +the day as commencing<span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span> with the Sun’s culmination, or noon, and find it +most convenient for the purpose of computation to reckon through the whole +twenty-four hours. Hipparchus reckoned the twenty-four hours from midnight +to midnight.</p> + +<p>The Roman day, from sunrise to sunset, and the night, from sunset to +sunrise, were each divided at all seasons of the year into twelve hours, +the hour being uniformly one-twelfth of the day or the night, of course, +varied in length with the length of the day or night at different seasons +of the year.</p> + +<p><i>Week</i>—Although the week did not enter into the calendar of the Greeks, +and was not introduced at Rome till after the reign of Theodosius, A. D. +292, it has been employed from time immemorial in almost all Eastern +countries; and as it forms neither an aliquot part of a year nor of the +lunar months, those who reject the Mosaic recital will be at a loss to +assign to it an origin having much semblance of probability. In the +Egyptian astronomy the order of the planets, beginning with the most +remote, is Saturn, Jupiter, Mars, the Sun, Venus, Mercury, the Moon. Now, +the day being divided into twenty-four hours, each hour was consecrated to +a particular planet, namely: One to Saturn, the following to Jupiter, +third to Mars, and so on according to the above order; and the day +received the name of the planet which presided over its first hour. If, +then, the first hour of a day was consecrated to Saturn, that planet would +also have the 8th, the 5th and the 22d hours; the 23d would fall to +Jupiter, the 24th to Mars, and the 25th or the first hour of the second +day would belong to the Sun. In like manner the<span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span> first hour of the third +day would fall to the Moon, the first hour of the fourth to Mars, of the +fifth to Mercury, of the sixth to Jupiter and the seventh to Venus. The +cycle being completed, the first hour of the eighth day would again return +to Saturn and all the others succeed in the same order. See table on the +17th page.</p> + +<p>It will be seen by the table, and it is also recorded by Dio Cassius, of +the second Century, that the Egyptian week commenced with Saturday. On +their flight from Egypt the Jews, from hatred to their ancient oppressors, +made Saturday the last day of the week. It is stated that the ancient +Saxons borrowed the week from some Eastern nation, and substituted the +names of their own divinities for those of the gods of Greece. The names +of the days are here given in Latin, Saxon and English. It will be seen +that the English names of the days are derived from the Saxon.</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td align="center"><small>LATIN.</small></td><td><span class="spacer"> </span></td> + <td align="center"><small>SAXON.</small></td><td><span class="spacer"> </span></td> + <td align="center"><small>ENGLISH.</small></td></tr> +<tr><td><i>Dies Solis.</i></td><td> </td> + <td>Sun’s Day.</td><td> </td> + <td><span class="smcap">Sunday.</span></td></tr> +<tr><td><i>Dies Lunae.</i></td><td> </td> + <td>Moon’s Day.</td><td> </td> + <td><span class="smcap">Monday.</span></td></tr> +<tr><td><i>Dies Martis.</i></td><td> </td> + <td>Tiw’s Day.</td><td> </td> + <td><span class="smcap">Tuesday.</span></td></tr> +<tr><td><i>Dies Mercurii.</i></td><td> </td> + <td>Woden’s Day.</td><td> </td> + <td><span class="smcap">Wednesday.</span></td></tr> +<tr><td><i>Dies Jovis.</i></td><td> </td> + <td>Thor’s Day.</td><td> </td> + <td><span class="smcap">Thursday.</span></td></tr> +<tr><td><i>Dies Veneris.</i></td><td> </td> + <td>Friga’s Day.</td><td> </td> + <td><span class="smcap">Friday</span>.</td></tr> +<tr><td><i>Dies Saturni.</i></td><td> </td> + <td>Seterne’s Day.</td><td> </td> + <td><span class="smcap">Saturday</span>.</td></tr></table> + +<p><i>Month</i>—The ancient Roman year contained but ten months and is indicated +by the names of the last four. September from Septem, seven; October from +Octo, eight; November from Novem, nine, and December from Decem, ten; July +and August were also denominated Quintilis and Sextilis, from Quintus +five, and Sex, six.</p> + +<p><span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span>Quintilis was changed to July in honor of Julius Cæsar, who was born on +the 12th of that month 98 B. C. Sextilis was changed to August by the +Roman Senate to flatter Augustus on his victories about 8 B. C. In the +reign of Numa Pompilius, about 700 B. C., two months were added to the +year, January at the beginning, and February at the end of the year. This +arrangement continued till 450 B. C., when the Decemvirs (ten magistrates) +changed the order, placing February after January, making March the third +instead of the first month of the Roman year.</p> + +<p><i>Year</i>—If the civil year correspond with the solar the seasons of the +year will always come at the same period. But if the civil year is +supposed to be too long (as is the case in the Julian year) the seasons +will go back proportionately; but if too short they will advance in the +same proportion. Now, as the ancient Egyptians reckoned thirty days to the +month invariably, and to complete the year, added five days, called +supplementary days, their year consisted of 365 days.</p> + +<p>They made use of no intercalation, and by losing one-fourth of a day every +year, the commencement of the year went back one day in every period of +four years, and consequently made a revolution of the seasons in 1460 +years. Hence the Egyptian year was called a vague or erratic year because +the first day of the year in the course of 1460 years wandered, as it +were, over all the seasons. Therefore 1460 Julian years of 365¼ days +each are equal to 1461 Egyptian years of 365 days each.</p> + +<p>The ancient Roman year consisted of twelve lunar months, of twenty-nine +and thirty days alternately,<span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span> which equals 354 days; but a day was added +to make the number odd, which was considered more fortunate, so that the +year consisted of 355 days.</p> + +<p>This differed from the solar year by ten whole days and a fraction; but to +restore the coincidence, Numa ordered an additional or intercalary month +to be inserted every second year between the 23d and 24th of February, +consisting of twenty-two and twenty-three days alternately, so that four +years contained 1465 days, and the mean length of the year was +consequently 366¼ days, so that the year was then too long by one day.</p> + +<p>As the error amounted to twenty-four days in as many years, it was ordered +that every third period of eight years, instead of containing four +intercalary months, two of twenty-two and two of twenty-three days, +amounting in all to ninety days, should contain only three of those months +of twenty-two days each, amounting to sixty-six days, thereby suppressing +twenty-four days in as many years, reducing the mean length of the year to +365¼ days.</p> + +<p>Had the intercalations been regularly made the concurrence of the solar +and the civil year would have been preserved very nearly. But its +regulation was left to the pontiffs, who, to prolong the term of a +magistracy or hasten an annual election, would give to the intercalary +month a greater or less number of days, and consequently the calendar was +thrown into confusion, so that in the time of Julius Cæsar there was a +discrepancy between the solar and the civil year of about three months; +the winter months being carried back into autumn and the autumnal into +summer.</p> + +<p><span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span>A table of the order and the names of the planets in the Egyptian +astronomy illustrating the origin of the names of the days of the week:</p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Saturn,<br />Saturday.</i></td> + <td class="btr" align="center"><i>Jupiter,<br />Thursday.</i></td> + <td class="btr" align="center"><i>Mars,<br />Tuesday.</i></td> + <td class="btr" align="center"><i>Sun,<br />Sunday.</i></td> + <td class="btr" align="center"><i>Venus,<br />Friday.</i></td> + <td class="btr" align="center"><i>Mercury,<br />Wednesday.</i></td> + <td class="bt" align="center"><i>Moon,<br />Monday.</i></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="btr" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="btr" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="btr" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="btr" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="btr" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center">11</td> + <td class="br" align="center">12</td> + <td class="br" align="center">13</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center">15</td> + <td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">18</td> + <td class="br" align="center">19</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">21</td></tr> +<tr><td class="br" align="center">22</td> + <td class="br" align="center">23</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">10</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center">12</td> + <td class="br" align="center">13</td> + <td class="br" align="center">14</td> + <td class="br" align="center">15</td> + <td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center">19</td> + <td class="br" align="center">20</td> + <td class="br" align="center">21</td> + <td class="br" align="center">22</td> + <td class="br" align="center">23</td> + <td class="br" align="center">24</td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center">11</td> + <td class="br" align="center">12</td> + <td class="br" align="center">13</td> + <td class="br" align="center">14</td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">18</td> + <td class="br" align="center">19</td> + <td class="br" align="center">20</td> + <td class="br" align="center">21</td> + <td class="dent" align="center">22</td></tr> +<tr><td class="br" align="center">23</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center">11</td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center">13</td> + <td class="br" align="center">14</td> + <td class="br" align="center">15</td> + <td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center">20</td> + <td class="br" align="center">21</td> + <td class="br" align="center">22</td> + <td class="br" align="center">23</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center">10</td> + <td class="br" align="center">11</td> + <td class="br" align="center">12</td> + <td class="br" align="center">13</td> + <td class="br" align="center">14</td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center">17</td> + <td class="br" align="center">18</td> + <td class="br" align="center">19</td> + <td class="br" align="center">20</td> + <td class="br" align="center">21</td> + <td class="br" align="center">22</td> + <td class="dent" align="center">23</td></tr> +<tr><td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center">11</td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center">14</td> + <td class="br" align="center">15</td> + <td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">18</td> + <td class="br" align="center">19</td> + <td class="dent" align="center">20</td></tr> +<tr><td class="br" align="center">21</td> + <td class="br" align="center">22</td> + <td class="br" align="center">23</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center">11</td> + <td class="br" align="center">12</td> + <td class="br" align="center">13</td> + <td class="br" align="center">14</td> + <td class="br" align="center">15</td> + <td class="br" align="center">16</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="bbr" align="center">18</td> + <td class="bbr" align="center">19</td> + <td class="bbr" align="center">20</td> + <td class="bbr" align="center">21</td> + <td class="bbr" align="center">22</td> + <td class="bbr" align="center">23</td> + <td class="bb" align="center">24</td></tr></table> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span></p> +<h2><a name="CHAPTER_III.1" id="CHAPTER_III.1"></a>CHAPTER III.</h2> +<p class="center"><span class="big">HISTORY OF THE REFORMATION OF THE CALENDAR BY JULIUS CÆSAR.</span></p> + +<p>In order to put an end to the disorders arising from the negligence or +ignorance of the pontiffs, Julius Cæsar, 46 B. C., abolished the use of +the lunar year and the intercalary month, and regulated the civil year +entirely by the Sun. With the advice and assistance of the astronomers, +especially Sosigenes of Alexandria, he fixed the mean length of the year +at 365¼ days, and decided that there should be three consecutive years +of 365 days, and a fourth of 366.</p> + +<p>In order to restore the vernal equinox to the 24th of March, the place it +occupied in the time of Numa, two months, together consisting of 67 days, +were inserted between the last day of November and the first day of +December of that year. An intercalary month of 23 days had already been +added to February of the same year according to the old method, so that +the first Julian year commenced with the first day of January, 45 years +before Christ, and 709 from the foundation of Rome, making the year A. U. +C. 708 to consist of the prodigious number of 445 days, (i. e. 355 + 23 + +67 = 445). Hence it was called by some the year of confusion; Macrobius +said it should be named the last year of confusion.</p> + +<p>There was also adopted at the same time a more commodious arrangement in +the distribution of the days throughout the several months. It was decided +to give to January, March, May, July, September and November each +thirty-one days; and the other months<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span> thirty, excepting February, which +in common years should have but twenty-nine days, but every fourth year +thirty; so that the average length of the Julian year was 365¼ days.</p> + +<p>Augustus Cæsar interrupted this order by taking one day from February, +reducing it to twenty-eight and giving it to August, that the month +bearing his name should have as many days as July, which was named in +honor of his great-uncle, Julius. In order that three months of thirty-one +days might not come together, September and November were reduced to +thirty days, and thirty-one given to October and December.</p> + +<p>In the Julian calendar a day was added to February every fourth year, it +being the shortest month, which was called the additional or intercalary +day, and was inserted in the calendar between the 23d and 24th of that +month. In the ancient Roman calendar the first day of every month was +invariably called the calends. The 24th of February then was the 6th of +the calends of March—Sexto calendas; the preceding, which was the +additional or intercalary day, was called bis-sexto calendas (from <i>bis</i>, +twice, and <i>sextus</i>, six), twice the sixth day. Hence the term bis-sextile +as applied to every fourth year, commonly called leap-year. <a href="#appenb">Appendix B.</a></p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span></p> +<h2><a name="CHAPTER_IV.1" id="CHAPTER_IV.1"></a>CHAPTER IV.</h2> +<p class="center"><span class="big">HISTORY OF THE REFORMATION OF THE JULIAN CALENDAR BY POPE GREGORY XIII.</span></p> + +<p>True enough, the year in which Julius Cæsar reformed the ancient Roman +calendar was the last year of confusion, and the method adopted by him a +commodious one, and answered a very good purpose for a short time; but as +the years rolled on and century after century had passed away, astronomers +began to discover the discrepancy between the solar and the civil year; +that the vernal equinox did not occupy the place it occupied in the time +of Cæsar, namely, the 24th of March, but was gradually retrograding +towards the beginning of the year, so that at the meeting of the Council +of Nice in 325 it fell on the 21st. <a href="#appenc">Appendix C.</a></p> + +<p>The venerable Bede, in the 8th century, observed that these phenomena took +place three or four days earlier than at the meeting of that council. +Roger Bacon, in the 13th century, wrote a treatise on this subject and +sent it to the Pope, setting forth the errors of the Julian calendar. The +discrepancy at that time amounted to seven or eight days.</p> + +<p>Thus the errors of the calendar continued to increase until 1582, when the +vernal equinox fell on the 11th instead of the 21st of March. Gregory, +perceiving that the measure (of reforming the calendar) was likely to +confer great eclat on his pontificate, undertook the long desired +reformation; and having found the governments of the principal Catholic +states ready to adopt his views, he issued a brief in the month of March, +1582, in which he abolished the use of the ancient calendar,<span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span> and +substituted that which has since been received in almost all Christian +countries under the name of the Gregorian calendar or New Style.</p> + +<p>The edict of the Pope took effect in October of that year, causing the 5th +to be called the 15th of that month, thus suppressing ten days and making +the year 1582 to consist of only 355 days. So we see that the ten days +that had been gained by incorrect computation during the past 1257 years, +were deducted from 1582, restoring the concurrence of the solar and the +civil year, and consequently the vernal equinox to the place it occupied +in 325, namely, the 21st of March.</p> + +<p>The Pope was promptly obeyed in Spain, Portugal, and Italy. The change +took place the same year in France, by calling the 10th the 20th of +December. Many other Catholic countries made the change the same year, and +the Catholic states of Germany the year following; but most of the +Protestant countries adhered to the Old Style until after the year 1700. +Among the last was Great Britain; she, after having suffered a great deal +of inconvenience for nearly two hundred years by using a different date +from the most of Europe, at length, by an act of Parliament, fixed on +September, 1752, as the time for making the much desired change, which was +done by calling the 3d of that month the 14th (as the error now amounted +to eleven days), adopting at the same time the Gregorian rule of +intercalation.</p> + +<p>Russia is the only Christian country that still adheres to the Old Style, +and by using a different date from the rest of Europe is now twelve days +behind the true time. The discrepancy between solar and civil<span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span> time does +not effect the day, for, as has already been shown, the mean length of the +day is twenty-four hours, and is marked by one revolution of the earth +upon its axis.</p> + +<p>Nor does it effect the week, for the week is uniformly seven of those +days. But it effects the year, the month and the day of the month.</p> + +<p>Russia, by adhering to the Old Style, has reckoned as many days and as +many weeks, and events have transpired on the same day of the week as they +have with us who have adopted the New Style; as Christian nations we are +observing the same day as the Sabbath.</p> + +<p>When it was Tuesday, the 20th day of December, 1888, in Russia, it was +Tuesday, the 1st day of January, 1889, in those countries which have +adopted the New Style. Columbus sailed from Palos, in Spain, on Friday, +August 3d, 1492, Old Style, which was Friday, August 12th, New Style. +Washington was born on Friday, February 11th, 1732, Old Style, which was +Friday, February 22d, New Style.</p> + +<p>Now, the difference in styles during the 15th century is nine days; during +the 16th and 17th centuries, ten days; the 18th century, eleven days, and +the 19th, twelve days. In regard to the sailing of Columbus, the change is +made by suppressing nine days, calling the 3d the 12th of August. In +regard to the birth of Washington, the change is effected by suppressing +eleven days, calling the 11th of February the 22d. As regards Russia, she +could have made the change last year by calling the 20th of December, +1888, the 1st day of January, 1889, thereby suppressing twelve days, and +making the year 1888 to consist of only 354 days, and the<span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span> month of +December twenty days. The methods of computation, both Old and New Styles, +will be explained in another chapter.</p> + +<p>To persons unacquainted with astronomy, the difference between Old and New +Styles would probably be better understood by the diagram on the 25th +page. The figures represent the ecliptic, which is the apparent path of +the Sun, or the real path of the Earth as seen from the Sun, in her annual +or yearly revolution around the Sun in the order of the months, as marked +on the ecliptic.</p> + +<p>Attention is called to four points on the ecliptic, namely, the vernal +equinox, the autumnal equinox, the winter solstice, and the summer +solstice. These occur, in the order given above, on the 21st of March, the +21st of September, the 21st of December and the 21st of June. It has +already been stated that if the civil year correspond with the solar, the +seasons of the year will always come at the same period. Julius Cæsar +found the ancient Roman year in advance of the solar; Gregory found the +Julian behind the solar year; so one reforms the calendar by +intercalation, the other by suppression. <a href="#append">Appendix D.</a></p> + +<p>Cæsar restored the coincidence of the solar and the civil year, but failed +to retain it by allowing what probably appeared to him at the time a +trifling error in his calendar. The error, which was 11 minutes and 10.38 +seconds every year, was hardly perceptable for a short period, but still +amounted to three days every 400 years. Hence the necessity in 1582 of +reforming the reformed calendar of Julius Cæsar to restore the +coincidence. <a href="#appene">Appendix E.</a></p> + +<p><span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span>From the meeting of the Council of Nice, in 325, to 1582, a period of 1257 +years, there was found to be an error in the Julian calendar of ten days. +Now, in 1257 years the Earth performs 1257 annual and 459,109 daily +revolutions, after which the vernal equinox was found to occur on the 21st +of March, true or solar time; thus concurring with the vernal equinox of +325. But the erroneous Julian calendar would make the Earth perform +459,119 daily revolutions to complete the 1257 years, a discrepancy of ten +days, making the vernal equinox to fall on the 11th instead of the 21st. +It will be seen by the diagram that the ten days were deducted from +October, in 1582, making it a short month, consisting of only twenty-one +days.</p> + +<p>The discrepancy between the Julian and Gregorian calendar amounts to +thirty days in 4000 years; three months in 12,175 years. Hence, in 12,175 +years the equinoxes would take the place of the solstices, and the +solstices the place of the equinoxes. In 24,350 years, the vernal equinox +would take the place of the autumnal equinox, and the winter solstice the +place of the summer solstice.</p> + +<p>And in 48,700 years, according to the Julian rule of intercalation, there +would be gained nearly 365¼ days, or one entire revolution of the +Earth. So, to restore the concurrence of the Julian and Gregorian years, +there would have to be suppressed 365¼ days, calling the 1st day of +January, 48,699, the 1st day of January, 48,700.</p> + +<p>Thus would disappear from the Julian calendar twelve months, or one whole +year, it having been divided among the thousands of the preceding years.</p> + + +<p> <span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span></p> +<div class="figcenter"><img src="images/fig_001tmb.jpg" alt="The Julian calendar, reformed by Gregory XIII, Oct. 5th, +1582, by suppressing ten days, calling the 5th of Oct. the 15th, making it +a short month of 21 days, and the year to consist of 355 days. The Roman calendar, reformed by Julius Cæsar, 46 B. C., by intercalating +90 days, making that year to consist of 445 days, that is, 355 + 23 + 67 = 445 days, and 'the last year of confusion.'" /><br /> +<a href="images/fig_001.jpg"><small>Larger Image</small></a></div> +<p> </p> + +<p><span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span>To make this subject better understood, let us suppose the solar year to +consist in round numbers of 365 days, and the civil year 366. It is +evident that at the end of the year of 365 days, there would still be +wanting one day to complete the civil year of 366 days, so one day must be +added to that year, and to every succeeding year, to complete the years of +366 days each, which would be the loss of one year of 365 days in 365 +years. Hence, 364 years of 366 days each are equal to 365 years of 365 +days each, wanting one day.</p> + +<p>Again, let us suppose the civil year to consist of 364 days. It is evident +that at the end of the supposed solar year of 365 days, there would be an +advance or gain of one day in that year and every succeeding year, so that +in 365 years there would be a gain of 365 days or one whole year. Hence, +366 years of 364 days each are equal to 365 years of 365 days each, +wanting one day. <a href="#appenf">Appendix F.</a></p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<h2><a name="CHAPTER_V.1" id="CHAPTER_V.1"></a>CHAPTER V.</h2> +<p class="center"><span class="big">PECULIARITIES OF THE ROMAN CALENDAR.</span></p> + +<p>The Romans, instead of distinguishing the days of the month by the ordinal +numbers, first, second, third, etc., counted backwards from three fixed +points, namely, the Calends, the Nones, and the Ides.</p> + +<p>Calends (Latin <i>Calandae</i>, from <i>Calare</i>, to call,) was so denominated +because it had been an ancient custom of the pontiffs to call the people +together on that day to apprise them of the festivals, or days that were +to be kept sacred during the month.</p> + +<p><span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span>Nones (Latin <i>nonae</i>, from <i>nonus</i>, the ninth,) the ninth day before the +Ides.</p> + +<p>Ides (Latin <i>idus</i>, supposed to be derived from an obsolete verb <i>iduare</i>, +to divide,) was near the middle of the month, either the 13th or the 15th +day.</p> + +<p>The first day of each month was invariably called the Calends. The Nones +were the fifth, and the Ides the thirteenth, except in March, May, July, +and October, in which the Nones occurred on the seventh day and the Ides +on the fifteenth.</p> + +<p>From these three points the days of the month were numbered—not forward, +but backward—as so many days before the Nones, the Ides, or the Calends, +the point of departure being counted in the reckoning, so that the last +day of every month was the second of the Calends of the following month.</p> + +<p>It will be seen by the Roman and English calendar found on the following +pages, that there are six days of Nones in March, May, July and October, +and four of all the other months; also that all the months have eight days +of Ides. The number of days of Calends depend upon the number of days in +the month, and the day of the month on which the Ides fall.</p> + +<p>If the month has thirty-one days and the Ides fall on the thirteenth, +there are nineteen days of Calends; but if the Ides fall on the fifteenth, +there are only seventeen days of Calends. As the Ides fall on the +thirteenth of all the months of thirty days, they have eighteen days of +Calends. February, the month of twenty-eight days, has only sixteen, +except in leap-year, when the sixth of the Calends is reckoned twice.</p> + +<p>It may also be seen from the calendar that the<span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span> Romans, after the first +day of the month, began to reckon so many days before the Nones, as 4th, +3d, 2d, then Nones; after the Nones, so many days before the Ides, as 8th, +7th, 6th, etc., and after the Ides, so many before the Calends of the next +month, the highest numbers being reckoned first.</p> + +<p>In reducing the Roman calendar to our own, it should be remembered that in +reckoning backward from a fixed point, that the point of departure is +counted; also, that the last day of the month is not the point from which +the Calends are reckoned, but the first day of the following month. We +have then this rule for finding the English expression for any Latin date:</p> + + +<p class="center"><br />RULE.</p> + +<p>If the given date be Calends, add two to the number of days in the month, +from which subtract the given date; if the date be Nones, or Ides, add one +to that of the day on which the Nones or Ides fall, from which subtract +the given date, and you will have the day of the month in our calendar. To +find the Latin expression for any English date, the preceding method is to +be reversed, upon the principle that if 5 - 3 = 2, then 5 - 2 = 3.</p> + +<p>But in reducing a Roman date to a date of February in leap-year, for the +first twenty-four days, proceed according to the preceding rule as if the +month had only twenty-eight days, and to obtain the proper expression for +the remaining five days, regard the month as having twenty-nine days, +taking the Roman date from 31 instead of 30. Thus 31 - 6 = 25, while 30 - +6 = 24; the former corresponding with sexto calendas, the latter with +bis-sexto calendas of the Julian calendar.<span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span> By referring to the table on +the 35th page, one may easily learn how to find the English expression for +any Latin date, or the Latin expression for any English date.</p> + +<p>It has already been stated that in January the Nones fall on the 5th, and +the Ides on the 13th, January then having thirty one days, the number from +which to subtract the Roman date to obtain the corresponding day of the +month is, for Nones, 5 + 1 = 6; for Ides, 13 + 1 = 14; for Calends, 31 + 2 += 33. Hence the first column in the table under January are the numbers 6, +14 and 33. February is the same as January for Nones and Ides. For Calends +in leap-year, for the first 24 days, it is 28 + 2 = 30; for the remaining +5 days it is 29 + 2 = 31. Hence for the first column under February are +the numbers 6, 14, 30 and 31. March is the same as January, except that +the Nones fall on the 7th and the Ides on the 15th, consequently we have +for Nones, 7 + 1 = 8, and for Ides, 15 + 1 = 16; hence, for the first +column under March we have the numbers 8, 16, and 33.</p> + +<p>In the table the three months are taken to illustrate how easily the +change may be made from Roman to English, or from English to Roman date. A +complete calendar for 1892, both in Roman and English, which will be very +convenient for reference, may be found on the four following pages.</p> + +<p>The first seven letters of the alphabet, used to represent the days of the +week, are placed in the calendar beside the days of the week. The letter +that represents Sunday is called the dominical or Sunday letter. The +letter that represents the first Sunday in any given year represents all +the Sundays in that year, unless it<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span> be leap-year, when two Sunday letters +are used. The first represents all the Sundays in January and February, +while the letter that precedes it represents all the Sundays for the rest +of the year.</p> + +<p>The reason of this is, the day intercalated, or thrust in, between the +28th day of February and the 1st day of March so interrupts the order of +the letters that D, which always represents the 1st day of March, now +represents the 29th day of February, so that in 1892 it represents Monday, +the 29th day of February, also Tuesday the 1st day of March. As it +represented all the Mondays in January and February, it will now represent +all the Tuesdays for the rest of the year, while C, the letter preceding, +represented all the Sundays, will now represent all the Mondays, and B all +the Sundays. For January and February we have then C, Sunday; D, Monday; +E, Tuesday; F, Wednesday; G, Thursday; A, Friday, and B, Saturday. For the +rest of the year we have B, Sunday; C, Monday; D, Tuesday; E, Wednesday; +F, Thursday; G, Friday, and A, Saturday. See <a href="#PART_SECOND">Part Second</a>, chapters <a href="#CHAPTER_IV.2">IV</a> and <a href="#CHAPTER_V.2">V</a>.</p> + +<p> <span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td colspan="4" class="btrdoub" align="center"><span class="smcap">Jan.</span>, 1892.</td> + <td colspan="4" class="btrdoub" align="center"><span class="smcap">Feb.</span>, 1892.</td> + <td colspan="4" class="bt" align="center"><span class="smcap">March</span>, 1892.</td></tr> +<tr><td class="btr" align="center"><span style="margin-left: 0.5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">a</td> + <td class="btrdoub">Fri.</td> + <td class="btr" align="center"><span style="margin-left: 0.5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">d</td> + <td class="btrdoub">Mon.</td> + <td class="btr" align="center"><span style="margin-left: 0.5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">d</td> + <td class="bt">Tues.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">5</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: 0.5em;">5</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">e</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">5</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">a</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">8</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">8</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: 0.5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">7</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">7</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">7</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: 0.5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">8</span></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: 0.5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">5</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">5</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: 0.5em;">7</span></td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">5</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">13</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">f</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">14</td> + <td class="br" align="center">19</td> + <td class="br" align="center">g</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">14</td> + <td class="br" align="center">16</td> + <td class="br" align="center">c</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">15</td> + <td class="br" align="center">18</td> + <td class="br" align="center">a</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">15</td> + <td class="br" align="center">15</td> + <td class="br" align="center">d</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">16</td> + <td class="br" align="center">14</td> + <td class="br" align="center">e</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">17</td> + <td class="br" align="center">16</td> + <td class="br" align="center">c</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">17</td> + <td class="br" align="center">13</td> + <td class="br" align="center">f</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">17</td> + <td class="br" align="center">16</td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">18</td> + <td class="br" align="center">15</td> + <td class="br" align="center">d</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">18</td> + <td class="br" align="center">12</td> + <td class="br" align="center">g</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">18</td> + <td class="br" align="center">15</td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">19</td> + <td class="br" align="center">14</td> + <td class="br" align="center">e</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">19</td> + <td class="br" align="center">11</td> + <td class="br" align="center">a</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">19</td> + <td class="br" align="center">14</td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">20</td> + <td class="br" align="center">13</td> + <td class="br" align="center">f</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">20</td> + <td class="br" align="center">10</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">20</td> + <td class="br" align="center">13</td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">21</td> + <td class="br" align="center">12</td> + <td class="br" align="center">g</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">21</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">9</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">21</td> + <td class="br" align="center">12</td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">22</td> + <td class="br" align="center">11</td> + <td class="br" align="center">a</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">22</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">8</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">22</td> + <td class="br" align="center">11</td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">23</td> + <td class="br" align="center">10</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">23</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">7</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">23</td> + <td class="br" align="center">10</td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">9</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">9</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">8</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">8</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">7</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">5</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">7</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">6</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">5</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">5</span></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">4</span></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"> </td> + <td class="br" align="center"> </td> + <td class="br" align="center"> </td> + <td class="brdoub"> </td> + <td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: 0.5em;">3</span></td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="bbr" align="center">31</td> + <td class="bbr" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="bbr" align="center">c</td> + <td class="bbrdoub">Sun.</td> + <td class="bbr" align="center"> </td> + <td class="bbr" align="center"> </td> + <td class="bbr" align="center"> </td> + <td class="bbrdoub"> </td> + <td class="bbr" align="center">31</td> + <td class="bbr" align="center"><span style="margin-left: 0.5em;">2</span></td> + <td class="bbr" align="center">f</td> + <td class="bb">Thur.</td></tr></table> + + +<p> <span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td colspan="4" class="btrdoub" align="center"><span class="smcap">April, 1892.</span></td> + <td colspan="4" class="btrdoub" align="center"><span class="smcap">May, 1892.</span></td> + <td colspan="4" class="bt" align="center"><span class="smcap">June, 1892.</span></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">g</td> + <td class="btrdoub">Fri.</td> + <td class="btr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">b</td> + <td class="btrdoub">Sun.</td> + <td class="btr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">e</td> + <td class="bt">Wed.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">b</td> + <td class="dent" align="center">Sun.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">13</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">14</td> + <td class="br" align="center">18</td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">14</td> + <td class="br" align="center">18</td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">15</td> + <td class="br" align="center">17</td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">15</td> + <td class="br" align="center">17</td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">16</td> + <td class="br" align="center">16</td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">16</td> + <td class="br" align="center">16</td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">17</td> + <td class="br" align="center">15</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">17</td> + <td class="br" align="center">16</td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">17</td> + <td class="br" align="center">15</td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">18</td> + <td class="br" align="center">14</td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">18</td> + <td class="br" align="center">15</td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">18</td> + <td class="br" align="center">14</td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">19</td> + <td class="br" align="center">13</td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">19</td> + <td class="br" align="center">14</td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">19</td> + <td class="br" align="center">13</td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">20</td> + <td class="br" align="center">12</td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">20</td> + <td class="br" align="center">13</td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">20</td> + <td class="br" align="center">12</td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">21</td> + <td class="br" align="center">11</td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">21</td> + <td class="br" align="center">12</td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">21</td> + <td class="br" align="center">11</td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">22</td> + <td class="br" align="center">10</td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">22</td> + <td class="br" align="center">11</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">22</td> + <td class="br" align="center">10</td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">23</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">23</td> + <td class="br" align="center">10</td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">23</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="bbr"> </td> + <td class="bbr"> </td> + <td class="bbr"> </td> + <td class="bbrdoub"> </td> + <td class="bbr" align="center">31</td> + <td class="bbr" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="bbr" align="center">d</td> + <td class="bbrdoub">Tues.</td> + <td class="bbr"> </td> + <td class="bbr"> </td> + <td class="bbr"> </td> + <td class="bb"> </td></tr></table> + + +<p> <span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td colspan="4" class="btrdoub" align="center"><span class="smcap">July, 1892.</span></td> + <td colspan="4" class="btrdoub" align="center"><span class="smcap">Aug., 1892.</span></td> + <td colspan="4" class="bt" align="center"><span class="smcap">Sept., 1892.</span></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">g</td> + <td class="btrdoub">Fri.</td> + <td class="btr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">c</td> + <td class="btrdoub">Mon.</td> + <td class="btr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">f</td> + <td class="bt">Thur.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">14</td> + <td class="br" align="center">19</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">14</td> + <td class="br" align="center">18</td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">15</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">15</td> + <td class="br" align="center">18</td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">15</td> + <td class="br" align="center">17</td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">16</td> + <td class="br" align="center">16</td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">17</td> + <td class="br" align="center">16</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">17</td> + <td class="br" align="center">16</td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">17</td> + <td class="br" align="center">15</td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">18</td> + <td class="br" align="center">15</td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">18</td> + <td class="br" align="center">15</td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">18</td> + <td class="br" align="center">14</td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">19</td> + <td class="br" align="center">14</td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">19</td> + <td class="br" align="center">14</td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">19</td> + <td class="br" align="center">13</td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">20</td> + <td class="br" align="center">13</td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">20</td> + <td class="br" align="center">13</td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">20</td> + <td class="br" align="center">12</td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">21</td> + <td class="br" align="center">12</td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">21</td> + <td class="br" align="center">12</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">21</td> + <td class="br" align="center">11</td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">22</td> + <td class="br" align="center">11</td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">22</td> + <td class="br" align="center">11</td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">22</td> + <td class="br" align="center">10</td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">23</td> + <td class="br" align="center">10</td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">23</td> + <td class="br" align="center">10</td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">23</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="bbr" align="center">31</td> + <td class="bbr" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="bbr" align="center">b</td> + <td class="bbrdoub">Sun.</td> + <td class="bbr" align="center">31</td> + <td class="bbr" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="bbr" align="center">e</td> + <td class="bbrdoub">Wed.</td> + <td class="bbr" align="center"> </td> + <td class="bbr" align="center"> </td> + <td class="bbr" align="center"> </td> + <td class="bb" align="center"> </td></tr></table> + + +<p> <span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td colspan="4" class="btrdoub" align="center"><span class="smcap">Oct., 1892.</span></td> + <td colspan="4" class="btrdoub" align="center"><span class="smcap">Nov., 1892.</span></td> + <td colspan="4" class="bt" align="center"><span class="smcap">Dec., 1892.</span></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">a</td> + <td class="btrdoub">Sat.</td> + <td class="btr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">d</td> + <td class="btrdoub">Tues.</td> + <td class="btr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="btr" align="center"><i>Cal.</i></td> + <td class="btr" align="center">f</td> + <td class="bt">Thur.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><i>Non.</i></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">14</td> + <td class="br" align="center">18</td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">14</td> + <td class="br" align="center">19</td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">15</td> + <td class="br" align="center"><i>Ides.</i></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">15</td> + <td class="br" align="center">17</td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">15</td> + <td class="br" align="center">18</td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">16</td> + <td class="br" align="center">16</td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">17</td> + <td class="br" align="center">16</td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">17</td> + <td class="br" align="center">15</td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">17</td> + <td class="br" align="center">16</td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">18</td> + <td class="br" align="center">15</td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">18</td> + <td class="br" align="center">14</td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">18</td> + <td class="br" align="center">15</td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">19</td> + <td class="br" align="center">14</td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">19</td> + <td class="br" align="center">13</td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">19</td> + <td class="br" align="center">14</td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">20</td> + <td class="br" align="center">13</td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">20</td> + <td class="br" align="center">12</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">20</td> + <td class="br" align="center">13</td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">21</td> + <td class="br" align="center">12</td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">21</td> + <td class="br" align="center">11</td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">21</td> + <td class="br" align="center">12</td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">22</td> + <td class="br" align="center">11</td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">22</td> + <td class="br" align="center">10</td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">22</td> + <td class="br" align="center">11</td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">23</td> + <td class="br" align="center">10</td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">23</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">23</td> + <td class="br" align="center">10</td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">a</td> + <td class="dent">Sat.</td></tr> +<tr><td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">b</td> + <td class="dent">Sun.</td></tr> +<tr><td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">c</td> + <td class="dent">Mon.</td></tr> +<tr><td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">f</td> + <td class="brdoub">Thur.</td> + <td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">d</td> + <td class="dent">Tues.</td></tr> +<tr><td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">g</td> + <td class="brdoub">Fri.</td> + <td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">c</td> + <td class="brdoub">Mon.</td> + <td class="br" align="center">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">e</td> + <td class="dent">Wed.</td></tr> +<tr><td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">a</td> + <td class="brdoub">Sat.</td> + <td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">d</td> + <td class="brdoub">Tues.</td> + <td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">f</td> + <td class="dent">Thur.</td></tr> +<tr><td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">b</td> + <td class="brdoub">Sun.</td> + <td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">e</td> + <td class="brdoub">Wed.</td> + <td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">g</td> + <td class="dent">Fri.</td></tr> +<tr><td class="bbr" align="center">31</td> + <td class="bbr" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="bbr" align="center">c</td> + <td class="bbrdoub">Mon.</td> + <td class="bbr" align="center"> </td> + <td class="bbr" align="center"> </td> + <td class="bbr" align="center"> </td> + <td class="bbrdoub"> </td> + <td class="bbr" align="center">31</td> + <td class="bbr" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="bbr" align="center">a</td> + <td class="bb">Sat.</td></tr></table> + +<p> <span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td colspan="5" class="btrdoub" align="center"><span class="smcap">January.</span></td> + <td colspan="5" class="btrdoub" align="center"><span class="smcap">February.</span></td> + <td colspan="5" class="bt" align="center"><span class="smcap">March.</span></td></tr> +<tr><td class="bt"> </td> + <td colspan="2" class="bt"><i>Cal.</i></td> + <td class="bt"> </td> + <td class="btrdoub" align="right">1</td> + <td class="bt"> </td> + <td colspan="2" class="bt"><i>Cal.</i></td> + <td class="bt"> </td> + <td class="btrdoub" align="right">1</td> + <td class="bt"> </td> + <td colspan="2" class="bt"><i>Cal.</i></td> + <td class="bt"> </td> + <td class="bt">1</td></tr> +<tr><td><span style="margin-left: .5em;">6</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">4</span></td> + <td>=</td> + <td align="right" class="brdoub">2</td> + <td class="dent"><span style="margin-left: .5em;">6</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">4</span></td> + <td>=</td> + <td align="right" class="brdoub">2</td> + <td class="dent"><span style="margin-left: .5em;">8</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">6</span></td> + <td>=</td> + <td class="dent">2</td></tr> +<tr><td><span style="margin-left: .5em;">6</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">3</span></td> + <td>=</td> + <td align="right" class="brdoub">3</td> + <td class="dent"><span style="margin-left: .5em;">6</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">3</span></td> + <td>=</td> + <td align="right" class="brdoub">3</td> + <td class="dent"><span style="margin-left: .5em;">8</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">5</span></td> + <td>=</td> + <td class="dent">3</td></tr> +<tr><td><span style="margin-left: .5em;">6</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">2</span></td> + <td>=</td> + <td align="right" class="brdoub">4</td> + <td class="dent"><span style="margin-left: .5em;">6</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">2</span></td> + <td>=</td> + <td align="right" class="brdoub">4</td> + <td class="dent"><span style="margin-left: .5em;">8</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">4</span></td> + <td>=</td> + <td class="dent">4</td></tr> +<tr><td> </td> + <td colspan="2"><i>Nones</i></td> + <td> </td> + <td class="brdoub" align="right">5</td> + <td> </td> + <td colspan="2"><i>Nones</i></td> + <td> </td> + <td class="brdoub" align="right">5</td> + <td class="dent"><span style="margin-left: .5em;">8</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">3</span></td> + <td>=</td> + <td class="dent">5</td></tr> +<tr><td>14</td> + <td>-</td> + <td><span style="margin-left: .5em;">8</span></td> + <td>=</td> + <td align="right" class="brdoub">6</td> + <td class="dent">14</td> + <td>-</td> + <td><span style="margin-left: .5em;">8</span></td> + <td>=</td> + <td align="right" class="brdoub">6</td> + <td class="dent"><span style="margin-left: .5em;">8</span></td> + <td>-</td> + <td><span style="margin-left: .5em;">2</span></td> + <td>=</td> + <td class="dent">6</td></tr> +<tr><td>14</td> + <td>-</td> + <td><span style="margin-left: .5em;">7</span></td> + <td>=</td> + <td align="right" class="brdoub">7</td> + <td class="dent">14</td> + <td>-</td> + <td><span style="margin-left: .5em;">7</span></td> + <td>=</td> + <td align="right" class="brdoub">7</td> + <td> </td> + <td colspan="2"><i>Nones</i></td> + <td> </td> + <td class="dent">7</td></tr> +<tr><td>14</td> + <td>-</td> + <td><span style="margin-left: .5em;">6</span></td> + <td>=</td> + <td align="right" class="brdoub">8</td> + <td class="dent">14</td> + <td>-</td> + <td><span style="margin-left: .5em;">6</span></td> + <td>=</td> + <td align="right" class="brdoub">8</td> + <td class="dent">16</td> + <td>-</td> + <td><span style="margin-left: .5em;">8</span></td> + <td>=</td> + <td class="dent">8</td></tr> +<tr><td>14</td> + <td>-</td> + <td><span style="margin-left: .5em;">5</span></td> + <td>=</td> + <td align="right" class="brdoub">9</td> + <td class="dent">14</td> + <td>-</td> + <td><span style="margin-left: .5em;">5</span></td> + <td>=</td> + <td align="right" class="brdoub">9</td> + <td class="dent">16</td> + <td>-</td> + <td><span style="margin-left: .5em;">7</span></td> + <td>=</td> + <td class="dent">9</td></tr> +<tr><td>14</td> + <td>-</td> + <td><span style="margin-left: .5em;">4</span></td> + <td>=</td> + <td align="right" class="brdoub">10</td> + <td class="dent">14</td> + <td>-</td> + <td><span style="margin-left: .5em;">4</span></td> + <td>=</td> + <td align="right" class="brdoub">10</td> + <td class="dent">16</td> + <td>-</td> + <td><span style="margin-left: .5em;">6</span></td> + <td>=</td> + <td>10</td></tr> +<tr><td>14</td> + <td>-</td> + <td><span style="margin-left: .5em;">3</span></td> + <td>=</td> + <td align="right" class="brdoub">11</td> + <td class="dent">14</td> + <td>-</td> + <td><span style="margin-left: .5em;">3</span></td> + <td>=</td> + <td align="right" class="brdoub">11</td> + <td class="dent">16</td> + <td>-</td> + <td><span style="margin-left: .5em;">5</span></td> + <td>=</td> + <td>11</td></tr> +<tr><td>14</td> + <td>-</td> + <td><span style="margin-left: .5em;">2</span></td> + <td>=</td> + <td align="right" class="brdoub">12</td> + <td class="dent">14</td> + <td>-</td> + <td><span style="margin-left: .5em;">2</span></td> + <td>=</td> + <td align="right" class="brdoub">12</td> + <td class="dent">16</td> + <td>-</td> + <td><span style="margin-left: .5em;">4</span></td> + <td>=</td> + <td>12</td></tr> +<tr><td> </td> + <td colspan="2"><i>Ides</i></td> + <td> </td> + <td class="brdoub" align="right">13</td> + <td> </td> + <td colspan="2"><i>Ides</i></td> + <td> </td> + <td class="brdoub" align="right">13</td> + <td class="dent">16</td> + <td>-</td> + <td><span style="margin-left: .5em;">3</span></td> + <td>=</td> + <td>13</td></tr> +<tr><td>33</td> + <td>-</td> + <td>19</td> + <td>=</td> + <td class="brdoub">14</td> + <td class="dent">30</td> + <td>-</td> + <td>16</td> + <td>=</td> + <td class="brdoub">14</td> + <td class="dent">16</td> + <td>-</td> + <td><span style="margin-left: .5em;">2</span></td> + <td>=</td> + <td>14</td></tr> +<tr><td>33</td> + <td>-</td> + <td>18</td> + <td>=</td> + <td class="brdoub">15</td> + <td class="dent">30</td> + <td>-</td> + <td>15</td> + <td>=</td> + <td class="brdoub">15</td> + <td> </td> + <td colspan="2"><i>Ides</i></td> + <td> </td> + <td>15</td></tr> +<tr><td>33</td> + <td>-</td> + <td>17</td> + <td>=</td> + <td class="brdoub">16</td> + <td class="dent">30</td> + <td>-</td> + <td>14</td> + <td>=</td> + <td class="brdoub">16</td> + <td class="dent">33</td> + <td>-</td> + <td>17</td> + <td>=</td> + <td>16</td></tr> +<tr><td>33</td> + <td>-</td> + <td>16</td> + <td>=</td> + <td class="brdoub">17</td> + <td class="dent">30</td> + <td>-</td> + <td>13</td> + <td>=</td> + <td class="brdoub">17</td> + <td class="dent">33</td> + <td>-</td> + <td>16</td> + <td>=</td> + <td>17</td></tr> +<tr><td>33</td> + <td>-</td> + <td>15</td> + <td>=</td> + <td class="brdoub">18</td> + <td class="dent">30</td> + <td>-</td> + <td>12</td> + <td>=</td> + <td class="brdoub">18</td> + <td class="dent">33</td> + <td>-</td> + <td>15</td> + <td>=</td> + <td>18</td></tr> +<tr><td>33</td> + <td>-</td> + <td>14</td> + <td>=</td> + <td class="brdoub">19</td> + <td class="dent">30</td> + <td>-</td> + <td>11</td> + <td>=</td> + <td class="brdoub">19</td> + <td class="dent">33</td> + <td>-</td> + <td>14</td> + <td>=</td> + <td>19</td></tr> +<tr><td>33</td> + <td>-</td> + <td>13</td> + <td>=</td> + <td class="brdoub">20</td> + <td class="dent">30</td> + <td>-</td> + <td>10</td> + <td>=</td> + <td class="brdoub">20</td> + <td class="dent">33</td> + <td>-</td> + <td>13</td> + <td>=</td> + <td>20</td></tr> +<tr><td>33</td> + <td>-</td> + <td>12</td> + <td>=</td> + <td class="brdoub">21</td> + <td class="dent">30</td> + <td>-</td> + <td><span style="margin-left: .5em;">9</span></td> + <td>=</td> + <td class="brdoub">21</td> + <td class="dent">33</td> + <td>-</td> + <td>12</td> + <td>=</td> + <td>21</td></tr> +<tr><td>33</td> + <td>-</td> + <td>11</td> + <td>=</td> + <td class="brdoub">22</td> + <td class="dent">30</td> + <td>-</td> + <td><span style="margin-left: .5em;">8</span></td> + <td>=</td> + <td class="brdoub">22</td> + <td class="dent">33</td> + <td>-</td> + <td>11</td> + <td>=</td> + <td>22</td></tr> +<tr><td>33</td> + <td>-</td> + <td>10</td> + <td>=</td> + <td class="brdoub">23</td> + <td class="dent">30</td> + <td>-</td> + <td><span style="margin-left: .5em;">7</span></td> + <td>=</td> + <td class="brdoub">23</td> + <td class="dent">33</td> + <td>-</td> + <td>10</td> + <td>=</td> + <td>23</td></tr> +<tr><td>33</td> + <td>-</td> + <td><span style="margin-left: .5em;">9</span></td> + <td>=</td> + <td class="brdoub">24</td> + <td class="dent">30</td> + <td>-</td> + <td><span style="margin-left: .5em;">6</span></td> + <td>=</td> + <td class="brdoub">24</td> + <td class="dent">33</td> + <td>-</td> + <td><span style="margin-left: .5em;">9</span></td> + <td>=</td> + <td>24</td></tr> +<tr><td>33</td> + <td>-</td> + <td><span style="margin-left: .5em;">8</span></td> + <td>=</td> + <td class="brdoub">25</td> + <td class="dent">31</td> + <td>-</td> + <td><span style="margin-left: .5em;">6</span></td> + <td>=</td> + <td class="brdoub">25</td> + <td class="dent">33</td> + <td>-</td> + <td><span style="margin-left: .5em;">8</span></td> + <td>=</td> + <td>25</td></tr> +<tr><td>33</td> + <td>-</td> + <td><span style="margin-left: .5em;">7</span></td> + <td>=</td> + <td class="brdoub">26</td> + <td class="dent">31</td> + <td>-</td> + <td><span style="margin-left: .5em;">5</span></td> + <td>=</td> + <td class="brdoub">26</td> + <td class="dent">33</td> + <td>-</td> + <td><span style="margin-left: .5em;">7</span></td> + <td>=</td> + <td>26</td></tr> +<tr><td>33</td> + <td>-</td> + <td><span style="margin-left: .5em;">6</span></td> + <td>=</td> + <td class="brdoub">27</td> + <td class="dent">31</td> + <td>-</td> + <td><span style="margin-left: .5em;">4</span></td> + <td>=</td> + <td class="brdoub">27</td> + <td class="dent">33</td> + <td>-</td> + <td><span style="margin-left: .5em;">6</span></td> + <td>=</td> + <td>27</td></tr> +<tr><td>33</td> + <td>-</td> + <td><span style="margin-left: .5em;">5</span></td> + <td>=</td> + <td class="brdoub">28</td> + <td class="dent">31</td> + <td>-</td> + <td><span style="margin-left: .5em;">3</span></td> + <td>=</td> + <td class="brdoub">28</td> + <td class="dent">33</td> + <td>-</td> + <td><span style="margin-left: .5em;">5</span></td> + <td>=</td> + <td>28</td></tr> +<tr><td>33</td> + <td>-</td> + <td><span style="margin-left: .5em;">4</span></td> + <td>=</td> + <td class="brdoub">29</td> + <td class="dent">31</td> + <td>-</td> + <td><span style="margin-left: .5em;">2</span></td> + <td>=</td> + <td class="brdoub">29</td> + <td class="dent">33</td> + <td>-</td> + <td><span style="margin-left: .5em;">4</span></td> + <td>=</td> + <td>29</td></tr> +<tr><td>33</td> + <td>-</td> + <td><span style="margin-left: .5em;">3</span></td> + <td>=</td> + <td class="brdoub">30</td> + <td colspan="5" class="brdoub"> </td> + <td class="dent">33</td> + <td>-</td> + <td><span style="margin-left: .5em;">3</span></td> + <td>=</td> + <td>30</td></tr> +<tr><td class="bb"><span style="margin-left: -.5em;">33</span></td> + <td class="bb">-</td> + <td class="bb">2</td> + <td class="bb">=</td> + <td class="bbrdoub">31</td> + <td colspan="5" class="bbrdoub"> </td> + <td class="bb">33</td> + <td class="bb">-</td> + <td class="bb">2</td> + <td class="bb">=</td> + <td class="bb"><span style="margin-left: -.5em;">31</span></td></tr></table> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span></p> +<p class="center"><span class="huge"><a name="PART_SECOND" id="PART_SECOND"></a>PART SECOND.</span></p> +<p class="center"><span class="big">MATHEMATICAL.</span></p> +<p> </p> +<h2><a name="CHAPTER_I.2" id="CHAPTER_I.2"></a>CHAPTER I.</h2> +<p class="center"><span class="big">ERRORS OF THE JULIAN CALENDAR.</span></p> + +<p>It will be necessary in the first place to understand the difference +between the Julian and Gregorian rule of intercalation. If the number of +any year be exactly divisible by four it is leap year; if the remainder be +1, it is the first year after leap-year; if 2, the second; if 3, the +third; thus:</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>1888 ÷ 4 = 472, no remainder.<br /> +1889 ÷ 4 = 472, remainder, 1.<br /> +1890 ÷ 4 = 472, remainder, 2.<br /> +1891 ÷ 4 = 472, remainder, 3.<br /> +1892 ÷ 4 = 473, no remainder.</td></tr></table> + +<p>And so on, every fourth year being leap-year of 366 days.</p> + +<p>This is the Julian rule of intercalation, which is corrected by the +Gregorian by making every centurial year, or the year that completes the +century, a common year, if not exactly divisible by 400; so that only +every fourth centurial year is leap-year; thus, 1,700, 1,800, and 1,900 +are common years, but 2,000, the fourth centurial year, is leap year, and +so on.</p> + +<p><span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span>By the Julian rule three-fourths of a day is gained every century, which +in 400 years amounts to three days. This is corrected by the Gregorian, by +making three consecutive centurial years common years, thus suppressing +three days in 400 years.</p> + + +<p class="center"><br />RULE.</p> + +<p>Multiply the difference between the Julian and the solar year by 100, and +we have the error in 100 years. Multiply this product by 4 and we have the +error in 400 years. Now, 400 is the tenth of 4,000; therefore, multiply +the last product by 10, and we have the error in 4,000 years. Now, as the +discrepancy between the Julian and Gregorian year is three days in 400 +years, making 3-400 of a day every year, so by dividing 365¼, the +number of days in a year, by 3-400, we have the time it would take to make +a revolution of the seasons.</p> + + +<p class="center"><br />SOLUTION.</p> + +<p>(365 d, 6 h.) - (365 d, 5 h, 48 m, 49.62 s.) = (11 m, 10.38 s.) Now, (11 +m, 10.38 s.) × 100 = 18 h, 37.3 m, the gain in 100 years. This is, +reckoned in round numbers, 18 hours, or three-fourths of a day. Now, (¾ +× 4) = (1 × 3) = 3: the Julian rule gaining three days, the Gregorian +suppressing three days in 400 years. (3 × 10) = 30, the number of days +gained by the Julian rule in 4,000 years. 365¼ ÷ <ins class="correction" title="Presented as in the original.">3 400</ins> = 48,700, so +that in this long period of time, this falling back ¾ of a day every +century would amount to 365¼ days; therefore, 48,699 Julian years are +equal to 48,700 Gregorian years.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span></p> +<h2><a name="CHAPTER_II.2" id="CHAPTER_II.2"></a>CHAPTER II.</h2> +<p class="center"><span class="big">ERRORS OF THE GREGORIAN CALENDAR.</span></p> + +<p>By reference to the preceding chapter it will be seen that there is an +error of 37.3 minutes in every 100 years not corrected by the Gregorian +calendar; this amounts to only .373 of a minute a year, or one day in +3,861 years, and one day and fifty-two minutes in 4,000 years.</p> + + +<p class="center"><br />RULE.</p> + +<p>To find how long it would take to gain one day: Divide the number of +minutes in a day by the decimal .373, that being the fraction of a minute +gained every year. To find how much time would be gained in 4,000 years, +multiply the decimal .373 by 4,000, and you will have the answer in +minutes, which must be reduced to hours.</p> + + +<p class="center"><br />SOLUTION.</p> + +<p>(24 × 60) ÷ .373 = 3,861, nearly; hence the error would amount to only one +day in 3,861 years.</p> + +<p>(.373 × 4,000) ÷ 60 = (24 h, 52 m,) = (1 d, 0 h, 52 m), the error in 4,000 years.</p> + +<p>This trifling error in the Gregorian calendar may be corrected by +suppressing the intercalations in the year 4,000, and its multiples, +8,000, 12,000, 16,000, etc., so that it will not amount to a day in +100,000 years.</p> + + +<p class="center"><br />RULE.</p> + +<p>Divide 100,000 by 4,000 and you will have the number of intercalations +suppressed in 100,000 years. Multiply 1 d, 52 m, (that being the error in +4,000 years) by this quotient, and you will have the <span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span>discrepancy between +the Gregorian and solar year for 100,000 years. By this improved method we +suppress 25 days, so that the error will only amount to 25 times 52 +minutes.</p> + + +<p class="center"><br />SOLUTION.</p> + +<p>100,000 ÷ 4,000 × (1 d, 52 m,) = (25d, 21 h, 40 m.) Now, (25d, 21 h, 40 +m,) - 25 d = (21 h, 40 m,) the error in 100,000.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<h2><a name="CHAPTER_III.2" id="CHAPTER_III.2"></a>CHAPTER III.</h2> +<p class="center"><span class="big">DOMINICAL LETTER.</span></p> + +<p>Dominical (from the Latin <i>Dominus</i>, Lord,) indicating the Lord’s day or +Sunday. Dominical letter, one of the first seven letters of the alphabet +used to denote the Sabbath or Lord’s day.</p> + +<p>For the sake of greater generality, the days of the week are denoted by +the first seven letters of the alphabet, A, B, C, D, E, F, G, which are +placed in the calendar beside the days of the year, so that A stands +opposite the first day of January, B opposite the second, C opposite the +third, and so on to G, which stands opposite the seventh; after which A +returns to the eighth, and so on through the 365 days of the year.</p> + +<p>Now, if one of the days of the week, Sunday for example, is represented by +F, Monday will be represented by G, Tuesday by A, Wednesday by B, Thursday +by C, Friday by D, and Saturday by E; and every Sunday throughout the year +will have the same character, F, every Monday G, every Tuesday A, and so +with regard to the rest.</p> + +<p><span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a></span>The letter which denotes Sunday is called the Dominical or Sunday letter +for that year; and when the dominical letter of the year is known, the +letters which respectively correspond to the other days of the week become +known also. Did the year consist of 364 days, or 52 weeks invariably, the +first day of the year and the first day of the month, and in fact any day +of any year, or any month, would always commence on the same day of the +week. But every common year consists of 365 days, or 52 weeks and 1 day, +so that the following year will begin one day later in the week than the +year preceding. Thus the year 1837 commenced on Sunday, the following +year, 1838, on Monday, 1839 on Tuesday, and so on.</p> + +<p>As the year consists of 52 weeks and 1 day, it is evident that the day +which begins and ends the year must occur 53 times; thus the year 1837 +begins on Sunday and ends on Sunday; so the following year, 1838, must +begin on Monday. As A represented all the Sundays in 1837 and as A always +stands for the first day of January, so in 1838 it will represent all the +Mondays, and the dominical letter goes back from A to G; so that G +represents all the Sundays in 1838, A all the Mondays, B all the Tuesdays, +and so on, the dominical letter going back one place in every year of 365 +days.</p> + +<p>While the following year commences one day later in the week than the year +preceding, the dominical letter goes back one place from the preceding +year; thus while the year 1865 commenced on Sunday, 1866 on Monday, 1867 +on Tuesday, the dominical letters are A, G and F, respectively. Therefore, +if every year <span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span>consisted of 365 days, the dominical cycle would be +completed in seven years, so that after seven years the first day of the +year would again occur on the same day of the week.</p> + +<p>But this order is interrupted every four years by giving February 29 days, +thereby making the year to consist of 366 days, which is 52 weeks and two +days, so that the following year would commence two days later in the week +than the year preceding, thus the year 1888 being leap-year, had two +dominical letters, A and G; A for January and February, and G for the rest +of the year. The year commenced on Sunday and ended on Monday, making 53 +Sundays and 53 Mondays, and the following year, 1889, to commence on +Tuesday. It now becomes evident that if the years all consisted of 364 +days, or 52 weeks, they would all commence on the same day of the week; if +they all consisted of 365 days, or 52 weeks and one day, they would all +commence one day later in the week than the year preceding; if they all +consisted of 366 days, or 52 weeks and two days, they would commence two +days later in the week; if 367 days or 52 weeks and three days, then three +days later, and so on, one day later for every additional day. It is also +evident that every additional day causes the dominical letter to go back +one place. Now in leap-year the 29th day of February is the additional or +intercalary day. So one letter for January and February, and another for +the rest of the year. If the number of years in the intercalary period +were two, and seven being the number of days in the week, their product +would be 2 × 7 = 14; fourteen, then, would be the number of years in the<span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span> +cycle. Again, if the number of years in the intercalary period were three, +and the number of days in the week being seven, their product would be 3 × +7 = 21; twenty-one would then be the number of years in the cycle. But the +number of years in the intercalary period is four, and the number of days +in the week is seven, therefore their product is 4 × 7 = 28; twenty-eight +is then the number of years in the cycle.</p> + +<p>This period is called the dominical or solar cycle, and restores the first +day of the year to the same day of the week. At the end of the cycle the +dominical letters return again in the same order, on the same days of the +month. Thus, for the year 1801, the dominical letter is D; 1802, C; 1803, +B; 1804, A and G; and so on, going back five places every four years for +twenty-eight years, when the cycle, being ended, D is again dominical +letter for 1829, C for 1830, and so on every 28 years forever, according +to the Julian rule of intercalation.</p> + +<p>But this order is interrupted in the Gregorian calendar at the end of the +century by the secular suppression of the leap-year. It is not +interrupted, however, at the end of every century, for the leap-year is +not suppressed in every fourth centurial year; consequently the cycle will +then be continued for two hundred years. It should be here stated that +this order continued without interruption from the commencement of the era +until the reformation of the calendar in 1582, during which time the +Julian calendar, or Old Style was used.</p> + +<p>It has already been shown that if the number of years in the intercalary +period be multiplied by seven, the number of days in the week, their +product will be<span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span> the number of years in the cycle. Now, in the Gregorian +calendar, the intercalary period is 400 years; this number being +multiplied by seven, their product would be 2,800 years, as the interval +in which the coincidence is restored between the days of the year and the +days of the week.</p> + +<p>This long period, however, may be reduced to 400 years; for since the +dominical letter goes back five places every four years, in 400 years it +will go back 500 places in the Julian and 497 in the Gregorian calendar, +three intercalations being suppressed in the Gregorian every 400 years. +Now 497 is exactly divisible by seven, the number of days in the week, +therefore, after 400 years the cycle will be completed, and the dominical +letters will return again in the same order, on the same days of the +month.</p> + +<p>In answer to the question, “Why two dominical letters for leap-year?” we +reply, because of the additional or intercalary day after the 28th of +February. It has already been shown that every additional day causes the +dominical letter to go back one place. As there are 366 days in leap-year, +the letter must go back two places, one being used for January and +February, and the other for the rest of the year. Did we continue one +letter through the year and then go back two places, it would cause +confusion in computation, unless the intercalation be made at the end of +the year. Whenever the intercalation is made there must necessarily be a +change in the dominical letter. Had it been so arranged that the +additional day was placed after the 30th of June or September, then the +first letter would be used until the intercalation is made in June or<span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span> +September, and the second to the end of the year. Or suppose that the end +of the year had been fixed as the time and place for the intercalation, +(which would have been much more convenient for computation,) then there +would have been no use whatever for the second dominical letter, but at +the end of the year we would go back two places; thus, in the year 1888, +instead of A being dominical letter for two months merely, it would be +continued through the year, and then passing back to F, no use whatever +being made of G, and so on at the end of every leap-year. Hence it is +evident that this arrangement would have been much more convenient, but we +have this order of the months, and the number of days in the months as +Augustus Cæsar left them eight years before Christ. The dominical letter +probably was not known until the Council of Nice, in the year of our Lord +325, where, in all probability, it had its origin.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<h2><a name="CHAPTER_IV.2" id="CHAPTER_IV.2"></a>CHAPTER IV.</h2> +<p class="center"><span class="big">RULE FOR FINDING THE DOMINICAL LETTER.</span></p> + +<p>Divide the number of the given year by 4, neglecting the remainders, and +add the quotient to the given number. Divide this amount by 7, and if the +remainder be less than three, take it from 3; but if it be 3 or more than +3, take it from 10 and the remainder will be the number of the letter +calling A, 1; B, 2; C, 3, etc.</p> + +<p>By this rule the dominical letter is found from the commencement of the +era to October 5th, 1582. O. S.<span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span> From October 15th, 1582, till the year +1700, take the remainder as found by the rule from 6, if it be less than +6, but if the remainder be 6, take it from 13, and so on according to +instructions given in the table on 49th page. It should be understood +here, that in <ins class="correction" title="original: leap-year">leap-years</ins> the letter found by the preceding rule will be +<ins class="correction" title="Not in the original.">the</ins> dominical letter for that part of the year that follows the 29th of +February, while the letter which follows it will be the one for January +and February.</p> + + +<p class="center"><br />EXAMPLES.</p> + +<p>To find the dominical letter for 1365, we have 1365 ÷ 4 = 341 +; 1365 + +341 = 1706; 1706 ÷ 7 = 243, remainder 5. Then 10 - 5 = 5; therefore E +being the fifth letter is the dominical letter for 1365.</p> + +<p>To find the dominical letter for 1620, we have 1620 ÷ 4 = 405; 1620 + 405 += 2025; 2025 ÷ 7 = 289, remainder 2. Then 6 - 2 = 4; therefore, D and E +are the dominical letters for 1620; E for January and February, and D for +the rest of the year. The process of finding the dominical letter is very +simple and easily understood, if we observe the following order:</p> + +<p>1st. Divide by 4.</p> + +<p>2d. Add to the given number.</p> + +<p>3d. Divide by 7.</p> + +<p>4th. Take the remainder from 3 or 10, from the commencement of the era to +October 5th, 1582. From October 15th, 1582 to 1700, from 6 or 13. From +1700 to 1800, from 7, and so on. See table on 49th page.</p> + +<p>We divide by 4 because the intercalary period is four years; and as every +fourth year contains the divisor 4 once more than any of the three +preceding years, so there is one more added to the fourth year than there<span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span> +is to any of the three preceding years; and as every year consists of 52 +weeks and one day, this additional year gives an additional day to the +remainder after dividing by 7. For example, the year</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>1 of the era consists of</td><td align="right">52 w. 1 d.</td></tr> +<tr><td>2 years consist of</td><td align="right">104 w. 2 d.</td></tr> +<tr><td>3 years consist of</td><td align="right">156 w. 3 d.</td></tr> +<tr><td>(4 ÷ 4) + 4 = 5 years consist of </td><td align="right">260 w. 5 d.</td></tr></table> + +<p>Hence the numbers thus formed will be 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, +15, and so on.</p> + +<p>We divide by 7, because there are seven days in the week, and the +remainders show how many days more than an even number of weeks there are +in the given year. Take, for example, the first twelve years of the era +after being increased by one-fourth, and we have</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td align="right">1 ÷ 7 = 0</td> + <td align="center">remainder</td> + <td align="center">1</td> + <td align="center">Then</td> + <td><span style="margin-left: .5em;">3 - 1 = 2 = B</span></td></tr> +<tr><td align="right">2 ÷ 7 = 0</td> + <td align="center">"</td> + <td align="center">2</td> + <td align="center">"</td> + <td><span style="margin-left: .5em;">3 - 2 = 1 = A</span></td></tr> +<tr><td align="right">3 ÷ 7 = 0</td> + <td align="center">"</td> + <td align="center">3</td> + <td align="center">"</td> + <td>10 - 3 = 7 = G</td></tr> +<tr><td align="right">5 ÷ 7 = 0</td> + <td align="center">"</td> + <td align="center">5</td> + <td align="center">"</td> + <td>10 - 5 = 5 = F E</td></tr> +<tr><td align="right">6 ÷ 7 = 0</td> + <td align="center">"</td> + <td align="center">6</td> + <td align="center">"</td> + <td>10 - 6 = 4 = D</td></tr> +<tr><td align="right">7 ÷ 7 = 1</td> + <td align="center">"</td> + <td align="center">0</td> + <td align="center">"</td> + <td><span style="margin-left: .5em;">3 - 0 = 3 = C</span></td></tr> +<tr><td align="right">8 ÷ 7 = 1</td> + <td align="center">"</td> + <td align="center">1</td> + <td align="center">"</td> + <td><span style="margin-left: .5em;">3 - 1 = 2 = B</span></td></tr> +<tr><td align="right">10 ÷ 7 = 1</td> + <td align="center">"</td> + <td align="center">3</td> + <td align="center">"</td> + <td>10 - 3 = 7 = A G</td></tr> +<tr><td align="right">11 ÷ 7 = 1</td> + <td align="center">"</td> + <td align="center">4</td> + <td align="center">"</td> + <td>10 - 4 = 6 = F</td></tr> +<tr><td align="right">12 ÷ 7 = 1</td> + <td align="center">"</td> + <td align="center">5</td> + <td align="center">"</td> + <td>10 - 5 = 5 = E</td></tr> +<tr><td align="right">13 ÷ 7 = 1</td> + <td align="center">"</td> + <td align="center">6</td> + <td align="center">"</td> + <td>10 - 6 = 4 = D</td></tr> +<tr><td align="right">15 ÷ 7 = 2</td> + <td align="center">"</td> + <td align="center">1</td> + <td align="center">"</td> + <td><span style="margin-left: .5em;">3 - 1 = 2 = C B</span></td></tr></table> + +<p>From this table it may be seen that it is these remainders representing +the number of days more than an even number of weeks in the given year, +that we have to deal with in finding the dominical letter.</p> + +<p>Did the year consist of 364 days, or 52 weeks, <span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span>invariably, there would be +no change in the dominical letter from year to year, but the letter that +represents Sunday in any given year would represent Sunday in every year. +Did the year consist of only 363 days, thus wanting one day of an even +number of weeks, then these remainders, instead of being taken from a +given remainder, would be added to that number, thus removing the +dominical letter forward one place, and the beginning of the year, instead +of being one day later, would be one day earlier in the week than in the +preceding year.</p> + +<p>Thus, if the year 1 of the era be taken from 3, we would have 3 - 1 = 2; +therefore, B being the second letter, is dominical letter for the year 1. +But if the year consist of only 363 days, then the 1 instead of being +taken from 3 would be added to 3; then we would have 3 + 1 = 4; therefore, +D being the fourth letter would be dominical letter for the year 1. The +former going back from C to B, the latter forward from C to D; or which +amounts to the same thing, make the year to consist of 51 weeks and 6 +days; then 10 - 6 = 4, making D the dominical letter as before.</p> + +<p>As seven is the number of days in the week, and the object of these +subtractions is to remove the dominical letter back one place every common +year, and two in leap-year, why not take these remainders from 7? We +answer, all depends upon the day of the week on which the era commenced. +Had G, the seventh letter been dominical letter for the year preceding the +era, then these remainders would be taken from 7; and 7 would be used +until change of style in 1582. But we know from computation that C, the +third letter, is dominical<span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span> letter for the year preceding the era; so we +commence with three, and take the smaller remainders, 1 and 2 from 3; that +brings us to A. We take the larger remainders, from 3 to 6, from 3 + 7 = +10. We add the 7 because there are seven days in the week. We use the +number 10 until we get back to C, the third letter, the place from whence +we started. For example, we have</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td><span style="margin-left: 0.5em;">3 - 1 = 2 = B</span></td></tr> +<tr><td><span style="margin-left: 0.5em;">3 - 2 = 1 = A</span></td></tr> +<tr><td>10 - 3 = 7 = G</td></tr> +<tr><td>10 - 4 = 6 = F</td></tr> +<tr><td>10 - 5 = 5 = E</td></tr> +<tr><td>10 - 6 = 4 = D</td></tr> +<tr><td><span style="margin-left: 0.5em;">3 - 0 = 3 = C</span></td></tr></table> + +<p>The cycle of seven days being completed, we commence with the number three +again, and so on until 1582, when on account of the errors of the Julian +calendar, ten days were suppressed to restore the coincidence of the solar +and civil year. Now every day suppressed removes the dominical letter +forward one place; so counting from C to C again is seven, D is eight, E +is nine, and F is ten. As F is the sixth letter, we take the remainders +from 1 to 5, from 6; if the remainder be 6, take it from 6 + 7 = 13. Then +6 or 13 is used till 1700, when, another day being suppressed, the number +is increased to 7. And again in 1800, for the same reason, a change is +made to 1 or 8; in 1900 to 2 or 9, and so on. It will be seen by the table +on the 49th page that the smaller numbers run from 1 to 7; the larger ones +from 8 to 13.</p> + +<p><span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span>From the commencement of the Christian era to October 5th, 1582, take the +remainders, after dividing by 7, from 3 or 10; from October 15th,</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>1582 to 1700</td><td><span class="spacer"> </span></td><td>from</td><td>6 or 13</td></tr> +<tr><td>1700 to 1800</td><td> </td><td align="center">"</td><td>7</td></tr> +<tr><td>1800 to 1900</td><td> </td><td align="center">"</td><td>1 or 8</td></tr> +<tr><td>1900 to 2100</td><td> </td><td align="center">"</td><td>2 or 9</td></tr> +<tr><td>2100 to 2200</td><td> </td><td align="center">"</td><td>3 or 10</td></tr> +<tr><td>2200 to 2300</td><td> </td><td align="center">"</td><td>4 or 11</td></tr> +<tr><td>2300 to 2500</td><td> </td><td align="center">"</td><td>5 or 12</td></tr> +<tr><td>2500 to 2600</td><td> </td><td align="center">"</td><td>6 or 13</td></tr> +<tr><td>2600 to 2700</td><td> </td><td align="center">"</td><td>7</td></tr> +<tr><td>2700 to 2900</td><td> </td><td align="center">"</td><td>1 or 8</td></tr> +<tr><td>2900 to 3000</td><td> </td><td align="center">"</td><td>2 or 9</td></tr> +<tr><td>3000 to 3100</td><td> </td><td align="center">"</td><td>3 or 10</td></tr> +<tr><td>3100 to 3300</td><td> </td><td align="center">"</td><td>4 or 11</td></tr> +<tr><td>3300 to 3400</td><td> </td><td align="center">"</td><td>5 or 12</td></tr> +<tr><td>3400 to 3500</td><td> </td><td align="center">"</td><td>6 or 13</td></tr> +<tr><td>3500 to 3700</td><td> </td><td align="center">"</td><td>7</td></tr> +<tr><td>3700 to 3800</td><td> </td><td align="center">"</td><td>1 or 8</td></tr> +<tr><td>3800 to 3900</td><td> </td><td align="center">"</td><td>2 or 9</td></tr> +<tr><td>3900 to 4000</td><td> </td><td align="center">"</td><td>3 or 10</td></tr> +<tr><td>4000 to 4100</td><td> </td><td align="center">"</td><td>4 or 11</td></tr> +<tr><td>4100 to 4200</td><td> </td><td align="center">"</td><td>5 or 12</td></tr> +<tr><td>4200 to 4300</td><td> </td><td align="center">"</td><td>6 or 13</td></tr> +<tr><td>4300 to 4500</td><td> </td><td align="center">"</td><td>7</td></tr> +<tr><td>4500 to 4600</td><td> </td><td align="center">"</td><td>1 or 8</td></tr> +<tr><td>4600 to 4700</td><td> </td><td align="center">"</td><td>2 or 9</td></tr> +<tr><td>4700 to 4900</td><td> </td><td align="center">"</td><td>3 or 10</td></tr> +<tr><td>4900 to 5000</td><td> </td><td align="center">"</td><td>4 or 11</td></tr> +<tr><td>5000 to 5100</td><td> </td><td align="center">"</td><td>5 or 12</td></tr></table> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span></p> +<h2><a name="CHAPTER_V.2" id="CHAPTER_V.2"></a>CHAPTER V.</h2> +<p class="center"><span class="big">RULE FOR FINDING THE DAY OF THE WEEK OF ANY GIVEN DATE, FOR BOTH OLD AND NEW STYLES.</span></p> + +<p>By arranging the dominical letters in the order in which the different +months commence, the day of the week on which any month of any year, or +day of the month has fallen or will fall, from the commencement of the +Christian era to the year of our Lord 4000, may be calculated. (<a href="#appeng">Appendix +G.</a>) They have been arranged thus in the following couplet, in which At +stands for January, Dover for February, Dwells for March, etc.</p> + +<p class="poem">At Dover Dwells George Brown, Esquire,<br /> +Good Carlos Finch, and David Fryer.</p> + +<p>Now if A be dominical or Sunday letter for a given year, then January and +October being represented by the same letter, begin on Sunday; February, +March and November, for the same reason, begin on Wednesday; April and +July on Saturday; May on Monday, June on Thursday, August on Tuesday, +September and December on Friday. It is evident that every month in the +year must commence on some one day of the week represented by one of the +first seven letters of the alphabet. Now let</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td colspan="7">January 1st be represented</td><td>by A, Sun.</td></tr> +<tr><td>Feb.</td><td>1st</td><td>(4 w. 3 d.</td><td>from</td><td>the</td><td>preceding</td><td>date)</td><td>by D, Wed.</td></tr> +<tr><td>Mar.</td><td>1st</td> + <td><span style="margin-left: .35em;">4 w. 0 d.</span></td> + <td align="center">"</td><td> </td> + <td align="center">"</td><td align="center">"</td> + <td>by D, Wed.</td></tr> +<tr><td>Apr.</td><td>1st</td> + <td><span style="margin-left: .35em;">4 w. 3 d.</span></td> + <td align="center">"</td><td> </td> + <td align="center">"</td><td align="center">"</td> + <td>by G, Sat.</td></tr> +<tr><td>May</td><td>1st</td> + <td><span style="margin-left: .35em;">4 w. 2 d.</span></td> + <td align="center">"</td><td> </td> + <td align="center">"</td><td align="center">"</td> + <td>by B, Mon.</td></tr> +<tr><td><span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span>June</td><td>1st</td> + <td><span style="margin-left: .35em;">4 w. 3 d.</span></td> + <td align="center">"</td><td> </td> + <td align="center">"</td><td align="center">"</td> + <td>by E, Thur.</td></tr> +<tr><td>July</td><td>1st</td> + <td><span style="margin-left: .35em;">4 w. 2 d.</span></td> + <td align="center">"</td><td> </td> + <td align="center">"</td><td align="center">"</td> + <td>by G, Sat.</td></tr> +<tr><td>Aug.</td><td>1st</td> + <td><span style="margin-left: .35em;">4 w. 3 d.</span></td> + <td align="center">"</td><td> </td> + <td align="center">"</td><td align="center">"</td> + <td>by C, Tues.</td></tr> +<tr><td>Sept.</td><td>1st</td> + <td><span style="margin-left: .35em;">4 w. 3 d.</span></td> + <td align="center">"</td><td> </td> + <td align="center">"</td><td align="center">"</td> + <td>by F, Fri.</td></tr> +<tr><td>Oct.</td><td>1st</td> + <td><span style="margin-left: .35em;">4 w. 2 d.</span></td> + <td align="center">"</td><td> </td> + <td align="center">"</td><td align="center">"</td> + <td>by A, Sun.</td></tr> +<tr><td>Nov.</td><td>1st</td> + <td><span style="margin-left: .35em;">4 w. 3 d.</span></td> + <td align="center">"</td><td> </td> + <td align="center">"</td><td align="center">"</td> + <td>by D, Wed.</td></tr> +<tr><td>Dec.</td><td>1st</td> + <td><span style="margin-left: .35em;">4 w. 2 d.</span></td> + <td align="center">"</td><td> </td> + <td align="center">"</td><td align="center">"</td> + <td>by F, Fri.</td></tr></table> + +<p>Now each of these letters placed opposite the months respectively +represents the day of the week on which the month commences, and they are +the first letters of each word in the preceding couplet.</p> + +<p>To find the day of the week on which a given day of any year will occur, +we have the following</p> + + +<p class="center"><br />RULE.</p> + +<p>Find the dominical letter for the year. Read from this to the letter which +begins the given month, always reading from A toward G, calling the +dominical letter Sunday, the next Monday, etc. This will show on what day +of the week the month commenced; then reckoning the number of days from +this will give the day required.</p> + + +<p class="center"><br />EXAMPLES.</p> + +<p>History records the fall of Constantinople on May 29th, 1453. On what day +of the week did it occur? We have then +<ins class="errata" title="Errata: On 51st page, ninth line from the bottom of the page, instead of 1453 ÷ 43 = 63+, should be 1453 ÷ 4 = 363+.">1453 ÷ +43 = 63 +</ins>; 1453 + 363 = 1816; 1816 ÷ 7 = 259, remainder 3. Then 10 - 3 = 7; therefore, G being the +seventh letter is dominical letter for 1453. Now reading from G to B, the +letter for May, we have G Sunday, A Monday, and B Tuesday; hence May +commenced on Tuesday and the 29th was Tuesday.</p> + +<p>The change from Old to New Style was made by Pope Gregory XIII, October +5th, 1582. On what day<span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span> of the week did it occur? We have then 1582 ÷ 4 = +395+; 1582 + 395 = 1977; 1977 ÷ 7 = 282, remainder 3. Then 10 - 3 = 7; +therefore, G being the seventh letter, is dominical letter for 1582. Now +reading from G to A, the letter for October, we have G Sunday, A Monday, +etc. Hence October commenced on Monday, and the 5th was Friday.</p> + +<p>On what day of the week did the 15th of the same month fall in 1582? We +have then 1582 ÷ 4 = 395+; 1582 + 395 = 1977; 1977 ÷ 7 = 282, remainder 3. +Then 6 - 3 = 3; therefore, C being the third letter, is the dominical +letter for 1582. Now reading from C to A, the letter for October, we have +C Sunday, D Monday, E Tuesday, etc. Hence October commenced on Friday, and +the 15th was Friday.</p> + +<p>How is this, says one? You have just shown by computation that October, +1582, commenced on Monday, you now say that it occurred on Friday. You +also stated that the 5th was Friday; you now say that the 15th was Friday. +This is absurd; ten is not a multiple of seven. There is nothing absurd +about it. The former computation was Old Style, the latter New Style, the +Old being ten days behind the new.</p> + +<p>As regards an interval of ten days between the two Fridays, there was +none; Friday, the 5th, and Friday, the 15th, was one and the same day; +there was no interval, nothing ever occurred, there was no time for +anything to occur; the edict of the Pope decided it; he said the 5th +should be called the 15th, and it was so.</p> + +<p>Hence to October the 5th, 1582, the computation should be Old Style; from +the 15th to the end of the year New Style.</p> + +<p><span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span>On what day of the week did the years 1, 2 and 3, of the era commence? +None of these numbers can be divided by 4; neither are they divisible by +7; but they may be treated as remainders after dividing by 7. Now each of +these numbers of years consists of an even number of weeks with remainders +of 1, 2 and 3 days respectively. Hence we have then for the year 1, 3 - 1 += 2; therefore, B being the second letter, is the dominical letter for the +year 1. Now reading from B to A, the letter for January, we have B Sunday, +C Monday, D Tuesday, etc. Hence January commenced on Saturday.</p> + +<p>Then we have for the year 2, 3 - 2 = 1; therefore A being the first +letter, is dominical letter for the year 2; hence it is evident that +January commenced on Sunday. Again we have for the year 3, 10 - 3 = 7; +therefore, G being the seventh letter, is dominical letter for the year 3. +Now reading from G to A, the letter for January, we have G Sunday, A +Monday; hence January commenced on Monday.</p> + +<p>On what day of the week did the year 4 commence? Now we have a number that +is divisible by 4, it being the first leap-year in the era, so we have 4 ÷ +4 = 1; 4 + 1 = 5; 5 ÷ 7 = 0, remainder 5. Then 10 - 5 = 5; therefore, E +being the 5th letter, is dominical letter for that part of the year which +follows the 29th of February, while F, the letter that follows it, is +dominical letter for January and February. Now reading from F to A, the +letter for January, we have F Sunday, G Monday, A Tuesday; hence January +commenced on Tuesday.</p> + +<p>Now we have disposed of the first four years of the<span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span> era; the dominical +letters being B, A, G, and F, E. Hence it is evident, while one year +consists of an even number of weeks and one day, two years of an even +number of weeks and two days, three years of an even number of weeks and +three days, that every fourth year, by intercalation, is made to consist +of 366 days; so that four years consist of an even number of weeks and +five days; for we have (4 ÷ 4) + 4 = 5, the dominical letter going back +from G in the year 3, to F, for January and February in the year 4, and +from F to E for the rest of the year, causing the following year to +commence two days later in the week than the year preceding.</p> + +<p>The year 1 had 53 Saturdays; the year 2, 53 Sundays; the year 3, 53 +Mondays, and the year 4, 53 Tuesdays and 53 Wednesdays, causing the year 5 +to commence on Thursday, two days later in the week than the preceding +year. Now what is true concerning the first four years of the era, is true +concerning all the future years, and the reason for the divisions, +additions and subtractions in finding the dominical letter is evident.</p> + +<p>The Declaration of Independence was signed July 4, 1776. On what day of +the week did it occur? We have then 1776 ÷ 4 = 444; 1776 + 444 = 2220; +2220 ÷ 7 = 317, remainder 1. Then 7 - 1 = 6, therefore F and G are the +dominical letters for 1776, G for January and February, and F for the rest +of the year. Now reading from F to G, the letter for July, we have F +Sunday, G Monday; hence July commenced on Monday, and the fourth was +Thursday. On what day of the week did Lee surrender to Grant, which +occurred<span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span> on April 9th, 1865? We have then 1865 ÷ 4 = 466+; 1865 + 466 = +2331; 2331 ÷ 7 = 333, remainder 0. Then 1 - 0 = 1; therefore, A being the +first letter, is dominical letter for 1865. Now reading from A to G, the +letter for April, we have A Sunday, B Monday, C Tuesday, etc. Hence April +commenced on Saturday, and the 9th was Sunday.</p> + +<p>Benjamin Harrison was inaugurated President of the United States on +Monday, March 4, 1889. On what day of the week will the 4th of March fall +in 1989? We have then 1989 ÷ 4 = 497+; 1989 + 497 = 2486; 2486 ÷ 7 = 355, +remainder 1. Then 2 - 1 = 1; therefore, A being the first letter, is +dominical letter for 1989. Now, reading from A to D, the letter for March, +we have A Sunday, B Monday, C Tuesday, and D Wednesday; hence March will +commence on Wednesday, and the 4th will fall on Saturday. Columbus landed +on the island of San Salvador on Friday, October 12, 1492. On what day of +the month and on what day of the week will the four hundredth anniversary +fall in 1892?</p> + +<p>The day of the month on which Columbus landed is, of course, the day to be +observed in commemoration of that event. The Julian calendar, which was +then in use throughout Europe, and the very best that had ever been given +to the world, made the year too long by more than eleven minutes. Those +eleven minutes a year had accumulated, from the council of Nice, in 325, +to the discovery of America, in 1492, to nine days, so that the civil year +was nine days behind the true or solar time; that is, when the Earth, in +her annual revolution, had arrived at that point of the ecliptic<span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span> +coinciding with the 21st of October, the civil year, according to the +Julian calendar, was the 12th.</p> + +<p>Now, to restore the coincidence, the nine days must be dropped, or +suppressed, calling what was erroneously called the 12th of October, the +21st. Since the Julian calendar was corrected by Gregory, in 1582, we have +so intercalated as to retain, very nearly, the coincidence of the solar +and the civil year. It has already been shown in Chapter III, (q. v.) that +in the Gregorian calendar, the cycle which restores the coincidence of the +day of the month and the day of the week, is completed in 400 years; so +that after 400 years, events will again transpire in the same order, on +the same day of the week. Now, as Columbus landed on Friday, October 21st, +1492, so Friday, October 21st, 1892, is the day of the month and also the +day of the week to be observed in commemoration of that event. We have +then 1892 ÷ 4 = 473; 1892 + 473 = 2365; 2365 ÷ 7 = 337, remainder 6. Then +8 - 6 = 2; therefore, B and C are dominical letters for 1892, C for +January and February, and B for the rest of the year. Now, reading from B +to A, the letter for October, we have B Sunday, C Monday, etc. Hence +October will commence on Saturday and the 21st will be Friday.</p> + +<p>Although there was an error of thirteen days in the Julian calendar when +it was reformed by Gregory, in 1582, there was a correction made of only +ten days. There was still an error of three days from the time of Julius +Cæsar to the Council of Nice, which remained uncorrected. Gregory restored +the vernal equinox to the 21st of March, its date at the meeting of that +council, not to the place it occupied in the time of<span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span> Cæsar, namely, the +24th of March. Had he done so it would now fall on the 24th, by adopting +the Gregorian rule of intercalation. <a href="#appenh">Appendix H.</a></p> + +<p>If desirable calculations may be made in both Old and New Styles from the +year of our Lord 300. There is no perceptible discrepancy in the +calendars, however, until the close of the 4th century, when it amounts to +nearly one day, reckoned in round numbers one day. Now in order to make +the calculation, proceed according to rule already given for finding the +dominical letter, and for New Style take the remainders after dividing by +seven from the numbers in the following table:</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>From</td><td><span style="margin-left: .5em;">400</span></td><td>to</td><td><span style="margin-left: .5em;">500</span></td> + <td><span class="spacer"> </span></td> + <td>From</td><td>4</td><td>or</td><td>11</td></tr> +<tr><td align="center">"</td><td><span style="margin-left: .5em;">500</span></td> + <td align="center">"</td><td><span style="margin-left: .5em;">600</span></td> + <td> </td> + <td align="center">"</td><td>5</td> + <td align="center">"</td><td>11</td></tr> +<tr><td align="center">"</td><td><span style="margin-left: .5em;">600</span></td> + <td align="center">"</td><td><span style="margin-left: .5em;">700</span></td> + <td> </td> + <td align="center">"</td><td>6</td> + <td align="center">"</td><td>13</td></tr> +<tr><td align="center">"</td><td><span style="margin-left: .5em;">700</span></td> + <td align="center">"</td><td><span style="margin-left: .5em;">900</span></td> + <td> </td> + <td align="center">"</td><td>7</td></tr> +<tr><td align="center">"</td><td><span style="margin-left: .5em;">900</span></td> + <td align="center">"</td><td>1000</td> + <td> </td> + <td align="center">"</td><td>1</td> + <td align="center">"</td><td><span style="margin-left: .5em;">8</span></td></tr> +<tr><td align="center">"</td><td>1000</td> + <td align="center">"</td><td>1100</td> + <td> </td> + <td align="center">"</td><td>2</td> + <td align="center">"</td><td><span style="margin-left: .5em;">9</span></td></tr> +<tr><td align="center">"</td><td>1100</td> + <td align="center">"</td><td>1300</td> + <td> </td> + <td align="center">"</td><td>3</td> + <td align="center">"</td><td>10</td></tr> +<tr><td align="center">"</td><td>1300</td> + <td align="center">"</td><td>1400</td> + <td> </td> + <td align="center">"</td><td>4</td> + <td align="center">"</td><td>11</td></tr> +<tr><td align="center">"</td><td>1400</td> + <td align="center">"</td><td>1500</td> + <td> </td> + <td align="center">"</td><td>5</td> + <td align="center">"</td><td>12</td></tr> +<tr><td align="center">"</td><td>1500</td> + <td align="center">"</td><td>1700</td> + <td> </td> + <td align="center">"</td><td>6</td> + <td align="center">"</td><td>11</td></tr></table> + +<p>It will be found by calculation that from the year</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td><span style="margin-left: .5em;">400</span></td><td>to</td><td><span style="margin-left: .5em;">500</span></td> + <td>the</td><td>discrepancy</td><td>is</td> + <td><span style="margin-left: .5em;">1</span></td><td>day</td></tr> +<tr><td><span style="margin-left: .5em;">500</span></td><td align="center">"</td><td><span style="margin-left: .5em;">600</span></td> + <td align="center">"</td><td align="center">"</td><td align="center">"</td> + <td><span style="margin-left: .5em;">2</span></td><td align="center">"</td></tr> +<tr><td><span style="margin-left: .5em;">600</span></td><td align="center">"</td><td><span style="margin-left: .5em;">700</span></td> + <td align="center">"</td><td align="center">"</td><td align="center">"</td> + <td><span style="margin-left: .5em;">3</span></td><td align="center">"</td></tr> +<tr><td><span style="margin-left: .5em;">700</span></td><td align="center">"</td><td><span style="margin-left: .5em;">900</span></td> + <td align="center">"</td><td align="center">"</td><td align="center">"</td> + <td><span style="margin-left: .5em;">4</span></td><td align="center">"</td></tr> +<tr><td><span style="margin-left: .5em;">900</span></td><td align="center">"</td><td>1000</td> + <td align="center">"</td><td align="center">"</td><td align="center">"</td> + <td><span style="margin-left: .5em;">5</span></td><td align="center">"</td></tr> +<tr><td>1000</td><td align="center">"</td><td>1100</td> + <td align="center">"</td><td align="center">"</td><td align="center">"</td> + <td><span style="margin-left: .5em;">6</span></td><td align="center">"</td></tr> +<tr><td>1100</td><td align="center">"</td><td>1300</td> + <td align="center">"</td><td align="center">"</td><td align="center">"</td> + <td><span style="margin-left: .5em;">7</span></td><td align="center">"</td></tr> +<tr><td>1300</td><td align="center">"</td><td>1400</td> + <td align="center">"</td><td align="center">"</td><td align="center">"</td> + <td><span style="margin-left: .5em;">8</span></td><td align="center">"</td></tr> +<tr><td>1400</td><td align="center">"</td><td>1500</td> + <td align="center">"</td><td align="center">"</td><td align="center">"</td> + <td><span style="margin-left: .5em;">9</span></td><td align="center">"</td></tr> +<tr><td>1500</td><td align="center">"</td><td>1700</td> + <td align="center">"</td><td align="center">"</td><td align="center">"</td> + <td>10</td><td align="center">"</td></tr></table> + +<p><span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span>Hence the necessity, in reforming the calendar in 1582, of suppressing ten +days. (See table on 59th page.) On what day of the week did January +commence in 450? We have then 450 ÷ 4 = 112+; 450 + 112 = 562; 562 ÷ 7 = +80, remainder 2. Then 3 - 2 = 1; therefore, A being the first letter, is +dominical letter for 450, Old Style, and January commenced on Sunday. For +New Style we have 4 - 2 = 2; therefore, B being the second letter, is +dominical letter for the year 450. Now reading from B to A, the letter for +January, we have B Sunday, C Monday, D Tuesday, etc.</p> + +<p>Hence, January commenced on Saturday. Old Style makes Sunday the first +day; New Style makes Saturday the first and Sunday the second. On what day +of the week did January commence in the year 1250? We have then 1250 ÷ 4 = +312+; 1250 + 312 = 1562; 1562 ÷ 7 = 223, remainder 1. Then 3 - 1 = 2; +therefore, B being the second letter, is dominical letter for the year +1250, Old Style. Now, reading from B to A, the letter for January, we have +B Sunday, C Monday, etc. Hence January commenced on Saturday. B is also +dominical letter, New Style; for we take the remainder after dividing by +7, from the same number.</p> + +<p>As both Old and New Styles have the same dominical letter, so both make +January to commence on the same day of the week; but Old Style, during +this century, is seven days behind the true time, so that when it is the +first day of January by the Old, it is the eighth by the New.</p> + +<p><span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59 & 60]</a></span></p> + +<p>It is here seen by the errors of the Julian Calendar the Vernal Equinox is made to occur +three days earlier every 400 years, so that in 1582 it fell on the 11th instead of the 21st of March.</p> + +<div class="figcenter"><img src="images/table_tmbBW.jpg" alt="" /><br /> +<a href="images/table.jpg"><small>Larger Image</small></a></div> + +<p><span style="margin-left: 2em;">By the Gregorian rule of intercalation the coincidence of the solar and +civil year is restored very nearly every 400 years. <a href="#appeni">Appendix I.</a></span></p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span></p> +<h2><a name="CHAPTER_VI.2" id="CHAPTER_VI.2"></a>CHAPTER VI.</h2> +<p class="center"><span class="big">A SIMPLE METHOD FOR FINDING THE DAY OF THE WEEK OF EVENTS WHICH OCCUR QUADRENNIALLY.</span></p> + +<p>The inaugural of the Presidents. The day of the week on which they have +occurred, and on which they will occur for the next one hundred years:</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>April 30th, 1789,</td><td>Thursday,</td><td>George Washington.</td></tr> +<tr><td>March 4th, 1793,</td> + <td>Monday,</td><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 3em;">"</span></td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1797,</span></td> + <td>Saturday,</td><td>John Adams</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1801,</span></td> + <td>Wednesday,</td><td>Thomas Jefferson.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1805,</span></td> + <td>Monday,</td><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 3em;">"</span></td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1809,</span></td> + <td>Saturday,</td><td>James Madison.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1813,</span></td> + <td>Thursday,</td><td><span style="margin-left: 1em;">"</span><span style="margin-left: 3em;">"</span></td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1817,</span></td> + <td>Tuesday,</td><td>James Monroe.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1821,</span></td> + <td>Sunday,</td><td><span style="margin-left: 1em;">"</span><span style="margin-left: 3em;">"</span></td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1825,</span></td> + <td>Friday,</td><td>John Q. Adams.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1829,</span></td> + <td>Wednesday,</td><td>Andrew Jackson.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1833,</span></td> + <td>Monday,</td><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 3em;">"</span></td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1837,</span></td> + <td>Saturday,</td><td>Martin Van Buren.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1841,</span></td> + <td>Thursday,</td><td>Wm. H. Harrison.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1845,</span></td> + <td>Tuesday,</td><td>James K. Polk.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1849,</span></td> + <td>Sunday,</td><td>Zachary Taylor.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1853,</span></td> + <td>Friday,</td><td>Franklin Pierce.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1857,</span></td> + <td>Wednesday,</td><td>James Buchanan.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1861,</span></td> + <td>Monday,</td><td>Abraham Lincoln.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1865,</span></td> + <td>Saturday,</td><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 3em;">"</span></td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1869,</span></td> + <td>Thursday,</td><td>Ulysses S. Grant.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1873,</span></td> + <td>Tuesday,</td><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 3em;">"</span></td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1877,</span></td> + <td>Sunday,</td><td>Rutherford B. Hays.</td></tr> +<tr><td><span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span> + <span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1881,</span></td> + <td>Friday,</td><td>James A. Garfield.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1885,</span></td> + <td>Wednesday,</td><td>Grover Cleveland.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1889,</span></td> + <td>Monday,</td><td>Benjamin Harrison.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1893,</span></td> + <td>Saturday,</td><td>Grover Cleveland.</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1897,</span></td> + <td>Thursday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1901,</span></td> + <td>Monday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1905,</span></td> + <td>Saturday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1909,</span></td> + <td>Thursday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1913,</span></td> + <td>Tuesday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1917,</span></td> + <td>Sunday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1921,</span></td> + <td>Friday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1925,</span></td> + <td>Wednesday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1929,</span></td> + <td>Monday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1933,</span></td> + <td>Saturday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1937,</span></td> + <td>Thursday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1941,</span></td> + <td>Tuesday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1945,</span></td> + <td>Sunday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1949,</span></td> + <td>Friday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1953,</span></td> + <td>Wednesday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1957,</span></td> + <td>Monday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1961,</span></td> + <td>Saturday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1965,</span></td> + <td>Thursday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1969,</span></td> + <td>Tuesday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1973,</span></td> + <td>Sunday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1977,</span></td> + <td>Friday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1981,</span></td> + <td>Wednesday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1985,</span></td> + <td>Monday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1989,</span></td> + <td>Saturday,</td></tr> +<tr><td><span style="margin-left: 1.5em;">"</span><span style="margin-left: 1.5em;">"</span><span style="margin-left: .75em;">1993,</span></td> + <td>Thursday.</td></tr></table> + +<p>Any one understanding what has been said in a preceding chapter concerning +the dominical letter, can very easily make out such a table without going +through the process of making calculations for every<span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span> year. As every +succeeding year, or any day of the year, commences one day later in the +week than the year preceding, and two days later in leap-year, which makes +five days every four years, and as the Presidential term is four years, so +every inaugural occurs five days later in the week than it did in the +preceding term.</p> + +<p>Now, as counting forward five days is equivalent to counting back two, it +will be much more convenient to count back two days every term. There is +one exception, however, to this rule; the year which completes the century +is reckoned as a common year (that is, three centuries out of four), +consequently we count forward only four days or back three.</p> + +<p>Commencing, then, with the second inaugural of Washington, which occurred +on Monday, March 4, <ins class="correction" title="original: 1993">1793</ins>, and counting back two days to Saturday in 1797, +three days to Wednesday in 1801 and two days to 1805, and so on two days +every term till 1901, when, for reasons already given, we count back three +days again for one term only, after which it will be two days for the next +two hundred years; hence anyone can make his calculations as he writes, +and as fast as he can write. See table on 61st page.</p> + +<p> <span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span></p> +<p class="center"><span class="big">SOME PECULIARITIES CONCERNING EVENTS WHICH FALL ON THE TWENTY-NINTH DAY OF FEBRUARY.</span></p> + +<p>The civil year and the day must be regarded as commencing at the same +instant. We cannot well reckon a fraction of a day, giving to February 28 +days and 6 hours, making the following month to commence six hours later +every year; if so, then March, for example, in</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>1888</td><td>would</td><td>commence</td><td>at</td><td>12 m. night.</td></tr> +<tr><td>1889</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td><span style="margin-left: .5em;">6 a. m.</span></td></tr> +<tr><td>1890</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>12 m.</td></tr> +<tr><td>1891</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td><span style="margin-left: .5em;">6 p. m.</span></td></tr> +<tr><td>1892</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>12 m. night,</td></tr></table> + +<p>again, and so on.</p> + +<p>Instead of doing so, we wait until the fraction accumulates to a whole +day; then give to February 29 days, and the year 366. Therefore, events +which fall on the 29th of February cannot be celebrated annually, but only +quadrennially; and at the close of those centuries in which the +intercalations are suppressed only octennially. For example: From the year +1696 to 1704, 1796 to 1804, and 1896 to 1904, there is no 29th day of +February; consequently no day of the month in the civil year on which an +event falling on the 29th of February could be celebrated. Therefore, a +person born on the 29th of February, 1896, could celebrate no birthday +till 1904, a period of eight years.</p> + +<p>In every common year February has 28 days, each day of the week being +contained in the number of days in the month four times; but in leap-year, +when February has 29 days, the day which begins and ends the<span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span> month is +contained five times. Let us suppose that in a certain year, when February +has 29 days, the month comes in on Friday; it also must necessarily end on +Friday.</p> + +<p>After four years it will commence on Wednesday, and end on Wednesday, and +so on, going back two days in the week every four years, until after 28 +years we come back to Friday again. This, as has already been explained, +is the dominical or solar cycle. For example: February in</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>The</td><td>year</td><td><span style="margin-left: .5em;">4</span></td> + <td>has</td><td>five</td><td>Fridays.</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td><span style="margin-left: .5em;">8</span></td> + <td align="center">"</td><td align="center">"</td><td>Wednesdays.</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td>12</td> + <td align="center">"</td><td align="center">"</td><td>Mondays.</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td>16</td> + <td align="center">"</td><td align="center">"</td><td>Saturdays.</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td>20</td> + <td align="center">"</td><td align="center">"</td><td>Thursdays.</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td>24</td> + <td align="center">"</td><td align="center">"</td><td>Tuesdays.</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td>28</td> + <td align="center">"</td><td align="center">"</td><td>Sundays.</td></tr> +<tr><td align="center">"</td><td align="center">"</td><td>32</td> + <td align="center">"</td><td align="center">"</td><td>Fridays.</td></tr></table> + +<p>So that after 28 years we come back to Friday again; and so on every 28 +years, until change of style in 1582, when the Gregorian rule of +intercalation being adopted by suppressing the intercalations in three +centurial years out of four interrupts this order at the close of these +three centuries. For example—1700, 1800 and 1900, after which the cycle +of 28 years will be continued until 2100, and so on. The cycle being +interrupted by the Gregorian rule of intercalation, causes all events +which occur between 28 and 12 years of the close of the centuries to fall +on the same day of the week again in 40 years; and those events that fall +within 12 years of the close of these centuries, to fall on the same day +of the week again in 12 years; after<span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span> which the cycle of 28 years will be +continued during the century. See following table:</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>1804</td><td>February</td><td>has</td><td>five</td><td>Wednesdays.</td></tr> +<tr><td>1808</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Mondays.</td></tr> +<tr><td>1812</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Saturdays.</td></tr> +<tr><td>1816</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Thursdays.</td></tr> +<tr><td>1820</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Tuesdays.</td></tr> +<tr><td>1824</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Sundays.</td></tr> +<tr><td>1828</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Fridays.</td></tr> +<tr><td>1832</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Wednesdays.</td></tr> +<tr><td>1836</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Mondays.</td></tr> +<tr><td>1840</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Saturdays.</td></tr> +<tr><td>1844</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Thursdays.</td></tr> +<tr><td>1848</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Tuesdays.</td></tr> +<tr><td>1852</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Sundays.</td></tr> +<tr><td>1856</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Fridays.</td></tr> +<tr><td>1860</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Wednesdays.</td></tr> +<tr><td>1864</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Mondays.</td></tr> +<tr><td>1868</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Saturdays.</td></tr> +<tr><td>1872</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Thursdays.</td></tr> +<tr><td>1876</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Tuesdays.</td></tr> +<tr><td>1880</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Sundays.</td></tr> +<tr><td>1884</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Fridays.</td></tr> +<tr><td>1888</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Wednesdays.</td></tr> +<tr><td>1892</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Mondays.</td></tr> +<tr><td>1896</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Saturdays.</td></tr> +<tr><td>1900</td></tr> +<tr><td>1904</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Mondays.</td></tr> +<tr><td>1908</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Saturdays.</td></tr> +<tr><td>1912</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Thursdays.</td></tr> +<tr><td>1916</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Tuesdays.</td></tr> +<tr><td>1920</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Sundays.</td></tr> +<tr><td>1924</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Fridays.</td></tr> +<tr><td>1928</td><td align="center">"</td><td align="center">"</td><td align="center">"</td><td>Wednesdays.</td></tr></table> + +<p><span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span>It will be seen from this table that in 1804 February had five Wednesdays; +and then again in 1832, 1860 and 1888; then suppressing the intercalation +in the year 1900 suppresses the 29th of February; so opposite 1900 in the +table is blank, and the 29th of February does not occur again till 1904, +and the five Wednesdays do not occur again till 1928—that is, 40 years +from 1888, when it last occurred.</p> + +<p>Again taking the five Mondays which occurred first in this century, in +1808, and then again in 1836, 1864 and in 1892, you will see, for reasons +already given, that it will occur again in 12 years, that is, in 1904; and +so on with all the days of the week, when it will be seen what is peculiar +concerning the 29th of February.</p> + +<p>But attention is particularly called to the five Thursdays, which occur +first in this century 1816, and then again in 1844 and 1872, the last date +being within 28 years of the close of the century. Suppressing the +intercalation suppresses the 29th of February; consequently the five +Thursdays do not occur again till 1912, that is 40 years from the +preceding date, after which the cycle will be continued for two hundred +years.</p> + +<p>Hence it may be seen that the dominical or solar cycle of 28 years is so +interrupted at the close of these centuries by the suppression of the +leap-year, that certain events do not occur again on the same day of the +week under 40 years, while others are repeated again on the same day of +the week in 12 years; also the number of years in the cycle, that is 28 + +12 = 40.</p> + +<p>And again the change of style in 1582, causes all events which occur +between 28 and 8 years of that<span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span> change, to fall again on the same day of +the week in 36 years, and all that occur within 8 years of that change to +be repeated again on the same day of the week in 8 years, after which the +cycle of 28 years is continued for 100 years; also that the number of +years in the cycle, that is, 28 + 8 = 36.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<h2><a name="CHAPTER_VII.2" id="CHAPTER_VII.2"></a>CHAPTER VII.</h2> +<p class="center"><span class="big">RULES FOR FINDING THE DAY OF THE WEEK OF EVENTS THAT TRANSPIRED PRIOR TO THE CHRISTIAN ERA.</span></p> + +<p>First, it should be understood that the year 4 is the first leap year in +our era, reckoning from the year 1 B. C., which must necessarily be leap +year; so that the odd numbers 1, 5, 9, 13, etc., are leap years. Hence +every year that is divisible by four and one remainder, is leap year; if +no remainder, it is the first year after leap-year; if 3, the second; if +2, the third, thus:</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>45 ÷ 4 = 11, remainder, 1,<br /> +44 ÷ 4 = 11, no remainder,<br /> +43 ÷ 4 = 10, remainder, 3,<br /> +42 ÷ 4 = 10, remainder, 2,<br /> +41 ÷ 4 = 10, remainder, 1,</td></tr></table> + +<p>and so on, every year being divided by four and 1 remainder is leap-year +of 366 days. It should be borne in mind that the same calendar was in use +without any correction from the days of Julius Cæsar 46 B. C. to Pope +Gregory XIII in 1582; consequently the method of finding the dominical +letter is, in some respects, similar<span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span> to the one already given on the 44th +page. But in some respects the one is the reverse of the other, for we +reckon backward and forward from a fixed point—the era; that is the +numbers increase each way from the era. Also the dominical letters occur +in the natural order of the letters in reckoning backward, but exactly the +reverse in reckoning forward. See table on the 73d page, where the +dominical letter is placed opposite each year from 45 B. C. to 45 A. D. +Now we use the same number 3, because C, the third letter is dominical +letter for the year 1 B. C., the point from which we reckon. But instead +of taking the remainder, after dividing by 7, <i>from</i> 3 or 10, to find the +number of the letter, as in <a href="#CHAPTER_IV.2">Part Second, Chapter IV</a>, (q. v.) we add the +remainder <i>to</i> 3; hence we have the following:</p> + + +<p class="center"><br />RULE.</p> + +<p>Divide the number of the given year by 4, neglecting the remainders, and +add the quotient to the given number, divide this amount by 7, and add the +remainder to 3, and that amount will give the number of the letter, +calling A, 1; B, 2; C, 3, etc.; except the first year after leap-year, +(which is the year exactly divisible by 4), the number of the letter is +one less than is indicated by the rule.</p> + +<p>This rule gives the dominical letter for January and February only, in +leap-year, while the letter that precedes it, is the letter for the rest +of the year. If the amount be greater than seven, we should reckon from A +to A or B again.</p> + +<p>It has already been stated in <a href="#CHAPTER_III.1">Part First, Chapter III</a>, (q. v.), that a +change was made by Augustus Cæsar about 8 B. C., in the number of days in +the month; and,<span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span> as this change effects the day of the week on which +certain events fall, it becomes necessary that they should be presented as +they were arranged by Julius Cæsar, and as corrected by Augustus. Julius +Cæsar gave to February 29 days in common years, and in leap-year 30. This +arrangement was the very best that could possibly be made, but, as has +already been shown, it was interrupted to gratify the vanity of Augustus.</p> + +<p>The left hand column in the table on the 72d page represents the number of +days in each month from the days of Julius Cæsar to Augustus, a period of +37 years. The right hand column represents the number of days in the +months as they now are, and have been since the change was made by +Augustus, 8 B. C. Consequently the rule for finding the day of the week on +which events have fallen for the 37 years prior to the last mentioned +date, is not perfectly exact, and needs a little explanation here.</p> + +<p>The rule itself is given, and fully explained in <a href="#CHAPTER_V.2">Part Second, Chapter V</a>, +(q. v.) but cannot be applied to the 37 years without some correction. In +all the months marked with a star, events fall one day later in the week +than that which is indicated by the rule. This should be borne in mind, +and make the event one day later in the week than that which is found by +the rule. For example, Julius Cæsar was assassinated on the 15th of March, +44 B. C. By giving to February 28 days the first day of March would fall +on Wednesday, and, of course, the 15th would be Wednesday. But Cæsar gave +to February 29 days, so that the first day of March fell on Thursday, and +the 15th was Thursday.</p> + +<p><span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span>Hence, every event from March to September will fall one day later in the +week than the rule indicates. But the rule is applicable to September, for +it will make no difference whether there are 29 days in February or 31 in +August, there are the same number of days from February to September. But +the 31 days in September will cause all events to fall one day later in +the week during the month of October, but they <ins class="correction" title="original: co-incide">coincide</ins> again during the +month of November. The order is interrupted again in December by giving 31 +days to November. See following table:</p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td align="center" class="br"><i>As Arranged by<br />Julius <ins class="correction" title="original: Caesar">Cæsar</ins>.</i></td> + <td align="center" class="dent"><i>As Corrected by<br />Augustus, 8 B. C.</i></td></tr> +<tr><td class="br"> </td></tr> +<tr><td class="br">January, 31</td><td class="dent2">January, 31</td></tr> +<tr><td class="br">February, 29</td><td class="dent2">February, 28</td></tr> +<tr><td class="br">March, 31*</td><td class="dent2">March, 31</td></tr> +<tr><td class="br">April, 30*</td><td class="dent2">April, 30</td></tr> +<tr><td class="br">May, 31*</td><td class="dent2">May, 31</td></tr> +<tr><td class="br">June, 30*</td><td class="dent2">June, 30</td></tr> +<tr><td class="br">July, 31*</td><td class="dent2">July, 31</td></tr> +<tr><td class="br">August, 30*</td><td class="dent2">August, 31</td></tr> +<tr><td class="br">September, 31</td><td class="dent2">September, 30</td></tr> +<tr><td class="br">October, 30*</td><td class="dent2">October, 31</td></tr> +<tr><td class="br">November, 31</td><td class="dent2">November, 30</td></tr> +<tr><td class="br">December, 30*</td><td class="dent2">December, 31</td></tr></table> + +<p> <span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="bt" align="center"><i>Year.</i></td></tr> +<tr><td class="btr" align="center"> </td> + <td class="btr" align="center">B. C.</td> + <td class="btr" align="center"> </td> + <td class="btr" align="center">B. C.</td> + <td class="btr" align="center"> </td> + <td class="btr" align="center">A. D.</td> + <td class="btr" align="center"> </td> + <td class="bt" align="center">A. D.</td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">45</td> + <td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">22</td> + <td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="dent" align="center">23</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">44</td> + <td class="br" align="center">ag</td> + <td class="br" align="center">21</td> + <td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">ba</td> + <td class="dent" align="center">24</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">43</td> + <td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">20</td> + <td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="dent" align="center">25</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">42</td> + <td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">19</td> + <td class="br" align="center">fe</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="dent" align="center">26</td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">41</td> + <td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">18</td> + <td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="dent" align="center">27</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">40</td> + <td class="br" align="center">cb</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">dc</td> + <td class="dent" align="center">28</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">39</td> + <td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="dent" align="center">29</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">38</td> + <td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center">ag</td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="dent" align="center">30</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">37</td> + <td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="dent" align="center">31</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">36</td> + <td class="br" align="center">ed</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center">fe</td> + <td class="dent" align="center">32</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">35</td> + <td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="dent" align="center">33</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">34</td> + <td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center">cb</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="dent" align="center">34</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">33</td> + <td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="dent" align="center">35</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">32</td> + <td class="br" align="center">gf</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center">ag</td> + <td class="dent" align="center">36</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="dent" align="center">37</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">ed</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="dent" align="center">38</td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="dent" align="center">39</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">28</td> + <td class="br" align="center">ba</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">18</td> + <td class="br" align="center">cb</td> + <td class="dent" align="center">40</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">19</td> + <td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="dent" align="center">41</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">gf</td> + <td class="br" align="center">20</td> + <td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="dent" align="center">42</td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">25</td> + <td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">21</td> + <td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="dent" align="center">43</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">24</td> + <td class="br" align="center">dc</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">d</td> + <td class="br" align="center">22</td> + <td class="br" align="center">ed</td> + <td class="dent" align="center">44</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="bbr" align="center">23</td> + <td class="bbr" align="center"> </td> + <td class="bbr" align="center"> </td> + <td class="bbr" align="center"> </td> + <td class="bbr" align="center"> </td> + <td class="bbr" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="bb" align="center">45</td></tr></table> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span></p> +<p class="center"><span class="giant"><a name="PART_THIRD" id="PART_THIRD"></a>PART THIRD.</span></p> +<p class="center"><span class="huge">CYCLES—JULIAN PERIOD—EASTER.</span></p> +<p class="center"><span class="big">HEBREW CALENDAR.</span></p> +<p> </p> +<h2><a name="CHAPTER_I.3" id="CHAPTER_I.3"></a>CHAPTER I.</h2> +<p class="center"><span class="big">THE SOLAR CYCLE.</span></p> + +<p>Cycle, (Latin <i>Cyclus</i>, ring or circle). The revolution of a certain +period of time which finishes and re-commences perpetually. Cycles were +invented for the purpose of chronology, and for marking the intervals in +which two or more periods of unequal length are each completed a certain +number of times, so that both begin exactly in the same circumstance as at +first. Cycles used in chronology are three: The solar cycle, the lunar +cycle, and the cycle of indiction.</p> + +<p>The solar cycle is a period of time after which the same days of the year +recur on the same days of the week. If every year contained 365 days, then +every year would commence one day later in the week than the year +preceding, and the cycle would be completed in seven years. For if the +first day of January, in any given year, fall on Sunday, then the +following year on Monday, the third on Tuesday, and so on to Sunday again +in seven years.</p> + +<p>But this order is interrupted in the Julian calendar every four years by +giving to February 29 days, and<span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span> +<ins class="correction" title="original: conseqently">consequently</ins> the year 366. Now the number +of years in the intercalary period being four and the days of the week +being seven, their product is 4 × 7 = 28; twenty-eight years then is a +period after which the first day of the year and the first day of every +month recur again in the same order on the same day of the week. This +period is called the solar cycle or the cycle of the sun, the origin of +which is unknown; but is supposed to have been invented about the time of +the Council of Nice, in the year of our Lord 325; but the first year of +the cycle is placed by chronologists nine years before the commencement of +the Christian era.</p> + +<p>Hence the year of the cycle corresponding to any given year in the Julian +calendar is found by the following rule: Add nine to the date and divide +the sum by twenty-eight; the quotient is the number of cycles elapsed, and +the remainder is the year of the cycle. Should there be no remainder, the +proposed year is the twenty-eighth, or last of the cycle. Thus, for the +year 1892, we have (1892 + 9) ÷ 28 = 67, remainder 25. Therefore, 67 is +the number of cycles, and 25 the number in the cycle.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span></p> +<h2><a name="CHAPTER_II.3" id="CHAPTER_II.3"></a>CHAPTER II.</h2> +<p class="center"><span class="big">THE LUNAR CYCLE.</span></p> + +<p>The Lunar cycle, or the cycle of the moon, is a period of nineteen years, +after which the new and full moons fall on the same days of the year as +they did nineteen years before. This cycle was invented by Meton, a +celebrated astronomer of Athens, and may be regarded as the masterpiece of +ancient astronomy. In nineteen solar years there are 235 lunations, a +number which, on being divided by nineteen, gives twelve lunations, with +seven of a remainder, to be distributed among the years of the period.</p> + +<p>The period of Meton, therefore, consisted of twelve years containing +twelve months each, and seven years containing thirteen mouths each, and +these last formed the third, fifth, eighth, eleventh, thirteenth, +sixteenth, and nineteenth years of the cycle. As it had now been +discovered that the exact length of the lunation is a little more than +twenty-nine and a half days, it became necessary to abandon the alternate +succession of full and deficient months; and, in order to preserve a more +accurate correspondence between the civil month and the lunation, Meton +divided the cycle into 125 full months of 30 days, and 110 deficient +months of 29 days each. The number of days in the period was, therefore, +6940; for (125 × 30) + (110 × 29) = 6940.</p> + +<p>In order to distribute the deficient months through the period in the most +equable manner, the whole period may be regarded as consisting of 235 full +months<span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span> of thirty days, or 7050 days, from which 110 days are to be +deducted; for (235 × 30) = 7050; 7050 - 110 = 6940, as before. This gives +one day to be suppressed in sixty-four, so that if we suppose the months +to contain each thirty days, and then omit every sixty-fourth day in +reckoning from the beginning of the period, those months in which the +omission takes place will, of course, be the deficient months.</p> + +<p>The number of days in the period being known, it is easy to ascertain its +accuracy both in respect of the solar and lunar motions. The exact length +of nineteen solar years is (<ins class="errata" title="Errata: On 76th page, twelfth line from the top of the page, 356 should be 365.">365</ins>d, +5h, 48m, 49.62s.) × 19 = 6939d, 14h, 27m, 42.78s.; hence, the period, which is exactly 6940 days, exceeds +nineteen annual revolutions of the earth by a little more than nine and a +half hours. On the other hand, the exact time of the synodic revolution of +the moon is 29d, 12h, 44m, 2.87s.; 235 lunations, therefore, contain 235 × +(29d, 12h, 44m, 2.87s.) = (6939d, 16h, 31m, 14.45s.), so that the period +exceeds 235 lunations by nearly seven and a half hours.</p> + +<p>At the end of four cycles, or seventy-six years, the accumulation of the +seven and a half hours of difference between the cycle and 235 lunations +amounts to thirty hours, or one whole day and six hours. Calippus, +therefore, in order to make a correction of the Metonic cycle, proposed to +quadruple the period of Meton, and deduct one day at the end of that time +by changing one of the full months into a deficient month. The period of +Calippus, therefore, consisted of three Metonic cycles of 6940 days each, +and a period of 6939 days; and its error in respect to the moon, +consequently,<span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span> amounted to only six hours, or to one day in 304 years. +This period exceeds seventy-six true solar years by 14h, 9m, 8.88s., but +coincides exactly with seventy-six Julian years; and in the time of +Calippus the length of the solar year was almost universally supposed to +be exactly 365¼ days.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<h2><a name="CHAPTER_III.3" id="CHAPTER_III.3"></a>CHAPTER III.</h2> +<p class="center"><span class="big">THE LUNAR CYCLE AND GOLDEN NUMBER.</span></p> + +<p>In connecting the lunar month with the solar year, the framers of the +ecclesiastical calendar adopted the period of Meton, or lunar cycle, which +they supposed to be exact. A different arrangement has, however, been +followed with respect to the distribution of the months. The lunations are +supposed to consist of twenty-nine and thirty days alternately, or the +lunar year of 354 days; and in order to make up nineteen solar years, six +embolismic or intercalary months, of thirty days each, are introduced in +the course of the cycle, and one of twenty-nine days is added at the end. +This gives (19 × 354) + (6 × 30) + 29 = 6935 days, to be distributed among +235 lunar months.</p> + +<p>But every leap-year one day must be added to the lunar month in which the +29th of February is included. Now if leap-year happened on the first, +second or third year of the period, there will be five leap-years in the +period, but only four when the first leap-year falls on the fourth. In the +former case the number of days in the period becomes 6940, and in the +latter 6939. The mean length of the cycle is, therefore, 6939¾ days,<span class="pagenum"><a name="Page_78" id="Page_78">[Pg 78]</a></span> +agreeing exactly with nineteen Julian years. By means of the lunar cycle +the new moons of the calendar were indicated before the reformation in +1582. As the cycle restores these phenomena to the same days of the civil +month, they will fall on the same days in any two years which occupy the +same place in the cycle; consequently a table of the moon’s phases for +nineteen years will serve for any year whatever when we know its number in +the cycle.</p> + +<p>The number of the year in the cycle is called the Golden Number; either +because it was so termed by the Greeks, who, on account of its utility, +ordered it to be inscribed in letters of gold in their temples, or more +probably because it was usual to distinguish it by red letters in the +calendar. The Golden Numbers were introduced into the calendar about the +year 530, but disposed as they would have been if they had been inserted +at the time of the Council of Nice. The cycle is supposed to commence with +the year in which the new moon falls on the first day of January, which +took place the year preceding the commencement of our era.</p> + +<p>Hence to find the Golden Number for any year, we have the following rule: +Add one to the date, divide the sum by nineteen; the quotient is the +number of cycles elapsed, and the remainder is the Golden Number. Should +there be no remainder, the proposed year is, of course, the last or +nineteenth of the cycle. Thus, for the year 1892, we have (1892 + 1) ÷ 19 += 99, remainder 12; therefore, 99 is the number of cycles, and 12 the +number in the cycle, or the Golden number.</p> + +<p>It ought to be remarked that the new moons determined in this manner, may +differ from the astronomical<span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span> new moons sometimes as much as two days. The +reason is, that the sum of the solar and lunar inequalities which are +compensated in the whole period, may amount in certain cases to 10 degrees +and thereby cause the new moon to arrive on the second day before or after +its mean time.</p> + +<p>The cycle of the sun brings back the days of the month to the same day of +the week; the cycle of the moon restores the new moons to the same day of +the month; therefore, 28 × 19 = 532 years, includes all the variations in +respect of the new moons and the dominical letter, and is consequently a +period after which the new moons again occur on the same day of the month +and the same day of the week. This is called the Dionysian or Great +Paschal Period, from its having been employed by Dionysius Exiguus in +determining Easter Sunday.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<h2><a name="CHAPTER_IV.3" id="CHAPTER_IV.3"></a>CHAPTER IV.</h2> +<p class="center"><span class="big">CYCLE OF INDICTION, AND THE JULIAN PERIOD.</span></p> + +<p>The cycle of Indiction or Roman Indiction, is a period of fifteen years; +not astronomical like the two former, but entirely arbitrary. Its origin +and the purpose for which it was established are alike uncertain; but it +is conjectured that it was introduced by Constantine the Great, about the +year 312 of the common era, and had reference to certain judicial acts +that took place under the Greek emperors at stated intervals of fifteen +years. In chronological reckoning, it is considered as having commenced on +the first day of January of the year 313.</p> + +<p><span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span>By extending it backward, it will be found that the cycle commenced three +years before the beginning of our era. In order, therefore, to find the +number of any year in the cycle of indiction, we have this rule: Add three +to the date, divide the number by fifteen; and the remainder is the year +of the indiction. Should there be no remainder, the proposed year is the +fifteenth or last of the cycle. Thus, for the year 1892, we have (1892 + +3) ÷ 15 = 126, remainder 5. Therefore, 5 is the number in the cycle.</p> + +<p>The Julian period, proposed by the celebrated Joseph Scaliger, as an +universal measure of chronology, is a period of 7980 years, and is formed +by the continual multiplication of the three numbers, 28, 19 and 15; that +is, of the cycle of the sun, the cycle of the moon, and the cycle of +indiction. Thus, (28 × 19 × 15) = 7980. In the course of this long period +no two years can be expressed by the same numbers in all the three cycles.</p> + +<p>The first year of the Christian era had 10 for its number in the cycle of +the sun, 2 in the cycle of the moon, and 4 in the cycle of the indiction. +Now, it is found by actual calculation, that the only number less than +7980 which, on being divided successively by 28, 19, and 15, leaves the +respective remainders 10, 2 and 4, is 4714. Hence, the first year of the +Christian era corresponded with the year 4714 of the Julian period, which +period coincides with the 710th before the common mundane era 4004 B. C.; +for 4004 + 710 = 4714. Hence, also, the year of our era corresponding to +any other year of the period, or <i>vice versa</i>, is found by the following +rule:</p> + +<p>When the given year is anterior to the commencement<span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span> of the era, subtract +the number of the year of the Julian period from 4714, and the remainder +is the year before Christ; or, subtract the year before Christ from 4714, +and the remainder is the corresponding year in the Julian period. Thus, +Rome was founded in the year 3960 of the Julian period. What was the year +before Christ? We have then 4714 - 3960 = 754. Julius Cæsar was +assassinated 44 years before Christ, what was the corresponding year of +the Julian period? We have then, 4714 - 44 = 4670.</p> + +<p>When the given year is after Christ, subtract 4713 from the year of the +period, and the remainder is the year of the era; or add 4713 to the year +of the era, and the sum is the corresponding year in the Julian period. +Thus, the Council of Nice was convened in the year 5038 of the Julian +period, what was the year of our era? We have then, 5038 - 4713 = 325. +What year of the Julian period corresponds with the present year, 1892? We +have then, 4713 + 1892 = 6605.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span></p> +<h2><a name="CHAPTER_V.3" id="CHAPTER_V.3"></a>CHAPTER V.</h2> +<p class="center"><span class="big">EASTER.</span></p> + +<p>Easter (Germ. <i>Ostern</i>, Old Saxon <i>Oster</i>, from <i>Osten</i>, signifying +rising). The English name is probably derived from Ostera or Eostre, the +Teutonic goddess of spring, whose festival occurred about the same time of +the year as the celebration of Easter. The Hebrew-Greek word Pascha has +passed into the name given to this feast by most Christian nations. This +festival is held in commemoration of our Lord’s resurrection.</p> + +<p>The Jews celebrated their passover, in conformity with the directions +given them by Moses, on the 14th day of the month Nisan, being the lunar +month of which the 14th day either falls on or next follows the day of the +vernal equinox. In the year of our Lord’s crucifixion this fell on a +Friday; the resurrection, therefore, took place on the first day of the +week, which from thence is denominated the Lord’s Day.</p> + +<p>The primitive Christians, in celebrating this anniversary, fell into two +different systems. The Western churches observed the nearest Sunday to the +full moon of Nisan, taking no account of the day on which the passover +would be celebrated. The Asiatics, on the other hand, following the Jewish +calendar, adopted the 14th of Nisan upon which to commemorate the +crucifixion, and observed the festival of Easter on the third day +following, upon whatever day of the week that might fall, hence they +obtained the name of Quartodecimans, (from quarto, four, and decem, ten,) +the<span class="pagenum"><a name="Page_83" id="Page_83">[Pg 83]</a></span> fourteenth day men. The former appealed to the authority of St. Peter +and St. Paul, the latter to that of St. John.</p> + +<p>The dispute which took place upon this point in the second and third +centuries of our era is remarkable, as connected with perhaps the first +event which can be brought to bear upon the question of the primacy of the +Roman bishop; and it is the more interesting as both parties are +accustomed to claim it as a testimony in favor of their own views. Victor, +bishop of Rome, wrote an imperious letter to the Asiatic bishops, +requiring their conformity to the Western rule; which was answered by +Polycrates, bishop of Ephesus, in the name of the rest, expressing their +resolution to maintain the custom handed down to them by their ancestors. +The Roman bishop thereupon broke off communion with them; but he was +rebuked by Irenaeus, of Lyons, and it was agreed by his mediation that +each party should retain its customs. Such continued to be the practice +till the time of Constantine, when the Council of Nice determined the +matter by the following Canons:</p> + +<p><i>a</i>—Easter must be celebrated on a Sunday.</p> + +<p><i>b</i>—This Sunday must follow the 14th day of the paschal moon, so that if +the 14th day of the paschal moon fall on a Sunday, then Easter must be +celebrated on the Sunday following.</p> + +<p><i>c</i>—The paschal moon is that moon of which the 14th day either falls on +or next follows the day of the vernal equinox.</p> + +<p><i>d</i>—The 21st of March is to be accounted the day of the vernal equinox. +(<a href="#appenl">Appendix L.</a>)</p> + +<p><span class="pagenum"><a name="Page_84" id="Page_84">[Pg 84]</a></span>Sometimes a misunderstanding has arisen from not observing that this +regulation is to be construed according to the tabular full moon as +determined from the epact, and not by the true full moon, which in +general, occurs one or two days earlier. From these conditions it follows, +that if the paschal full moon fall on Saturday, the 21st of March, then +Easter will happen on the 22d, its earliest possible date. For if the full +moon arrive on the 20th, it would not be the paschal full moon, which +cannot happen before the 21st, consequently the following moon is the +paschal full moon, which happens 30 days after the 20th of March, which is +the 19th of April. Now, if in this case the 19th of April is Sunday, then +Easter must be celebrated the following Sunday, or the 26th of April. +Hence, Easter Sunday cannot happen earlier than the 22d of March, or later +than the 26th of April.</p> + +<p>The observance of these rules renders it necessary to reconcile three +periods which have no common measure, namely, the week, the lunar month, +and the solar year; and as this can be done only approximately, and within +certain limits, the determination of Easter is an affair of considerable +nicety and complication. It has already been shown that the lunar cycle +contained 6939 days and 18 hours; also, that the exact time of 235 +lunations is 6939d, 16h, 31m, 14.45s. The difference, which is 1h, 28m, +45.55s., amounts to a day in 308 years, so that at the end of this time +the new moons occur one day earlier than they are indicated by the Golden +Numbers. During the 1257 years that elapsed between the Council of Nice +and the reformation, the error had accumulated to four days, so that<span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span> the +new moons, which were marked in the calendar as happening, for example, on +the 5th of the month, actually fell on the 1st.</p> + +<p>It would have been easy to correct this error by placing the Golden +Numbers four lines higher in the new calendar, but the suppression of ten +days had already rendered it necessary to place them ten lines lower, and +to carry those which belonged, for example, to the 5th and 6th of the +month, to the 15th and 16th. But supposing this correction to have been +made, it would have become necessary, at the end of 308 years, to place +them one line higher, in consequence of the accumulation of the error of +the cycle to a whole day. On the other hand, as the Golden Numbers were +only adapted to the Julian calendar, every omission of the centenary +intercalation would require them to be placed one line lower, opposite the +6th, for example, instead of the 5th of the month, so that, generally +speaking, the places of the Golden Numbers would have to be changed every +century. On this account Lilius thought fit to reject the Golden Numbers +from the Calendar, and supply their places by another set of numbers +called Epacts, the use of which we shall now proceed to explain.</p> + +<p>Epact, (Greek <i>epaktos</i>, added or introduced). The excess of the solar +year beyond the lunar, employed in the calendar to signify the moon’s age +at the beginning of the year. The common solar year consisted of 365 days +and the lunar year only 354 days, the difference is eleven; whence, if a +new moon fall on the first day of January in any year, the moon will be +eleven days old on the first day of the following year, and<span class="pagenum"><a name="Page_86" id="Page_86">[Pg 86]</a></span> twenty-two +days old on the first of the third year. The numbers eleven and twenty-two +are therefore the epacts of those years respectively. Another addition of +eleven gives thirty-three for the epact of the fourth year; but in +consequence of the insertion of the intercalary month in each third year +of the lunar cycle, this epact is reduced to three; for 33 - 30 = 3. In +like manner the epacts of all the following years of the cycle are +obtained by successively adding eleven to the epact of the former year, +and rejecting thirty as often as the sum exceeds or equals that number.</p> + +<p>In order to show how the epacts are connected with the Golden Numbers, let +a cypher represent the new moon on the first day of January in any year, +then the epacts and Golden Numbers for a whole lunar cycle would be +represented thus:</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td align="center">1</td><td><span class="spacer"> </span></td> + <td align="center">2</td><td><span class="spacer"> </span></td> + <td align="center">3</td><td><span class="spacer"> </span></td> + <td align="center">4</td><td><span class="spacer"> </span></td> + <td align="center">5</td><td><span class="spacer"> </span></td> + <td align="center">6</td><td><span class="spacer"> </span></td> + <td align="center">7</td><td><span class="spacer"> </span></td> + <td align="center">8</td><td><span class="spacer"> </span></td> + <td align="center">9</td></tr> +<tr><td align="center">0</td><td> </td> + <td align="center">11</td><td> </td> + <td align="center">22</td><td> </td> + <td align="center">3</td><td> </td> + <td align="center">14</td><td> </td> + <td align="center">25</td><td> </td> + <td align="center">6</td><td> </td> + <td align="center">17</td><td> </td> + <td align="center">28</td></tr></table> + +<table width="50%" border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td align="center">10</td><td><span class="spacer"> </span></td> + <td align="center">11</td><td><span class="spacer"> </span></td> + <td align="center">12</td><td><span class="spacer"> </span></td> + <td align="center">13</td><td><span class="spacer"> </span></td> + <td align="center">14</td><td><span class="spacer"> </span></td> + <td align="center">15</td><td><span class="spacer"> </span></td> + <td align="center">16</td><td><span class="spacer"> </span></td> + <td align="center">17</td><td><span class="spacer"> </span></td> + <td align="center">18</td><td><span class="spacer"> </span></td> + <td align="center">19</td></tr> +<tr><td align="center">9</td><td> </td> + <td align="center">20</td><td> </td> + <td align="center">1</td><td> </td> + <td align="center">12</td><td> </td> + <td align="center">23</td><td> </td> + <td align="center">4</td><td> </td> + <td align="center">15</td><td> </td> + <td align="center">26</td><td> </td> + <td align="center">7</td><td> </td> + <td align="center">18</td></tr></table> + +<p>But the order is interrupted at the end of the cycle; for the epact of the +following year found in the same manner would be 18 + 11 = 29, whereas it +ought to be a cipher to correspond with the moon’s age and the Golden +Number 1. The reason for this is, that the intercalary month, inserted at +the end of the cycle, contains only twenty-nine days instead of thirty; +whence, after 11 has been added to the epact of the year corresponding to +the Golden Number 19, we must reject twenty-nine instead of thirty, in +order to have the epact of the succeeding year; or, which comes to the +same thing, we must add twelve to the epact of the last year of the cycle, +and then reject thirty as before. Thus,<span class="pagenum"><a name="Page_87" id="Page_87">[Pg 87]</a></span> 18 + 12 = 30; 30 - 30 = 0; the +cipher corresponding with the Golden Number 1.</p> + +<p>This method of forming the epacts might have been continued indefinitely +if the Julian intercalation had been followed without correction and the +cycle had been perfectly exact; but as neither of these suppositions is +true, two equations or corrections must be applied, one depending on the +error of the Julian year, which is called the solar equation; the other on +the errors of the lunar cycle, which is called the lunar equation. The +solar equation occurs three times in 400 years, namely, in every secular +year which is not a leap-year; for in this case the omission of the +intercalary day causes the new moons to arrive one day later in all the +following months, so that the moon’s age at the end of the month is one +day less than it would have been if the intercalation had been made, and +the epacts must accordingly be all diminished by unity. Thus, the epacts +11, 22, 3, 14, etc., become 10, 21, 2, 13, etc.</p> + +<p>On the other hand, when the time by which the new moons anticipate the +lunar cycle amounts to a whole day, which, as we have seen, it does in 308 +years, the new moons will arrive one day earlier and the epacts must, +consequently, be increased by unity. Thus, the epacts 11, 22, 3, 14, etc., +in consequence of the lunar equation, becomes 12, 23, 4, 15, etc. In order +to preserve the uniformity of the calendar, the epacts are changed only at +the commencement of the century; the correction of the error of the lunar +cycle is therefore made at the end of 300 years. In the Gregorian calendar +this error is assumed to amount to a day in<span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span> 312½ years, or eight days +in 2500 years, an assumption which requires the line of epacts to be +changed seven times successively at the end of each period of 300 years, +and once at the end of 400 years; and from the manner in which the epacts +were disposed at the reformation, it was found most correct to suppose one +of the periods of 2500 years to terminate with the year 1800.</p> + +<p>The years in which the solar equation occurs, counting from the +reformation, are 1700, 1800, 1900, 2100, 2200, 2300, 2500, etc. Those in +which the lunar equation occurs are 1800, 2100, 2400, 2700, 3000, 3300, +3600, 3900, after which 4300, 4600, and so on. When the solar equation +occurs, the epacts are diminished by unity; when the lunar equation +occurs, the epacts are augmented by unity; and when both equations occur +together, as in 1800, 2100, 2700, etc., they compensate each other, and +the epacts are not changed.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<h2><a name="CHAPTER_VI.3" id="CHAPTER_VI.3"></a>CHAPTER VI.</h2> +<p class="center"><span class="big">A NEW AND EASY METHOD OF FIXING THE DATE OF EASTER.</span></p> + +<p>In determining the date of Easter, we make use of the numbers called +epacts; and, as these numbers have already been explained in the preceding +chapter, (q. v.) it will be necessary to give them only a brief notice +here. Epact, as has already been defined, is the excess of the solar year +beyond the lunar, employed in the calendar to signify the moon’s age at +the beginning of the year; that is, if a new moon fall on the first day +of<span class="pagenum"><a name="Page_89" id="Page_89">[Pg 89]</a></span> January in any year, it will be eleven days old on the first day of +the following year, and twenty-two days old on the first day of the third +year, and so on.</p> + +<p>Now, in this work, in fixing the date of Easter, we abandon the use of the +new moons altogether, and make calculations wholly from the paschal full +moons, which cannot happen earlier than the 21st of March, nor later than +the 19th of April. <a href="#appenj">Appendix J.</a> The epacts are here used to show the day of +the month on which the paschal full moons fall; that is, if the paschal +moon fall on a given day of the month in any year, it will happen eleven +days earlier the following year, and twenty-two days earlier the third +year, and so on. To illustrate, suppose the paschal moon fall on the 18th +of April in any given year, on the following year it would fall on the +7th, in the third year on the 27th of March; and in the fourth year the +moon would full on the 16th of March, but that would not be the paschal +moon, which cannot happen earlier than the 21st; so the following moon +would be the paschal moon, which happens thirty days later, or the 15th of +April; then the fifth year it would fall on the 4th of April, and so on.</p> + +<p>The solar and lunar equations or corrections are not made by change of +epacts, for only one line of epacts is used in this work, but these +corrections are made by a change of the day of the month on which the +cycle commences. This change is made at the beginning of a century, and, +of course, does not occur but once in a hundred years, and frequently no +change is made for two, and even three hundred years. The reason for +making these changes has been given in the preceding<span class="pagenum"><a name="Page_90" id="Page_90">[Pg 90]</a></span> chapter, (q. v.), +and will again be noticed in the proper place. The line of epacts used are +thus represented, commencing with a cipher as the point of departure: 0, +11, 22, 3, 14, 25, 6, 17, 28, 9, 20, 1, 12, 23, 4, 15, 26, 7, 18. It +should be borne in mind that the epacts are obtained by successively +adding eleven to the epact of the former year, and rejecting thirty as +often as the sum exceeds or equals that number. But, as the intercalary +month inserted at the end of the cycle contains only 29 days, add twelve +instead of eleven, to eighteen, the last of the cycle, and then reject +thirty as before; thus, 18 + 12 = 30; then 30 - 30 = 0. The cycle being +completed, we again commence with the cipher as the point of departure.</p> + +<p>After having found the paschal full moons for one lunar cycle, a period of +nineteen years, then the paschal moons again occur in the same order, on +the same days of the month, as they did nineteen years before. Now, as has +also been shown in the preceding chapter, this cycle might have been +continued indefinitely had the Julian intercalation been followed without +correction, and the cycle been perfectly exact; but neither of these being +true, two equations or corrections must be made, one depending on the +error of the Julian calendar, which is called the solar-equation; the +other on the error of the lunar cycle, which is called the lunar equation.</p> + +<p>Every omission of the intercalary day, which occurs three times in 400 +years, will cause the full moons to fall one day later; for example, on +the 13th of the month instead of the 12th. On the other hand, as has also +been shown in the preceding chapter, the error of<span class="pagenum"><a name="Page_91" id="Page_91">[Pg 91]</a></span> the lunar cycle is one +day in 300 years; so that at the end of every 300 years the full moons +will fall one day earlier, for example, on the 11th of the month instead +of the 12th. Now, when both equations occur together, they compensate each +other; that is, while the solar equation would cause the full moon to fall +on the 13th, the lunar equation would make it fall on the 11th; therefore, +no correction is to be made—there is nothing to correct. Had they +occurred singly, the full moon, at the beginning of the cycle, would have +fallen either on the 13th or the 11th; but as they occur together, no +change is made; and the full moons of the calendar will remain as they are +for the next one hundred years.</p> + +<p>Hence, the date of Easter may very easily be determined, as indicated in +the following tables (q. v.). It is known by actual calculation that the +paschal full moon fell on the 12th of April in the year 1596, which moon +was the first of a cycle after the reformation of the calendar by Gregory. +Now, by taking the epact of the following years of the cycle, which are +11, 22, 3, 14, 25, etc., from 12, the date of the first paschal moon, and +you will have all the moons of the cycle. Of course, the epacts 22, 25, +etc., cannot be taken from 12, but being carried back from the 12th of +April, they will show on what day in March the full moons fall. When the +epacts are greater than 12, it would be more convenient to take them from +43, as the number of days in March being 31, so 12 + 31 = 43.</p> + +<p>To find the paschal moons of the cycle, we have then this rule: If the +epact is less than 12, take it from 12; if greater, take it from 43, and +the remainder will<span class="pagenum"><a name="Page_92" id="Page_92">[Pg 92]</a></span> be the date of the paschal moon; unless the full moon +fall before the 21st of March, in which case the following moon will be +the paschal moon, which happens thirty days later. But when the solar +equation occurs in 1710, causing the cycle to commence with the 13th of +April, then the epacts must be taken from 13, or 13 + 31 = 44. And again +in 1900, the correction makes the cycle commence on the 14th of April; so +the number from which the epacts are taken is 14, or 14 + 31 = 45, and so +on. Whenever there is a change of date of the paschal moon in the +beginning of the cycle, as there is again in 2204, 2318 and 2413, etc., as +may be seen in the following tables, then the epacts must be taken from +that date, or that date plus 31, the number of days in March.</p> + +<p>Or the date of the paschal moons may very easily be determined by taking +eleven successively from the date of every preceding full moon, and that +will give the date of the paschal moons; only it should be borne in mind +that, whenever the full moon falls before the 21st of March, the following +moon is the paschal moon, which happens thirty days later.</p> + +<p>As Easter Sunday is the first Sunday after the paschal full moon, so all +that remains to be done in fixing the date of Easter, is to find the day +of the month on which that Sunday falls; and as this can easily be done by +the use of the dominical letter, which letter and its use in fixing dates +having been fully explained in <a href="#PART_SECOND">Part Second</a>, Chapters <a href="#CHAPTER_IV.2">IV</a> and <a href="#CHAPTER_V.2">V</a>, (q. v.), a +repetition seems to be unnecessary here.</p> + +<p> <span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center">gf</td> + <td class="btr" align="center">1596</td> + <td class="bt">April</td><td align="center" class="btr">12</td> + <td class="btr" align="center">14</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1597</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1598</td> + <td class="dent">March</td><td align="center" class="br">21</td> + <td class="br" align="center">22</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1599</td> + <td class="dent">April</td><td align="center" class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1600</td> + <td class="dent">March</td><td align="center" class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1601</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">22</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1602</td> + <td class="dent" align="center">"</td><td align="right" class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1603</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">30</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1604</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">18</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1605</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1606</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">26</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1607</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1608</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1609</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">26</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1610</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1611</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1612</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">22</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1613</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1614</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">30</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1615</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">19</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1616</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1617</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">26</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1618</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1619</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center">31</td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1620</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">19</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1621</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1622</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">27</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1623</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">16</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1624</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1625</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">30</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1626</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1627</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1628</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">23</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1629</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1630</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center">31</td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1631</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">20</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1632</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="bbr" align="center">1633</td> + <td class="bb">March</td><td class="bbr">25</td> + <td class="bbr" align="center">27</td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />By close examination of the above tables, it will be seen that there is +just eleven days difference in the date of these paschal moons, from year +to year, through the whole lunar cycle, and through all lunar cycles. In +determining the date of Easter, it will also be seen, that whenever the +full moon falls before the 21st of March, then the following moon, which +happens thirty days later, is the paschal moon, as the 21st of March is +its earliest possible date. Also when the cycle is</p> + +<p> <span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="btr" align="center">1634</td> + <td class="bt">April</td><td align="center" class="btr">12</td> + <td class="btr" align="center">16</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1635</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1636</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">23 </td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1637</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1638</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1639</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">24</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1640</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1641</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">31</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1642</td> + <td class="dent">April</td><td class="br">24</td> + <td class="br" align="center">20</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1643</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1644</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">27</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1645</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1646</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1647</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">21</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1648</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1649</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1650</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1651</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1652</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">31</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1653</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1654</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1655</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">28</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1656</td> + <td class="dent">April</td><td class="br">9</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1657</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1658</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">21</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1659</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1660</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">28</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1661</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">17</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1662</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1663</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">25</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1664</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1665</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1666</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">25</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1667</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1668</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1669</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">21</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1670</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="bbr" align="center">1671</td> + <td class="bb">March</td><td class="bbr">25</td> + <td class="bbr" align="center">29</td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />completed, then the paschal moons again occur in the same order, on the same day of the month +as they did nineteen years before. Now this cycle is six times repeated in +a period of 114 years, when the intercalary day being suppressed in 1700, +causes the first paschal moon of the cycle to fall on the 13th of April +instead of the 12th, and all the moons of the cycle to fall one day later +than they would had the correction not been made. The cycle is now +repeated ten times without</p> + +<p> <span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center">cb</td> + <td class="btr" align="center">1672</td> + <td class="bt">April</td><td align="center" class="btr">12</td> + <td class="btr" align="center">17</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1673</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1674</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">25</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1675</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1676</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1677</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">18</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1678</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1679</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1680</td> + <td class="dent">April</td><td class="br">24</td> + <td class="br" align="center">21</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1681</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1682</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">29</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1683</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">18</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1684</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1685</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">22</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1686</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1687</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center">30</td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1688</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">18</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1689</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1690</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">26</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1691</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1692</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1693</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">22</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1694</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1695</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1696</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">22</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1697</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1698</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">30</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1699</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">19</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1700</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1701</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">27</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1702</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1703</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1704</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">20</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1705</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1706</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1707</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1708</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="bbr" align="center">1709</td> + <td class="bb">March</td><td class="bbr">25</td> + <td class="bbr" align="center">31</td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />correction, that is, till the year 1900, a period of 190 years, when the intercalation being again suppressed, causes +the first paschal moon of the cycle to fall on the 14th of April, and, of +course, all the other moons of the cycle to fall one day later. The reason +the correction is not made the first year of the century is, the lunar +cycle must first be completed, and that did not occur until 1710. As 100 +is not a multiple of 19, the number of years in the cycle, and, as the +corrections</p> + +<p> <span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="btr" align="center">1710</td> + <td class="bt">April</td><td align="center" class="btr">13</td> + <td class="btr" align="center">20</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1711</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1712</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">27</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1713</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1714</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1715</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">21</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1716</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1717</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center">28</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1718</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">17</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1719</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1720</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">31</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1721</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1722</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1723</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">28</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1724</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1725</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1726</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">21</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1727</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1728</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">28</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1729</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1730</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1731</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">25</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1732</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1733</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1734</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">25</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1735</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1736</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center"><ins class="correction" title="original: 1736">1737</ins></td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">21</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1738</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1739</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">29</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1740</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1741</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1742</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">25</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1743</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1744</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1745</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">18</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1746</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="bbr" align="center">1747</td> + <td class="bb">March</td><td class="bbr">26</td> + <td class="bbr" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />cannot be made only at the beginning of the cycle, so they +cannot be made the first year of the century only once in 1900 years. It +may be seen from one of the above tables that the correction is made in +the year 1900, for the reason that that is the first century which is a +multiple of 19. The next centurial year that is exactly divisible by 19, +is 3800. Therefore, none of the corrections for the next 1900 years, will +occur on the first year of the century. It may also be seen from</p> + +<p> <span class="pagenum"><a name="Page_97" id="Page_97">[Pg 97]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center">gf</td> + <td class="btr" align="center">1748</td> + <td class="bt">April</td><td align="center" class="btr">13</td> + <td class="btr" align="center">14</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1749</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1750</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">29</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1751</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1752</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1753</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">22</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1754</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1755</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center">30</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1756</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">18</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1757</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1758</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">26</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1759</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1760</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1761</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">22</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1762</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1763</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1764</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">22</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1765</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1766</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">30</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1767</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">19</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1768</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1769</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">26</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1770</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1771</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center">31</td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1772</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">19</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1773</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1774</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1775</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">16</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1776</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1777</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">30</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1778</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">19</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1779</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1780</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">26</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1781</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1782</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center">31</td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1783</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">20</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1784</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="bbr" align="center">1785</td> + <td class="bb">March</td><td class="bbr">26</td> + <td class="bbr" align="center">27</td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />the above tables, that, though the intercalary day was suppressed in the year 1800, +no change is made in the date of the paschal moon. The reason is, the +lunar equation also occurred; while the former correction would cause the +paschal moon to fall one day later, that is on the 14th day of April, the +latter would make it fall one day earlier, that is on the 12th; so they +compensate each other, and there is no correction to be made until the +year 1900, when the solar equation</p> + +<p> <span class="pagenum"><a name="Page_98" id="Page_98">[Pg 98]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="btr" align="center">1786</td> + <td class="bt">April</td><td align="center" class="btr">13</td> + <td class="btr" align="center">16</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1787</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1788</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">23</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1789</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1790</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1791</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">24</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1792</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1793</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center">31</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1794</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">20</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1795</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1796</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">27</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1797</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1798</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1799</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">24</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1800</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1801</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1802</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">18</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1803</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1804</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1805</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1806</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1807</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">29</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1808</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1809</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1810</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">22</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1811</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1812</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center">29</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1813</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">18</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1814</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1815</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">26</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1816</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1817</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1818</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">22</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1819</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1820</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1821</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">22</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1822</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="bbr" align="center">1823</td> + <td class="bb">March</td><td class="bbr">26</td> + <td class="bbr" align="center">30</td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />again occurs, and the first paschal moon of the cycle falls on the 14th; which cycle is repeated sixteen times +in a period of 304 years, after which, in 2204, the date of the first +paschal moon is the 15th of April. The reason there is no correction to +make in this long period is, first, the year 2000 is a common year in the +Gregorian calendar; second, in the year 2100 both the solar and the lunar +equations again occur, and occurring together, they compensate each other; +consequently</p> + +<p> <span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span></p> + + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center">dc</td> + <td class="btr" align="center">1824</td> + <td class="bt">April</td><td align="center" class="btr">13</td> + <td class="btr" align="center">17</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1825</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1826</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">25</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1827</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1828</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1829</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">18</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1830</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1831</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1832</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">21</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1833</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1834</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">29</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1835</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">18</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1836</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1837</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">22</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1838</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1839</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center">30</td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1840</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">18</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1841</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1842</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">26</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1843</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1844</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1845</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">22</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1846</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1847</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1848</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">22</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1849</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1850</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center">30</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1851</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">19</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1852</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1853</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">27</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1854</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1855</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1856</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">20</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1857</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1858</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1859</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">17</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1860</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="bbr" align="center">1861</td> + <td class="bb">March</td><td class="bbr">26</td> + <td class="bbr" align="center">31</td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />the cycle is continued until 2204, after which, as has +already been stated, the date of the first paschal moon is the 15th of +April. This cycle is repeated six times in a period of 114 years, when in +2318, for reasons already given, the date of the first paschal moon of the +next cycle falls on the 16th, and is repeated five times in a period of 95 +years, when, in 2413, the lunar equation occurs alone, and the date of the +first paschal moon for the next 95 years, that is till the year 2508,</p> + +<p> <span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="btr" align="center">1862</td> + <td class="bt">April</td><td align="center" class="btr">13</td> + <td class="btr" align="center">20</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1863</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1864</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">27</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1865</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1866</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1867</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">21</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1868</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1869</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center">28</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1870</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">17</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1871</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1872</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">31</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1873</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1874</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1875</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">28</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1876</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1877</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1878</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">21</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1879</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1880</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">28</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1881</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1882</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1883</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">25</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1884</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1885</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1886</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">25</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1887</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1888</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1889</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">21</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1890</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1891</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">29</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1892</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1893</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1894</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">25</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1895</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1896</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1897</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">18</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1898</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="bbr" align="center">1899</td> + <td class="bb">March</td><td class="bbr">26</td> + <td class="bbr" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + + +<p><br />falls back to the 15th of April. After which the 16th, on account of the +solar equation, is again the date of the first paschal moon of the cycle +for another period of 95 years; that is till the year 2603, when the solar +equation causes the first paschal moon to fall on the 17th, which cycle is +repeated sixteen times during another period of 304 years, after which, in +2907, the correction makes the date of the first paschal moon of the</p> + +<p> <span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="btr" align="center">1900</td> + <td class="bt">April</td><td align="center" class="btr">14</td> + <td class="btr" align="center">15</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1901</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1902</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">30</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1903</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1904</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1905</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">23</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1906</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1907</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center">31</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1908</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">19</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1909</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1910</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">27</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1911</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1912</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1913</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">23</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1914</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1915</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1916</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">23</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1917</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1918</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center">31</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1919</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">20</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1920</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1921</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">27</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1922</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1923</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1924</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">20</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1925</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1926</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1927</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1928</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1929</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">31</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1930</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">20</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1931</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1932</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">27</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1933</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1934</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1935</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">21</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1936</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="bbr" align="center">1937</td> + <td class="bb">March</td><td class="bbr">27</td> + <td class="bbr" align="center">28</td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />cycle, the 18th of April, which cycle is continued without correction till +the year 3116, a period of 209 years. By reference to the above tables, it +will be seen that the solar and lunar equations occur together in the year +2700 and compensate each other; also, that the year 2800 is a common year +in the Gregorian calendar; consequently there is no correction to make +from 2603 to 2907; also the two equations occur together</p> + +<p> <span class="pagenum"><a name="Page_102" id="Page_102">[Pg 102]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="btr" align="center">1938</td> + <td class="bt">April</td><td align="center" class="btr">14</td> + <td class="btr" align="center">17</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1939</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1940</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">24</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1941</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1942</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1943</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">25</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1944</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1945</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1946</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">21</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center">e</td> + <td class="br" align="center">1947</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">1948</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">28</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1949</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1950</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1951</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">25</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1952</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1953</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1954</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">25</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1955</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1956</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1957</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">21</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1958</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1959</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">29</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1960</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1961</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1962</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">22</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1963</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1964</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center">29</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1965</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">18</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1966</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1967</td> + <td class="dent">March </td><td class="br">25</td> + <td class="br" align="center">26</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1968</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1969</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1970</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">29</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1971</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">1972</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1973</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">22</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1974</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="bbr" align="center">1975</td> + <td class="bb">March</td><td class="bbr">27</td> + <td class="bbr" align="center">30</td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />again in the year 3000 and compensate each other, is the reason there is no correction to +make from 2907 to 3116, after which the first paschal moon falls on the +19th, and is repeated fifteen times in a period of 285 years, that is till +the year 3401, when the correction makes the 20th of April, the date of +the full moon, but that cannot be the paschal moon, which cannot happen +later than the 19th; consequently the</p> + +<p> <span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center">dc</td> + <td class="btr" align="center">1976</td> + <td class="bt">April</td><td align="center" class="btr">14</td> + <td class="btr" align="center">18</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1977</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1978</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">26</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1979</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">1980</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1981</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">26</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1982</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1983</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">1984</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">22</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1985</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1986</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">30</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1987</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">19</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">1988</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1989</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">26</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">1990</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">1991</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center">31</td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">1992</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">19</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1993</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center">7</td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">1994</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">1995</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">1996</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">1997</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">30</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">1998</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">1999</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">2000</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">23</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2001</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2002</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center">31</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2003</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">20</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">2004</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">2005</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">27</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2006</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2007</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">2008</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">23</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2009</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2010</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">2011</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">24</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">2012</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">7</td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="bbr" align="center">2013</td> + <td class="bb">March</td><td class="bbr">27</td> + <td class="bbr" align="center">31</td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />moon that precedes it by thirty days, and which falls on the 21st of March, is the date of the first +paschal moon of the cycle which commences with the year 3401. The day of +the month on which Easter Sunday has fallen or will fall, from the year +1596 to 2013, is already determined, and may be seen by reference to the +above tables. From 2013 to 3401, the date of Easter is determined for one +lunar cycle only, at the</p> + +<p> <span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center">ag</td> + <td class="btr" align="center">2204</td> + <td class="bt">April</td><td align="center" class="btr">15</td> + <td class="btr" align="center">22</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2205</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2206</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">30</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2207</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">19</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">2208</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2209</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">26</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2210</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2211</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center">31</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">2212</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">19</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2213</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">2214</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">27</td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2215</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">2216</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2217</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">30</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2218</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2219</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">2220</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">23</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2221</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2222</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center">31</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2318</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">21</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2319</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">2320</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">28</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">2321</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2322</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2323</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">25</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">2324</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">13</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2325</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2326</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">25</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">2327</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">2328</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2329</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">21</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2330</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2331</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">29</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">2332</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2333</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2334</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">25</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2335</td> + <td class="dent">April</td><td class="br">9</td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center">ed</td> + <td class="bbr" align="center">2336</td> + <td class="bb">March</td><td class="bbr">29</td> + <td class="bbr" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />beginning of each period; for the reason that it +was deemed unnecessary, because the paschal moons, the epacts, and the +Golden Numbers are the same for every cycle in the period. Therefore, all +that remains to be done is to find the day of the month on which the first +Sunday, after the paschal moon, falls. The dominical letters for any +period may very easily be found by counting backwards one letter each year +for every common</p> + +<p> <span class="pagenum"><a name="Page_105" id="Page_105">[Pg 105]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center">f</td> + <td class="btr" align="center">2413</td> + <td class="bt">April</td><td align="center" class="btr">15</td> + <td class="btr" align="center">21</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2414</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2415</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">29</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">2416</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2417</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2418</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">25</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2419</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">2420</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2421</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">18</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">2422</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2423</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">2424</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">21</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2425</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2426</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">29</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2427</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">18</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">2428</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2429</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">22</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2430</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">14</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2431</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center">30</td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">2508</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">22</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2509</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2510</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">30</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2511</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">19</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">2512</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2513</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">26</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2514</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2515</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center">31</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">2516</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">19</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2617</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">2518</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2519</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">2520</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2521</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">30</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2522</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">19</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2523</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">2524</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">26</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2525</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="bbr" align="center">2526</td> + <td class="bb">March</td><td class="bbr">29</td> + <td class="bbr" align="center">31</td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />year, and two for leap-year, the fourth letter being +dominical letter for January and February and the fifth for the rest of +the year; thus, if G be dominical letter for any given year, we would have +then, G, F, E, DC; B, A, G, FE; D, C, B, AG; F, E, D, CB, etc. By counting +these letters backwards, or in the tables, from the bottom of the column +upwards, they will occur in alphabetical order. Again it may be seen by +reference</p> + +<p> <span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span></p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="btr" align="center">2603</td> + <td class="bt">April</td><td align="center" class="btr">17</td> + <td class="btr" align="center">24</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">2604</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2605</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">31</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2606</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">20</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2607</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">2608</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">27</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2609</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2610</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2611</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">21</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">2612</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2613</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">2614</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">17</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2615</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">2616</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">31</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2617</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">20</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2618</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2619</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">28</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">2620</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2621</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">2907</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">2908</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2909</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center">31</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2910</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">20</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2911</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">2912</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">27</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2913</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">2914</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">2915</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">24</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">2916</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2917</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">2918</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">2919</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">2920</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">31</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">2921</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">20</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">2922</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">2923</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">28</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center">ba</td> + <td class="br" align="center">2924</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="bbr" align="center">2925</td> + <td class="bb">March</td><td class="bbr">31</td> + <td class="bbr" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />to these tables, that Easter occurs less frequently on the 22d +of March, its earliest possible date, and the 25th of April, which has +hitherto been considered its latest possible date, than any of the days +intervening. It cannot happen on the 22d, only when the paschal moon falls +on the 21st, and that day must be Saturday. It fell on the 22d, first, +after the reformation of the calendar by Gregory in 1598; again in 1693, 1761,</p> + +<p> <span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span></p> +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td class="btr" align="center"><i>Dominical<br />Letter.</i></td> + <td class="btr" align="center"><i>Year.</i></td> + <td colspan="2" class="btr" align="center"><i>Paschal<br />Full<br />Moon.</i></td> + <td class="btr" align="center"><i>Easter.</i></td> + <td class="btr" align="center"><i>Epact.</i></td> + <td class="bt" align="center"><i>Golden<br />Number.</i></td></tr> +<tr><td class="btr" align="center">ba</td> + <td class="btr" align="center">3116</td> + <td class="bt">April</td><td align="center" class="btr">19</td> + <td class="btr" align="center">23</td> + <td class="btr" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="bt" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">3117</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">15</td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">3118</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center">31</td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">3119</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">20</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center">dc</td> + <td class="br" align="center">3120</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">3121</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">27</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">3122</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">3123</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">2</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center">fe</td> + <td class="br" align="center">3124</td> + <td class="dent">March</td><td class="br">22</td> + <td class="br" align="center">23</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">3125</td> + <td class="dent">April</td><td class="br">10</td> + <td class="br" align="center">12</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">3126</td> + <td class="dent">March</td><td class="br">30</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">3127</td> + <td class="dent">April</td><td class="br">18</td> + <td class="br" align="center">24</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">3128</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">3129</td> + <td class="dent">March</td><td class="br">27</td> + <td class="br" align="center">31</td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">3130</td> + <td class="dent">April</td><td class="br">15</td> + <td class="br" align="center">20</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">3131</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">4</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">3132</td> + <td class="dent">March</td><td class="br">24</td> + <td class="br" align="center">27</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">3133</td> + <td class="dent">April</td><td class="br">12</td> + <td class="br" align="center">16</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">3134</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">1</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">18</td> + <td class="dent" align="center">19</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">3401</td> + <td class="dent">March</td><td class="br">21</td> + <td class="br" align="center">22</td> + <td class="br" align="center"><span style="margin-left: .5em;">0</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">1</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">3402</td> + <td class="dent">April</td><td class="br"><span style="margin-left: .5em;">9</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center">11</td> + <td class="dent" align="center"><span style="margin-left: .5em;">2</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">3403</td> + <td class="dent">March</td><td class="br">29</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">22</td> + <td class="dent" align="center"><span style="margin-left: .5em;">3</span></td></tr> +<tr><td class="br" align="center">ag</td> + <td class="br" align="center">3404</td> + <td class="dent">April</td><td class="br">17</td> + <td class="br" align="center">22</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">4</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">3405</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">6</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">14</td> + <td class="dent" align="center"><span style="margin-left: .5em;">5</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">3406</td> + <td class="dent">March</td><td class="br">26</td> + <td class="br" align="center">30</td> + <td class="br" align="center">25</td> + <td class="dent" align="center"><span style="margin-left: .5em;">6</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">3407</td> + <td class="dent">April</td><td class="br">14</td> + <td class="br" align="center">19</td> + <td class="br" align="center"><span style="margin-left: .5em;">6</span></td> + <td class="dent" align="center"><span style="margin-left: .5em;">7</span></td></tr> +<tr><td class="br" align="center">cb</td> + <td class="br" align="center">3408</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">10</td> + <td class="br" align="center">17</td> + <td class="dent" align="center"><span style="margin-left: .5em;">8</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">3409</td> + <td class="dent">March</td><td class="br">23</td> + <td class="br" align="center">26</td> + <td class="br" align="center">28</td> + <td class="dent" align="center"><span style="margin-left: .5em;">9</span></td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">g</span></td> + <td class="br" align="center">3410</td> + <td class="dent">April</td><td class="br">11</td> + <td class="br" align="center">15</td> + <td class="br" align="center"><span style="margin-left: .5em;">9</span></td> + <td class="dent" align="center">10</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">f</span></td> + <td class="br" align="center">3411</td> + <td class="dent">March</td><td class="br">31</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">20</td> + <td class="dent" align="center">11</td></tr> +<tr><td class="br" align="center">ed</td> + <td class="br" align="center">3412</td> + <td class="dent">April</td><td class="br">19</td> + <td class="br" align="center">26</td> + <td class="br" align="center"><span style="margin-left: .5em;">1</span></td> + <td class="dent" align="center">12</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="br" align="center">3413</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">8</span></td> + <td class="br" align="center">11</td> + <td class="br" align="center">12</td> + <td class="dent" align="center">13</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">b</span></td> + <td class="br" align="center">3414</td> + <td class="dent">March</td><td class="br">28</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="br" align="center">23</td> + <td class="dent" align="center">14</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">a</span></td> + <td class="br" align="center">3415</td> + <td class="dent">April</td><td class="br">16</td> + <td class="br" align="center">23</td> + <td class="br" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="dent" align="center">15</td></tr> +<tr><td class="br" align="center">gf</td> + <td class="br" align="center">3416</td> + <td class="dent" align="center">"</td><td class="br"><span style="margin-left: .5em;">5</span></td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="br" align="center">15</td> + <td class="dent" align="center">16</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">e</span></td> + <td class="br" align="center">3417</td> + <td class="dent">March</td><td class="br">25</td> + <td class="br" align="center">30</td> + <td class="br" align="center">26</td> + <td class="dent" align="center">17</td></tr> +<tr><td class="br" align="center"><span style="margin-left: .5em;">d</span></td> + <td class="br" align="center">3418</td> + <td class="dent">April</td><td class="br">13</td> + <td class="br" align="center">19</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">18</td></tr> +<tr><td class="bbr" align="center"><span style="margin-left: .5em;">c</span></td> + <td class="bbr" align="center">3419</td> + <td class="bb" align="center">"</td><td class="bbr"><span style="margin-left: .5em;">2</span></td> + <td class="bbr" align="center"><span style="margin-left: .5em;">4</span></td> + <td class="bbr" align="center">18</td> + <td class="bb" align="center">19</td></tr></table> + +<p><br />and in 1818. It has not occurred since, nor will not again till +2285, a period of 467 years. The reason that it does not occur on the 22d +of March in this long period is, the paschal moon does not fall on the +21st, from the year 1900 to 2204, a period of 304 years. We refer to the +tabular moon, not to the true or astronomical moon, which may occur on the +21st more than once in this long period.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span></p> +<h2><a name="CHAPTER_VII.3" id="CHAPTER_VII.3"></a>CHAPTER VII.</h2> +<p class="center"><span class="big">CHURCH FEASTS AND FASTS WHOSE DATE DEPEND ON THE DATE OF EASTER.</span></p> + +<p>Feasts, or Festivals, are days set apart by the church, either for the +grateful memorial of the most remarkable events connected with the plan of +redemption, or upon which to commemorate the actions and sufferings of +such persons as have been most instrumental in carrying forward the +designs of God for the salvation of mankind.</p> + +<p>The ecclesiastical year is divided into eight seasons, namely: +Advent-tide, Christmas-tide, Epiphany-tide, Lenten-tide, Easter-tide, +Ascension-tide, Whitsun-tide, and Trinity-tide. The first day of each of +these seasons has been, and is now observed by the church in commemoration +of some of the most remarkable events connected with the plan of +redemption. All these will be noticed in the order in which they occur in +the ecclesiastical year, while many other days intervening, which are +observed as feasts or fasts, will be given a passing notice.</p> + +<p><i>a</i>—Advent Sunday, which is the day nearest St. Andrew’s Day (Nov. 30), +or the first Sunday after the 26th of November, has been recognized since +the sixth century as the first day of the ecclesiastical year.</p> + +<p>Advent (Latin <i>Adventus</i>, the coming,) signifies the coming of our +Saviour, the period of the approach of the nativity. As Advent-tide lasts +from Advent Sunday to Christmas, the length of the season depends upon<span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span> +the day of the month on which Advent Sunday falls. As it may happen as +early as the 27th of November or as late as the 3d of December, so +Advent-tide will contain no more than twenty-eight days nor less than +twenty-two. It should be borne in mind that, though this festival is +classed among the movable feasts, it does not depend upon the date of +Easter, but upon the day of the month on which Advent Sunday falls. The +four Sundays before Christmas were made preparation days for the festival +of Christmas, and were called the first, second, third, and fourth Sundays +in Advent.</p> + +<p>Ember days and Ember weeks are the four seasons set apart by the Western +church for special prayer and fasting, and the ordination of clergy; known +in the church as <i>quatuor tempora</i>, (the four seasons.) The Ember weeks +are the weeks next following St. Lucy’s Day (Dec. 13th), the first Sunday +in Lent, Whitsun Day, and Holy Cross Day (Sept. 14th). The Wednesdays, +Fridays and Saturdays of these weeks are the Ember days distinctively. The +name by some is supposed to be derived from a German word signifying +Abstinence; by others it is supposed to signify Ashes.</p> + +<p><i>b</i>—Christmas (from Christ and the Saxon <i>maess</i>, signifying the mass and +a feast), is a festival held in commemoration of the nativity of our +Saviour throughout nearly the whole of Christendom. It is occupied, +therefore, with the event (the incarnation) which forms the center and +turning point of the history of the world. Though the day of Christ’s +birth cannot be ascertained from the New Testament, nor from any other +source, yet the whole Christian world for more than 1300 years have +concurred in celebrating the nativity on the 25th<span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span> of December. This is +the first of the four great feasts in the ecclesiastical year; the other +three are Easter, Ascension, and Whitsun Day. The length of Christmas-tide +or season is twelve days, lasting from the 25th of December to Epiphany.</p> + +<p><i>c</i>—Epiphany (Greek <i>Epiphania</i>, <i>Theophania</i> or <i>Christophania</i>,) is a +festival in commemoration of the manifestation of Jesus Christ to the +world as the Son of God, and referring to the appearance of the star which +announced our Saviour’s birth to the Gentiles, and the visit of the Magi, +or wise Men of the East to the infant Jesus. This festival is held on the +6th of January invariably, consequently is not a movable feast, though the +length of Epiphany-tide depends upon the date of Easter. As Easter may +happen as early as the 22d of March or as late as the 26th of April (a +variation of thirty-five days), so Epiphany-tide may consist of no less +than twelve days nor more than forty-seven, as the season always ends the +day before Septuagesima Sunday. (See <a href="#tables">tables</a> at the close of this chapter.)</p> + +<p>Septuagesima, Sexagesima, Quinquagesima. There being exactly fifty days +between the Sunday next before Lent and Easter Day, inclusive, that Sunday +was termed Quinquagesima, i. e., the fiftieth; and the two immediately +preceding Sundays were called from the next round numbers Sexagesima, the +sixtieth; and Septuagesima, the seventieth.</p> + +<p>The Paschal Season extends from Septuagesima Sunday to Low Sunday, a +period of seventy days. It takes its name from the Paschal festival or +Easter, whose services end with Low Sunday, the octave, or eighth day, of +Easter. It begins with Septuagesima Sunday<span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span> because the church services +then begin to prepare the minds of the faithful for the services of Lent, +which are themselves the preparation for Easter. May not Septuagesima +Sunday be so called because there are just seventy days in the Paschal +Season?</p> + +<p>Shrove-tide literally means confession-time, and is the name given to the +days immediately preceding Ash Wednesday. These days were so called +because on them, and especially on the last of them (Shrove Tuesday) +people were accustomed to confess their sins as a preparation for Lent. In +most Roman Catholic countries it begins with Quinquagesima Sunday, the +Sunday before Lent.</p> + +<p>Ash Wednesday, the first day of Lent, (Latin <i>dies cinerum</i>, the day of +Ashes), was so called because it was customary on that day for penitents +to appear in sackcloth, upon which occasion ashes were sprinkled upon +them.</p> + +<p><i>d</i>—Lent, (Anglo-Saxon <i>lengten</i>. Perhaps from <i>lenegan</i>, to lengthen, +because at this season the days lengthen) the forty days fast, is the +preparation for Easter, and is observed in commemoration of our Lord’s +fast in the wilderness. In most languages the name given to this fast +signifies the number of days—forty; but our word Lent signifies the +Spring Fast, for Lenten-tide in the Anglo-Saxon language was the Season of +Spring, in German, Lenz.</p> + +<p>The six Sundays in the Lenten-tide of forty-six days are not counted in +the fast, as all Sundays in the year are reckoned as feast days, because +our Saviour arose from the dead on the first day of the week.</p> + +<p>Quadragesima Sunday, the first Sunday in Lent, is<span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span> so called by analogy +with the three Sundays which precede Lent, and which (as has already been +stated) are called respectively Septuagesima, seventieth; Sexagesima, +sixtieth; Quinquagesima, fiftieth; and then Quadragesima, fortieth; in +round numbers forty days before Easter.</p> + +<p>Holy Week, the last week in Lent, called also Passion Week, because within +it is commemorated our Lord’s sufferings. The days specially solemnized +are Palm Sunday, Spy Wednesday, Holy, or Maundy Thursday, and Good Friday.</p> + +<p>Palm Sunday (Latin <i>Dominica Palmarium</i>, or <i>Dominica</i> in <i>Palmis</i>) is the +name usually given the Sunday before Easter; a day celebrated in +commemoration of Christ’s triumphal entry into Jerusalem, so called +because the people who had come to the feast, when they heard that Jesus +was coming, took branches of palm trees and went forth to meet him, and +cried, “Hosanna; blessed is the King of Israel that cometh in the name of +the Lord.”</p> + +<p>Spy Wednesday, so called in allusion to the betrayal of Christ by Judas, +or the day on which he made the bargain to deliver him into the hands of +his enemies for thirty pieces of silver.</p> + +<p>Maundy Thursday (from <i>Dies mandati</i>, mandate Thursday), so called either +from the command given his disciples to love one another, or to +commemorate the sacrament of His supper.</p> + +<p>Good Friday, so called in acknowledgment of the benefit derived from the +death of Christ.</p> + +<p>The closing scenes in the life of Christ, the events of Wednesday, +Thursday and Friday of Holy Week, are<span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span> events of much more importance than +were ever before crowded into any one week in the history of the world. +The betrayal on Wednesday, the institution of the sacrament on Thursday +night, also the words of our Saviour as recorded in John’s gospel, from +the 14th to the 17th chapters inclusive, the agony and the bloody sweat in +the garden, the arrest and trial during Thursday night and Friday morning, +the crucifixion at the third hour, the darkness that was over all the land +from the sixth to the ninth hour, and the last words of the blessed Jesus, +“It is finished,” (tasted death for every man); these we say, are events +of more importance to man than were ever before crowded into any one week +in the world’s history.</p> + +<p>The prophets who prophesied of these things, inquired and searched +diligently, “searching what, or what manner of time the Spirit of Christ +which was in them did signify, when it testified beforehand the sufferings +of Christ and the glory that should follow.” And about an hour before this +prophecy began to be fulfilled our Saviour uttered these words: “Verily, +verily, I say unto you, that ye shall weep and lament, but the world shall +rejoice; and ye shall be sorrowful, but your sorrow shall be turned into +joy.” It was probably not more than an hour from the time these words fell +from the Saviour’s lips, that he was arrested and led away to undergo a +trial; cruel mocking and scourging, crucifixion and death upon the cross.</p> + +<p>Then cometh Joseph of Arimathea, bringing fine linen, and Nicodemus with +his hundred pounds of myrrh and aloes, and they two took the body of the +Lord Jesus and wrapped it in the linen with the spices,<span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span> and laid it in +Joseph’s own new tomb, which he had hewn out in a rock, wherein never man +before was laid, and rolled a great stone against the door of the +sepulcher and departed. Thus endeth Passion Week. While the body of Jesus +is in the sepulcher the world is rejoicing, and the disciples are weeping +and lamenting, according to the words of the Saviour, “Ye shall weep and +lament, but the world shall rejoice.”</p> + +<p class="poem">He dies! the friend of sinners dies!<br /> +<span style="margin-left: 1em;">Lo! Salem’s daughters weep around;</span><br /> +A solemn darkness veils the skies,<br /> +<span style="margin-left: 1em;">A sudden trembling shakes the ground.</span></p> + +<p><i>e</i>—Easter (German, <i>Ostern</i>, Old Saxon <i>Oster</i>, from <i>osten</i>, signifying +rising,) is a church festival in commemoration of the resurrection of our +Lord from the dead. But the apparent victory which the enemies of Christ +had gained was of short duration, the rejoicing of the world did not long +continue, the remaining words of our Saviour must needs be fulfilled: “But +your sorrow shall be turned into joy.” Now, upon the first day of the +week, very early in the morning, (Easter morning) the two Marys came to +the sepulcher bringing the sweet spices and ointments which they had +prepared for the purpose of anointing the body of the Lord Jesus, but were +greatly astonished when they saw that the great stone, which they had seen +rolled against the door of the sepulcher on Friday afternoon, was rolled +away, and an angel sitting upon it whose <ins class="correction" title="original: countenace">countenance</ins> was like lightning, +and for fear of whom the keepers did shake and become as dead men. But to +the women he said, “Fear not ye; for I know that ye seek Jesus which was +crucified, He is not here, for He is risen.”<span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span> That you may know for a +certainty that He is risen, come and see the place where you saw Him laid +only a few hours ago. Now go quickly and tell His disciples that He is +risen from the dead, and behold He goeth before you into Galilee, there +shall ye see Him. And they departed quickly from the sepulcher with fear +and great joy, and did run to carry the good news to the disciples. But +how much greater their joy soon after their departure when Jesus himself +met them with the comforting words, “Be not afraid, but go tell my +brethren that they go into Galilee, and there shall they see Me.”</p> + +<p>The subject for conversation for the past two days had been Jesus and the +crucifixion, but now Jesus and the resurrection. Some believed, but some +doubted. Others ran to the sepulcher and found it even as the women had +said. While the chief priests and elders hired the soldiers to say that +the disciples came by night and stole him away while we slept. But how +should they know what had become of Him if they were sleeping? The truth +was they were so overcome with fear by the brightness of the angels’ +countenance that they became as dead men, not knowing what was transpiring +around them. But it was truly good tidings and great joy to the disciples +of Christ on that Easter morning.</p> + +<p class="poem">The rising God forsakes the tomb;<br /> +In vain the tomb forbids His rise;<br /> +Vain the stone, the watch, the seal,<br /> +Christ has burst the gates of hell;<br /> +Death in vain forbids His rise;<br /> +Christ hath opened Paradise.</p> + +<p>The spirit of Christ in the prophets had testified beforehand the +suffering of Christ and the glory that<span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span> should follow. That morning and +that day was not only joyful to the disciples of Christ, but <i>glorious</i>; +it was “joy unspeakable and <i>full</i> of glory.” Although 1863 years have +rolled around since that Easter morning, yet we are as much interested in +what then and there transpired as were the Marys, and Peter, and John, who +were the first at the sepulcher, and who were permitted the same day to +see their risen Lord, whom having not seen, we love; in whom, though now +we see Him not, yet believing, we [as well as they] rejoice “with joy +unspeakable and full of glory.”</p> + +<p>Low Sunday. The first Sunday after Easter is so called because it was +customary to repeat on this day some part of the solemnity which was used +on Easter day, whence it took the name of Low Sunday, being celebrated as +a feast, but of a lower degree than Easter day itself. The next Sunday +after Easter has been popularly, so called in England, perhaps by +corruption for close, (<i>Pascha Clausum</i>) close of Easter. <i>Dominica</i> in +<i>Albis</i>, (the Sunday of white garments) a title anciently given to the +first Sunday after Easter, because on this day those persons who had been +baptized at Easter appear for the last time in the chrysomes, or white +robes which they received at baptism. These were laid up in the church as +evidences of their baptismal profession.</p> + +<p>Rogation Days, (Latin <i>rogare</i>, to beseech,) are the Monday, Tuesday and +Wednesday after Rogation Sunday and before Ascension Day, (Holy Thursday.) +About the middle of the fifth century Mamertus, bishop of Vienna, upon the +prospect of a great fire that threatened his diocese, appointed that +<span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span>extraordinary prayer and supplication should be offered up to God, with +fasting, for averting the impending evils upon the above mentioned days; +from which supplications (called by the Latins <i>rogationes</i>) these days +have ever since been called Rogation Days. As retained in our present +calendar, they are simply private fasts.</p> + +<p><i>f</i>—Ascension Day, or Holy Thursday, one of the great religious festivals +of the Roman Catholic and Episcopal churches, is held on the fortieth day +after Easter, and ten days before Whitsun Day, to commemorate the +Ascension of our Lord into heaven. Ascension Day has been observed at +least since the year of our Lord 64, and perhaps earlier. Saint Augustine +believed it to have been instituted either by the apostles themselves, or +the bishops immediately succeeding them.</p> + +<p>Expectation Week is the whole of the interval between Ascension Day and +Whitsun Day, so called because at this time the apostles, according to the +command of our Saviour, continued at Jerusalem, in earnest prayer and +expectation of the Holy Comforter which was to abide with them forever. +The Sunday between Ascension Day and Whitsun Day is called Expectation +Sunday.</p> + +<p>Pentecost, (Greek, <i>Pentecostos</i>, fiftieth), a Jewish festival; so called +because it was observed on the fiftieth day after the feast of unleavened +bread, called also the feast of weeks, being celebrated seven weeks from +the feast of the Passover. It also commemorated the giving of the law on +Mount Sinai upon that day. The origin of the Anglo-Saxon name of White +Sunday, which also occurs in Icelandic, is somewhat obscure, for in the +Roman churches the <i>Dominica</i> in <i>Albis</i>, (Low <span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span>Sunday, q. v.) so called +from the white robes then worn by the persons baptized at Easter, has +always been the Sunday immediately following Easter. It hardly seems +probable that there should be another Sunday of White Garments within six +weeks. In German it is known by the name <i>Pfingsten</i>, old German +<i>Wingsten</i>, old English <i>Whitsun</i>, hence, probably, our word Whitsun Day, +not White Sunday.</p> + +<p><i>g</i>—Whitsun Day, or Pentecost, is the last of the four <i>great</i> festivals +in the ecclesiastical year, held in commemoration of the outpouring of the +Holy Spirit on the infant church ten days after the Ascension. Among the +last words of our Saviour to the apostles on the very day that He was +taken up, were “Behold I send the promise of my Father upon you, but tarry +ye in the city of Jerusalem until ye be endowed with power from on high.” +After ten days of earnest, believing prayer, and expectation, suddenly, +but not unexpectedly, there came a sound from heaven as a rushing, mighty +wind, and it filled all the house where they were sitting, and there +appeared unto them cloven tongues like as of fire, and it sat upon each of +them; and they were all filled with the Holy Ghost, and began to speak +with other tongues as the Spirit gave them utterance; and the multitude +came together, and were amazed, saying one to the other what meaneth this? +Others mocking said, these men are full of new wine. But Peter lifted up +his voice and said, these are not drunken as ye suppose, seeing it is but +the third hour of the day, (nine o’clock in the morning,) men are not +usually drunk so early in the morning; but this is that which the prophet +Joel eight hundred years ago said should come to pass<span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span> in these last days; +the promise of the Father, the baptism of the Holy Ghost for which they +had been waiting for the past ten days; something of that <i>glory</i> that +should follow the crucifixion, death, resurrection and ascension of the +Lord Jesus into Heaven, the glory of the Christian church, of the +Christian dispensation, and which is destined to fill the whole earth.</p> + +<p class="poem">“Waft, Waft, ye winds his story,<br /> +<span style="margin-left: 1em;">And you, ye waters, roll,</span><br /> +Till like a sea of glory,<br /> +<span style="margin-left: 1em;">It spreads from pole to pole.”</span></p> + +<p><i>h</i>—Trinity Sunday, the octave, or eighth day of the feast of Pentecost, +is a church festival held in commemoration of the doctrine of the Trinity. +The introduction of this day into the calendar is of comparatively recent +date, it being established by Pope Benedict XI, in the year of our Lord +1305. It is probable that the zeal of many Christians against the use of +images in the eighth and ninth centuries may have been the first cause of +the appointment of a distinct day for meditating upon the nature of the +Holy Trinity in unity, or the one true God as distinguished from idols. +The reason for its late introduction is that in the creed of the church, +and in its psalms, hymns, and doxologies, great prominence was given to +this doctrine, and it was thought that there was no need to set apart a +particular day for that which was done every day. This is the last of the +movable feasts in the ecclesiastical year, being held eight weeks after +Easter; so it may happen as early as the 17th of May or as late as the +20th of June. The length of both Epiphany and Trinity-tide depend upon the +date of Easter. As Epiphany-tide is shortened<span class="pagenum"><a name="Page_120" id="Page_120">[Pg 120]</a></span> by the early date of +Easter, so Trinity-tide is lengthened proportionately, and as +Epiphany-tide is lengthened by the later date of Easter so Trinity-tide is +shortened proportionately; so Trinity-tide may contain no more than 196 +days nor less than 161. (See <a href="#tables">tables</a> at the close of this chapter.)</p> + +<p>All Saints Day, or All hallowmass (Anglo-Saxon <i>all</i>, and <i>halig</i>, holy) a +festival celebrated by the Roman Catholic and Episcopal churches on the +first day of November, in honor of all Saints and martyrs. It was +introduced into the Western church in the beginning of the seventh century +by Boniface. The number of saints being exceedingly multiplied, it was +found too burdensome to dedicate a feast day to each, there being, indeed, +scarcely hours enough in the year to distribute among them all. It was +therefore resolved to commemorate on one day all who had no particular +day. By order of Gregory IV, it was celebrated on the first of November, +834; formerly the first of May was the day appointed. It was introduced +into England about 870, and is still observed in the English and Lutheran +churches, as well as the Church of Rome on the first of November.</p> + +<p>All-Souls’ Day, a festival held by Roman Catholics on the 2d of November, +for special prayer in behalf of all the faithful dead. It was first +introduced in 998, by Odilon, Abbot of Clugni, who enjoined it on his own +order. It was soon after adopted by neighboring churches. It is the day on +which, in the Romish church, extraordinary masses are repeated for the +relief of souls said to be in purgatory. Formerly on this day persons +dressed in black perambulated the towns and<span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span> cities, each provided with a +bell of dismal tone, which was rung in public places by way of exhortation +to the people to remember the souls in purgatory. In some parts of the +west of England it is still the custom for the village children to go +around to all their neighbors souling, as they call it, collecting small +contributions, and singing the following verses, taken down from two of +the children themselves:</p> + +<p class="poem">Soul! Soul! for a soul-cake,<br /> +Pray good mistress, for a soul-cake,<br /> +One for Peter, two for Paul,<br /> +Three for Him that made us all.<br /> +<br /> +Soul! soul! for an apple or two;<br /> +If you’ve got no apples, pears will do,<br /> +Up with your kettle, and down with your pan,<br /> +Give me a good big one and I’ll be gone.</p> + +<p>The soul cake referred to in the verses is a sort of bun which the people +used to make, and to give to one another on the 2d of November.</p> + +<p>In the following tables there is presented at one view the day of the +month on which the principal feasts and fasts fall in the ecclesiastical +year 1817-18 and 1885-86. In the former Easter happens at its earliest +possible date, in the latter at its latest date in this century:</p> + +<p> <span class="pagenum"><a name="Page_122" id="Page_122">[Pg 122]</a></span></p> +<p><a name="tables" id="tables"></a></p> +<table width="75%" border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td colspan="2" class="btr" align="center" valign="middle"><i>YEAR 1817-18.</i></td> + <td class="btr" align="center"><i>Days<br />in Each<br />Season.</i></td> + <td class="bt" align="center"><i>Sundays<br />in Each<br />Season.</i></td></tr> +<tr><td class="bt"><i>a</i>—</td> + <td class="btr">Advent Sunday, November 30th; Advent-tide.</td> + <td class="btr" align="center">25</td> + <td class="bt" align="center">4</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>1st</i></td> + <td class="br">Ember Week, after December 13th; Ember Days, Wednesday, Friday and Saturday.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>b</i>—</td> + <td class="br">Christmas, December 25th; Christmas-tide.</td> + <td class="br" align="center">12</td> + <td class="dent" align="center">2</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>c</i>—</td> + <td class="br">Epiphany, January 6th; Epiphany-tide.</td> + <td class="br" align="center">12</td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Septuagesima Sunday, January 18th.</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Paschal season from Jan. 18th to March 29th, 70 days.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Sexagesima Sunday, January 25th.</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Quinquagesima Sunday, February 1st.</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Shrove-tide, (confession time) Shrove Tues., Feb. 3d.</td> + <td class="br" align="center"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>d</i>—</td> + <td class="br">Ash Wednesday, Feb 4th, Lent begins; Lenten-tide.</td> + <td class="br" align="center">46</td> + <td class="dent" align="center">6</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">First Sunday in Lent (Quadragesima) February 8th.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent" valign="top"><i>2d</i></td> + <td class="br">Ember Week after first Sunday in Lent; Ember Days, Wednesday, Friday and Saturday.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Holy Week, the week before Easter; Special Days, Palm Sunday, Spy Wednesday,<br />Maundy Thursday, and Good Friday, March 15th, 18th, 19th and 20th.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>e</i>—</td> + <td class="br">Easter Sunday, March 22d; Easter-tide.</td> + <td class="br" align="center">39</td> + <td class="dent" align="center">6</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Low Sunday, March 29th; Paschal Season ends.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Rogation Sunday, April 26th; Rogation Days, the Monday, Tuesday and Wednesday after Rogation Sunday.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>f</i>—</td> + <td class="br">Ascension Day (Holy Thursday), April 30th; Ascension-tide.</td> + <td class="br" align="center">10</td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Expectation Sunday, First Sunday after Ascension, May 3d.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>g</i>—</td> + <td class="br">Whitsun Day, (Pentecost) May 10th; Whitsun-tide.</td> + <td class="br" align="center">7</td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>3d</i></td> + <td class="br">Ember Week, after Whitsun Day; Ember Days, Wednesday, Friday and Saturday.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>h</i>—</td> + <td class="br">Trinity Sunday, May 17th; Trinity-tide.</td> + <td class="br" align="center"><span style="margin-left: -.5em;">196</span></td> + <td class="dent" align="center"><span style="margin-left: -.5em;">28</span></td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>4th</i></td> + <td class="br">Ember Week, after September 14th; Ember Days, Wednesday, Friday and Saturday.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">All Saints’ Day, November 1st.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">All Souls’ Day, November 2d.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td colspan="2" class="bbr" align="center"><a href="#appenk">Appendix K.</a></td> + <td class="bbtr" align="center"><span style="margin-left: -.5em;">364</span></td> + <td class="bbt" align="center"><span style="margin-left: -.5em;">52</span></td></tr></table> + + +<p> <span class="pagenum"><a name="Page_123" id="Page_123">[Pg 123]</a></span></p> + +<table width="75%" border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td colspan="2" class="btr" align="center" valign="middle"><i>YEAR 1885-86.</i></td> + <td class="btr" align="center"><i>Days<br />in Each<br />Season.</i></td> + <td class="bt" align="center"><i>Sundays<br />in Each<br />Season.</i></td></tr> +<tr><td class="bt"><i>a</i>—</td> + <td class="btr">Advent Sunday, November 29th; Advent-tide.</td> + <td class="btr" align="center">26</td> + <td class="bt" align="center">4</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>1st</i></td> + <td class="br">Ember Week, after December 13th; Ember Days, Wednesday, Friday and Saturday.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>b</i>—</td> + <td class="br">Christmas, December 25th; Christmas-tide.</td> + <td class="br" align="center">12</td> + <td class="dent" align="center">2</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>c</i>—</td> + <td class="br">Epiphany, January 6th; Epiphany-tide.</td> + <td class="br" align="center">46</td> + <td class="dent" align="center">6</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Septuagesima Sunday, February 21st.</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Paschal season, from Feb. 21st to May 2d, 70 days.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Sexagesima Sunday, February 28th.</td> + <td class="br" align="center"><span style="margin-left: .5em;">7</span></td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Quinquagesima Sunday, March 7th.</td> + <td class="br" align="center"><span style="margin-left: .5em;">3</span></td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Shrove-tide, (confession time) Shrove Tues., Mar. 9th.</td> + <td class="br" align="center"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>d</i>—</td> + <td class="br">Ash Wednesday, March 10th, Lent begins; Lenten-tide.</td> + <td class="br" align="center">46</td> + <td class="dent" align="center">6</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">First Sunday in Lent (Quadragesima) March 14th.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent" valign="top"><i>2d</i></td> + <td class="br">Ember Week after first Sunday in Lent; Ember Days, Wednesday, Friday and Saturday.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Holy Week, the week before Easter; Special Days, Palm Sunday, Spy Wednesday,<br />Maundy Thursday, and Good Friday, April 18th, 21st, 22d and 23d.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>e</i>—</td> + <td class="br">Easter Sunday, April 25th; Easter-tide.</td> + <td class="br" align="center">39</td> + <td class="dent" align="center">6</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Low Sunday, May 2d, Paschal Season ends.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Rogation Sunday, May 30th; Rogation Days, the Monday, Tuesday and Wednesday after Rogation Sunday.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>f</i>—</td> + <td class="br">Ascension Day (Holy Thursday), June 3d; Ascension-tide.</td> + <td class="br" align="center">10</td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">Expectation Sunday, first Sunday after Ascension, June 6th.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>g</i>—</td> + <td class="br">Whitsun Day, (Pentecost) June 13th; Whitsun-tide.</td> + <td class="br" align="center">7</td> + <td class="dent" align="center">1</td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>3d</i></td> + <td class="br">Ember Week, after Whitsun Day; Ember Days, Wednesday, Friday and Saturday.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>h</i>—</td> + <td class="br">Trinity Sunday, June 20th; Trinity-tide.</td> + <td class="br" align="center"><span style="margin-left: -.5em;">161</span></td> + <td class="dent" align="center"><span style="margin-left: -.5em;">23</span></td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td class="dent"><i>4th</i></td> + <td class="br">Ember Week, after September 14th; Ember Days, Wednesday, Friday and Saturday.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">All Saints’ Day, November 1st.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td> </td> + <td class="br">All Souls’ Day, November 2d.</td> + <td class="br"> </td></tr> +<tr><td> </td><td class="br"> </td><td class="br"> </td></tr> +<tr><td colspan="2" class="bbr" align="center"><a href="#appenk">Appendix K.</a></td> + <td class="bbtr" align="center"><span style="margin-left: -.5em;">364</span></td> + <td class="bbt" align="center"><span style="margin-left: -.5em;">52</span></td></tr></table> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span></p> +<h2><a name="CHAPTER_VIII.3" id="CHAPTER_VIII.3"></a>CHAPTER VIII.</h2> +<p class="center"><span class="big">HEBREW CALENDAR.</span></p> + +<p>To the Bible student a knowledge of the Hebrew calendar is indispensable, +if he would know how the date of events recorded in the Bible are made to +correspond with our present English calendar. From the exodus (1491 B. C.) +downward, the Hebrew month was lunar, and commenced invariably with the +new moon.</p> + +<p>Dr. Smith, author of Bible Dictionary, says that the terms for month and +moon have the same close connection in the Hebrew language as in our own, +only the Hebrew Codesh (that is new moon) is, perhaps, more distinctive +than the corresponding term in our language; for it expresses not simply +the idea of a lunation, but the recurrence of a period commencing +definitely with the new moon. Though the identification of the Jewish +month with our own cannot be effected with precision on account of the +variations that must necessarily exist between the lunar and the solar +month, each of the former ranging over portions of two of the latter, +still it can be shown how they may be made to coincide very nearly by a +systematic method of intercalation.</p> + +<p>Now from new moon to new moon again, is about 29½ days; therefore, the +Hebrew year consisted of 354 days, for 29½ × 12 = 354; so that the +epact, (which is the excess of the solar year beyond the lunar) is eleven +days. Hence, had they no method of intercalation,<span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span> the commencement of +their year would go back eleven days every year, and consequently make a +revolution of the seasons every thirty-three years, for 365 ÷ 11 = 33 +nearly.</p> + +<p>To illustrate, let us suppose that the new moon of Nisan, which is the +first month in the Sacred year, should on any given year fall on the 10th +of April, then the following year it would fall on the 30th of March, +which is eleven days earlier; the second year it would fall on the 19th of +March or twenty-two days earlier; the third year the new moon would fall +on the 8th of March or thirty-three days earlier, but that would not be +the new moon of Nisan, which cannot happen earlier than the 11th, so the +following moon which happens thirty days later on the 7th of April is the +new moon of Nisan. Hence it may be seen that by intercalating a full month +every three years, or which comes nearer to accuracy seven times in +nineteen years, restores the coincidence of the solar and the lunar year, +and consequently the moons to the same day of the month on which they fell +nineteen years before.</p> + +<p>The method of designating the months previous to the exodus, was by their +numerical order, as the ancient Hebrews had no particular name to express +their month. They said the first, second and third month, and so on. No +names of months appear in the Bible until about the time of the +institution of the passover, when the Lord spake unto Moses and Aaron in +the land of Egypt, saying this month, (Abib, which appears to have had its +origin in Egypt,) shall be unto you the beginning of months; it shall be +the first month of the year to you.</p> + +<p><span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span>The names of the months appear to belong to two distinct periods. In the +first place we have those peculiar to the Jews previous to the captivity, +viz: Abib, the first month in commemoration of the exodus; Zif, the +second, Ethanim, the seventh, and Bul, the eighth. These names are of +Hebrew origin, and have reference to the characteristics of the seasons, a +circumstance which clearly shows that the months, by intercalation, were +made to return at the same period of the year. Thus, Abib was the month of +the ears of corn, that is the month in which the ears of corn became full, +or ripe on the 16th day, that is the 2d day of the feast of unleavened +bread. Zif, the month of blossoms or the bloom of flowers. Ethanim, the +month of gifts, that is of fruits, and Bul, the month of rain. These were +superceded after the captivity, by Nisan, Iyar, Tisri and Hesvan, or +Marchesvan.</p> + +<p>Marchesvan, coinciding as it does with the rainy season in Palestine, is +considered a pure Hebrew term. The modern Jews consider it a compound +word, from mar, drop, and Chesvan; the former betokening that it was wet, +and the latter being the proper name of the month. Hence the name +indicates the wet month. In the second place we have the names of six +others which appear in the Bible subsequently to the Babylonian captivity, +viz.: Sivan, the third; Elul, the sixth; Kislev, the ninth; Tebet, the +tenth; Sebat, the eleventh, and Adar, the twelfth. There are two other +months whose names do not appear in the Bible, viz.: Tamuz, the fourth, +and Ab, the fifth. The name of the intercalary month is called Ve-Adar, or +2d Adar because placed in the calendar after Adar and before Nisan.</p> + +<p><span class="pagenum"><a name="Page_127" id="Page_127">[Pg 127]</a></span>Dr. Smith says these names are probably borrowed from the Syrians in whose +regular calendar we find names answering to most of them. He also says it +was the opinion of the Talmudists, that these names were introduced by the +Jews who returned from the Babylonish captivity, and also that they are +certainly used exclusively by writers of the post-Babylonian period.</p> + +<p>Inasmuch as the Hebrew months coincided with the seasons, as we have +already shown, it follows as a matter of course, that an additional month +must have been inserted every third year, which would bring the number up +to thirteen. No notice, however, is taken of this month in the Bible, +neither have we reason to think that it was inserted according to any +exact rule, but it was added whenever it was discovered that the barley +harvest did not coincide with the ordinary return of the month Abib. It +has already been shown that in the modern Jewish calendar the intercalary +month is introduced seven times in nineteen years, according to the +Metonic, or lunar cycle which was adopted by the Jews about 360 A. D.</p> + +<p>The Hebrew calendar is dated from the creation, which is supposed to have +taken place 3761 years before Christ. Hence, to find the number of cycles +elapsed since the creation, also the number in the cycle, we have the +following rule: Add 3761 to the date, divide the sum by nineteen; the +quotient is the number of cycles, and the remainder is the number in the +cycle. Should there be no remainder, the proposed year is, of course, the +last or nineteenth of the cycle. Thus, for the year 1883, we have 1883 + +3761 ÷ 19 = 297, remainder 1; therefore, 297 is the number of<span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span> cycles, and +1 the number in the cycle. Again, for the year 1893, we have 1893 + 3761 ÷ +19 = 297, remainder 11; therefore 297 is the number of cycles, and 11 the +number in the cycle. Again for the year 1901, we have 1901 + 3761 ÷ 19 = +298, remainder 0; therefore 298 is the number of cycles, and 19 the last +of the cycle. Hence it may be seen that the present cycle commenced with +1883, that 11 is the number in the cycle for the present year 1893, also +that the cycle ends with 1901; so that the next cycle commences with 1902. +If the remainder after dividing by nineteen be 3, 6, 8, 11, 14, 17 or 19 +(0), the year is intercalary or embolismic, consisting of 384 days; if +otherwise it is ordinary, containing only 354 days; so that in a cycle of +nineteen years, we have twelve ordinary years of 354 days each, and seven +embolismic years of 384 days each. But, in either case, the year is +sometimes made a day more, and sometimes a day less, in order that certain +festivals may fall on proper days of the week for their due observance. +Hence the ordinary year may consist of 353, 354 or 355 days, and the +embolismic year of 383, 384 or 385 days.</p> + +<p>In the modern Jewish calendar the New Year commences with the new moon of +Tisri, which may happen as early as the 5th of September or as late as the +5th of October. The new moon of Nisan, which is the first month in the +Sacred year, may happen as early as the 11th of March or as late as the +11th of April. It should be borne in mind that the names of the months +Abib, Zif, Ethanim and Bul were superceded after the captivity, by Nisan, +Iyar, Tisri and Hesvan or Marchesvan; also the name of the third month in +the civil<span class="pagenum"><a name="Page_129" id="Page_129">[Pg 129]</a></span> year, Chisleu in the Bible, Kislev in the modern Jewish +calendar. In table No. 1 we have the names of the months in numerical +order, also the number of days in each month. Though the months consist of +30 and 29 days alternately, yet, in the embolismic year, Adar, which in +common years has 29 days, is given 30 days, and 2d Adar 29; so that two +months of 30 days come together. Table No. 2 shows the earliest and the +latest possible date of the new moons of each of the months respectively.</p> + +<p class="center"><br />TABLE 1. HEBREW MONTHS.</p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td align="center"><i>Sacred Year.</i></td><td class="br"> </td><td align="center"><i>Civil Year.</i></td></tr> +<tr><td>Nisan</td><td class="br">30</td><td class="dent">Tisri</td><td>30</td></tr> +<tr><td>Iyar</td><td class="br">29</td><td class="dent">Hesvan</td><td>29</td></tr> +<tr><td>Sivan</td><td class="br">30</td><td class="dent">Kislev</td><td>30</td></tr> +<tr><td>Tamuz</td><td class="br">29</td><td class="dent">Tebet</td><td>29</td></tr> +<tr><td>Ab</td><td class="br">30</td><td class="dent">Sebat</td><td>30</td></tr> +<tr><td>Elul</td><td class="br">29</td><td class="dent">Adar</td><td>30</td></tr> +<tr><td>Tisri</td><td class="br">30</td><td class="dent">2d Adar, Embolismic</td><td>29</td></tr> +<tr><td>Hesvan</td><td class="br">29</td><td class="dent">Nisan</td><td>30</td></tr> +<tr><td>Kislev</td><td class="br">30</td><td class="dent">Iyar</td><td>29</td></tr> +<tr><td>Tebet</td><td class="br">29</td><td class="dent">Sivan</td><td>30</td></tr> +<tr><td>Sebat</td><td class="br">30</td><td class="dent">Tamuz</td><td>29</td></tr> +<tr><td>Adar</td><td class="br">30</td><td class="dent">Ab</td><td>30</td></tr> +<tr><td>2d Adar, Embolismic</td><td class="br">29</td><td class="dent">Elul</td><td>29</td></tr></table> + + +<p class="center"><br />TABLE II. HEBREW MONTHS.</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>Nisan,</td> + <td>March 11th</td> + <td>or</td> + <td>April 11th</td></tr> +<tr><td>Iyar,</td> + <td>April 11th</td> + <td align="center">"</td> + <td>May 10th</td></tr> +<tr><td>Sivan,</td> + <td>May 10th</td> + <td align="center">"</td> + <td>June 9th</td></tr> +<tr><td>Tamuz,</td> + <td>June 9th</td> + <td align="center">"</td> + <td>July 9th</td></tr> +<tr><td>Ab,</td> + <td>July 9th</td> + <td align="center">"</td> + <td>August 7th</td></tr> +<tr><td>Elul,</td> + <td>August 7th</td> + <td align="center">"</td> + <td>September 5th</td></tr> +<tr><td><span class="pagenum"><a name="Page_130" id="Page_130">[Pg 130]</a></span>Tisri,</td> + <td>September 5th</td> + <td align="center">"</td> + <td>October 5th</td></tr> +<tr><td>Hesvan,</td> + <td>October 6th</td> + <td align="center">"</td> + <td>November 4th</td></tr> +<tr><td>Kislev,</td> + <td>November 4th</td> + <td align="center">"</td> + <td>December 3d</td></tr> +<tr><td>Tebet,</td> + <td>December 3d</td> + <td align="center">"</td> + <td>January 2d</td></tr> +<tr><td>Sebat,</td> + <td>January 3d</td> + <td align="center">"</td> + <td>February 10th</td></tr> +<tr><td>Adar,</td> + <td>February 10th</td> + <td align="center">"</td> + <td>March 12th</td></tr></table> + +<p><br />The charts on the three following pages are used to illustrate the +correspondence of the Hebrew months with our own. Each chart represents +the ecliptic, which is the apparent path of the Sun or real path of the +Earth, also the names of the months as they occur in their seasons. The +figures represent the days of the month on which the new moons of the +Hebrew calendar fall. These charts represent the month and the day of the +month on which both the Sacred and the Civil year begins and ends for +three successive years. Hence it may be seen that by intercalating a month +every three years the new moons are restored, very nearly, to the place +they occupied three years before.</p> + +<p> <span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span></p> +<p class="center">CHART I.</p> +<div class="figcenter"><img src="images/chart_001tmb.jpg" alt="This chart represents the day of the month on which all the +new moons fall in the year 1891-92. The sacred year commenced with the new +moon of Nisan on the 9th of April, and the civil year with the new moon of +Tisri on the 3d of October, 1891, and ended respectively with the 28th of March and the 21st of September, 1892." /><br /> +<a href="images/chart_001.jpg"><small>Larger Image</small></a></div> +<p> </p> + + +<p> <span class="pagenum"><a name="Page_132" id="Page_132">[Pg 132]</a></span></p> +<p class="center">CHART II.</p> +<div class="figcenter"><img src="images/chart_002tmb.jpg" alt="This chart represents the day of the month on which all the +new moons fall in the year 1892-93. It may be here seen that the year +begins and ends about eleven days earlier than the year preceding, also +that all the new moons fall eleven days earlier than they did in the preceding year." /><br /> +<a href="images/chart_002.jpg"><small>Larger Image</small></a></div> +<p> </p> + + +<p> <span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span></p> +<p class="center">CHART III.</p> +<div class="figcenter"><img src="images/chart_003tmb.jpg" alt="This chart represents the year 1893-94. Though the year +begins about eleven days earlier than the preceding, viz.: the 17th of +March, yet it being the year in which a 2d Adar is intercalated, instead +of falling back eleven days, the beginning of the following year is +carried forward 20 days, making a year of 384 days; so that the year +1894-95 will commence with April 5. In 1891 we commenced with April 9. It +will be 19 years before we commence on the 9th of April again." /><br /> +<a href="images/chart_003.jpg"><small>Larger Image</small></a></div> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><span class="pagenum"><a name="Page_134" id="Page_134">[Pg 134]</a></span></p> +<h2>APPENDIX.</h2> + +<p><a name="appena" id="appena"></a></p> +<p class="center"><br />A.—PAGE <a href="#Page_12">12</a>.</p> + +<p>Authors differ in regard to the length of the solar year. One gives 365 +days, 5 hours, 47 minutes and 51.5 seconds; another, 365 days, 5 hours, 48 +minutes and 46 seconds; and still another, 365 days, 5 hours, 48 minutes +and 49.62 seconds. In this work the last has been accepted as the true +length of the solar year, and all calculations have been made accordingly.</p> + +<p><a name="appenb" id="appenb"></a></p> +<p class="center"><br />B.—PAGE <a href="#Page_19">19</a>.</p> + +<p>There is an apparent discrepancy among authors in regard to the +intercalary day. While one asserts that it was between the 24th and 25th +of February, another equally reliable, says that the 25th was the sexto +calendas and the 24th was the bis-sexto calendas of the Julian calendar. +Now it should be borne in mind that the Julian calendar is the basis of +our own, and is identical with it in the number of months in the year, and +in the number of days in the month. Also when the method of numbering the +days from the beginning of the month was adopted, the intercalation was +made to correspond with the intercalary day in the Julian calendar.</p> + +<p>As in the Julian calendar there were twice the sixth day, so in the +reformed calendar there were twice the 24th day, which was equivalent to +29 days in February. When the calendar was again corrected, making the +29th the intercalary day, then the 24th corresponded with the bis-sexto +calendas of the Julian calendar.<span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span> This reconciles the apparent +discrepancy. While one author refers to the calendar in which the Julian +rule of intercalation is adopted, another refers to the calendar when so +corrected as to make the 29th of February the intercalary day. See +following table:</p> + +<table border="0" cellpadding="0" cellspacing="0" summary="table"> +<tr><td align="center" colspan="3" class="btrdoub">JULIAN METHOD<br />OF INTERCALATION.</td> + <td align="center" colspan="3" class="bt">MODERN METHOD<br />OF INTERCALATION.</td></tr> +<tr><td align="right" class="btr">1</td> + <td align="center" class="btr"><i>Cal.</i></td> + <td class="btrdoub">Calendae</td> + <td align="right" class="btr">1</td> + <td align="center" class="btr"><i>Cal.</i></td> + <td class="bt">Calendae</td></tr> +<tr><td align="right" class="br">2</td> + <td align="center" class="br"><span style="margin-left: .5em;">4</span></td> + <td class="brdoub">Quarto Nonas</td> + <td align="right" class="br">2</td> + <td align="center" class="br"><span style="margin-left: .5em;">4</span></td> + <td class="dent">Quarto Nonas</td></tr> +<tr><td align="right" class="br">3</td> + <td align="center" class="br"><span style="margin-left: .5em;">3</span></td> + <td class="brdoub">Tertio Nonas</td> + <td align="right" class="br">3</td> + <td align="center" class="br"><span style="margin-left: .5em;">3</span></td> + <td class="dent">Tertio Nonas</td></tr> +<tr><td align="right" class="br">4</td> + <td align="center" class="br"><span style="margin-left: .5em;">2</span></td> + <td class="brdoub">Pridie Nonas</td> + <td align="right" class="br">4</td> + <td align="center" class="br"><span style="margin-left: .5em;">2</span></td> + <td class="dent">Pridie Nonas</td></tr> +<tr><td align="right" class="br">5</td> + <td align="center" class="br"><i>Nomes</i></td> + <td class="brdoub"><span class="spacer"> </span>Nonae</td> + <td align="right" class="br">5</td> + <td align="center" class="br"><i>Nomes</i></td> + <td class="dent"><span class="spacer"> </span>Nonae</td></tr> +<tr><td align="right" class="br">6</td> + <td align="center" class="br"><span style="margin-left: .5em;">8</span></td> + <td class="brdoub">Octavo Idus</td> + <td align="right" class="br">6</td> + <td align="center" class="br"><span style="margin-left: .5em;">8</span></td> + <td class="dent">Octavo Idus</td></tr> +<tr><td align="right" class="br">7</td> + <td align="center" class="br"><span style="margin-left: .5em;">7</span></td> + <td class="brdoub">Septimo Idus</td> + <td align="right" class="br">7</td> + <td align="center" class="br"><span style="margin-left: .5em;">7</span></td> + <td class="dent">Septimo Ides</td></tr> +<tr><td align="right" class="br">8</td> + <td align="center" class="br"><span style="margin-left: .5em;">6</span></td> + <td class="brdoub">Sexto Idus</td> + <td align="right" class="br">8</td> + <td align="center" class="br"><span style="margin-left: .5em;">6</span></td> + <td class="dent">Sexto Idus</td></tr> +<tr><td align="right" class="br">9</td> + <td align="center" class="br"><span style="margin-left: .5em;">5</span></td> + <td class="brdoub">Quinto Idus</td> + <td align="right" class="br">9</td> + <td align="center" class="br"><span style="margin-left: .5em;">5</span></td> + <td class="dent">Quinto Idus</td></tr> +<tr><td align="right" class="br">10</td> + <td align="center" class="br"><span style="margin-left: .5em;">4</span></td> + <td class="brdoub">Quarto Idus</td> + <td align="right" class="br">10</td> + <td align="center" class="br"><span style="margin-left: .5em;">4</span></td> + <td class="dent">Quarto Idus</td></tr> +<tr><td align="right" class="br">11</td> + <td align="center" class="br"><span style="margin-left: .5em;">3</span></td> + <td class="brdoub">Tertio Idus</td> + <td align="right" class="br">11</td> + <td align="center" class="br"><span style="margin-left: .5em;">3</span></td> + <td class="dent">Tertio Idus</td></tr> +<tr><td align="right" class="br">12</td> + <td align="center" class="br"><span style="margin-left: .5em;">2</span></td> + <td class="brdoub">Pridie Idus</td> + <td align="right" class="br">12</td> + <td align="center" class="br"><span style="margin-left: .5em;">2</span></td> + <td class="dent">Pridie Idus</td></tr> +<tr><td align="right" class="br">13</td> + <td align="center" class="br"><i>Ides</i></td> + <td class="brdoub"><span class="spacer"> </span>Idus</td> + <td align="right" class="br">13</td> + <td align="center" class="br"><i>Ides</i></td> + <td class="dent"><span class="spacer"> </span>Idus</td></tr> +<tr><td align="right" class="br">14</td> + <td align="center" class="br">16</td> + <td class="brdoub">Sextodecimo Calendas</td> + <td align="right" class="br">14</td> + <td align="center" class="br">16</td> + <td class="dent">Sextodecimo Calendas</td></tr> +<tr><td align="right" class="br">15</td> + <td align="center" class="br">15</td> + <td class="brdoub">Quintodecimo Calendas</td> + <td align="right" class="br">15</td> + <td align="center" class="br">15</td> + <td class="dent">Quintodecimo Calendas</td></tr> +<tr><td align="right" class="br">16</td> + <td align="center" class="br">14</td> + <td class="brdoub">Quartodecimo Calendas</td> + <td align="right" class="br">16</td> + <td align="center" class="br">14</td> + <td class="dent">Quartodecimo Calendas</td></tr> +<tr><td align="right" class="br">17</td> + <td align="center" class="br">13</td> + <td class="brdoub">Tertiodecimo Calendas</td> + <td align="right" class="br">17</td> + <td align="center" class="br">13</td> + <td class="dent">Tertiodecimo Calendas</td></tr> +<tr><td align="right" class="br">18</td> + <td align="center" class="br">12</td> + <td class="brdoub">Duodecimo Calendas</td> + <td align="right" class="br">18</td> + <td align="center" class="br">12</td> + <td class="dent">Duodecimo Calendas</td></tr> +<tr><td align="right" class="br">19</td> + <td align="center" class="br">11</td> + <td class="brdoub">Undecimo Calendas</td> + <td align="right" class="br">19</td> + <td align="center" class="br">11</td> + <td class="dent">Undecimo Calendas</td></tr> +<tr><td align="right" class="br">20</td> + <td align="center" class="br">10</td> + <td class="brdoub">Decimo Calendas</td> + <td align="right" class="br">20</td> + <td align="center" class="br">10</td> + <td class="dent">Decimo Calendas</td></tr> +<tr><td align="right" class="br">21</td> + <td align="center" class="br"><span style="margin-left: .5em;">9</span></td> + <td class="brdoub">Nono Calendas</td> + <td align="right" class="br">21</td> + <td align="center" class="br"><span style="margin-left: .5em;">9</span></td> + <td class="dent">Nono Calendas</td></tr> +<tr><td align="right" class="br">22</td> + <td align="center" class="br"><span style="margin-left: .5em;">8</span></td> + <td class="brdoub">Octavo Calendas</td> + <td align="right" class="br">22</td> + <td align="center" class="br"><span style="margin-left: .5em;">8</span></td> + <td class="dent">Octavo Calendas</td></tr> +<tr><td align="right" class="br">23</td> + <td align="center" class="br"><span style="margin-left: .5em;">7</span></td> + <td class="brdoub">Septimo Calendas</td> + <td align="right" class="br">23</td> + <td align="center" class="br"><span style="margin-left: .5em;">7</span></td> + <td class="dent">Septimo Calendas</td></tr> +<tr><td align="right" class="br">24</td> + <td align="center" class="br"><span style="margin-left: .5em;">6</span></td> + <td class="brdoub">Bis-Sexto Calendas</td> + <td align="right" class="br">24</td> + <td align="center" class="br"><span style="margin-left: .5em;">6</span></td> + <td class="dent">Bis-sexto Calendas</td></tr> +<tr><td align="right" class="br">24</td> + <td align="center" class="br"><span style="margin-left: .5em;">6</span></td> + <td class="brdoub">Sexto Calendas</td> + <td align="right" class="br">25</td> + <td align="center" class="br"><span style="margin-left: .5em;">6</span></td> + <td class="dent">Sexto Calendas</td></tr> +<tr><td align="right" class="br">25</td> + <td align="center" class="br"><span style="margin-left: .5em;">5</span></td> + <td class="brdoub">Quinto Calendas</td> + <td align="right" class="br">26</td> + <td align="center" class="br"><span style="margin-left: .5em;">5</span></td> + <td class="dent">Quinto Calendas</td></tr> +<tr><td align="right" class="br">26</td> + <td align="center" class="br"><span style="margin-left: .5em;">4</span></td> + <td class="brdoub">Quarto Calendas</td> + <td align="right" class="br">27</td> + <td align="center" class="br"><span style="margin-left: .5em;">4</span></td> + <td class="dent">Quarto Calendas</td></tr> +<tr><td align="right" class="br">27</td> + <td align="center" class="br"><span style="margin-left: .5em;">3</span></td> + <td class="brdoub">Tertio Calendas</td> + <td align="right" class="br">28</td> + <td align="center" class="br"><span style="margin-left: .5em;">3</span></td> + <td class="dent">Tertio Calendas</td></tr> +<tr><td align="right" class="bbr">28</td> + <td align="center" class="bbr"><span style="margin-left: .5em;">2</span></td> + <td class="bbrdoub">Pridie Calendas</td> + <td align="right" class="bbr">29</td> + <td align="center" class="bbr"><span style="margin-left: .5em;">2</span></td> + <td class="bb">Pridie Calendas</td></tr></table> + + +<p><span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span></p> +<p><a name="appenc" id="appenc"></a></p> +<p class="center"><br />C.—PAGE <a href="#Page_20">20</a>.</p> + +<p>The city where the great council was convened in 325 is not in France, as +some have supposed, that being a more modern city of the same orthography, +but pronounced Nees. The city which is so frequently referred to in this +work is in Bythinia, one of the provinces of Asia Minor, situated about 54 +miles southeast of Constantinople, of the same orthography as the former, +but pronounced Ni´ce, and was so named by Lysimachus, a Greek general, +about 300 years before Christ, in honor of his wife Nicea.</p> + +<p><a name="append" id="append"></a></p> +<p class="center"><br />D.—PAGE <a href="#Page_23">23</a>.</p> + +<p>Between the 23d and 24th of February, 46 years before Christ, there was +intercalated a month of 23 days according to an established method, but +still the civil year was in advance of the solar year by 67 days; so that +when the Earth in her annual revolutions should arrive to that point of +the ecliptic marked the 22d of October, it would be the 1st day of January +in the Roman year.</p> + +<p>Cæsar and his astronomers, knowing this fact and fixing on the 1st day of +January, 45 years before Christ and 709 from the foundation of Rome, for +the reformed calendar to take effect, were under the necessity of +intercalating two months, together consisting of 67 days. Now, as the +civil year would end on the 22d of October, true or solar time, it would +be reckoned in the old calendar the 1st day of January; so they let the +old calendar come to a stand while the Earth performs 67 diurnal +revolutions, and thereby restored the concurrence of the solar and the +civil year.</p> + +<p><span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span>As an illustration, let us suppose that in a certain shop where hangs a +regulator are two clocks to be regulated. Both are set with the regulator +at 8 a. m. to see how they will run for ten consecutive hours. It was +found that when it was 6 p. m., by the first clock, it was 5:50 by the +regulator, the clock having gained one minute every hour.</p> + +<p>To rectify this discrepancy we must intercalate 10 minutes by stopping the +clock until it is 6 by the regulator. By this means the coincidence is +restored, and the time lost in the preceding hours is now reckoned in this +last hour, making it to consist of 70 minutes. By this it may be seen how +Cæsar reformed the Roman calendar. The Roman year was too short, by reason +of which the calendar was thrown into confusion, being 90 days in advance +of the true time, so that December, January and February took the place in +the seasons of September, October and November, and September, October and +November the place of June, July and August. To make the correction he +must stop the old Roman clock (the calendar) while the Earth performs 90 +diurnal revolutions to restore the concurrence of the solar and the civil +year, making the year 46 B. C. to consist of 445 days.</p> + +<p>It was also found that when it was 6 p. m., by the regulator, it was only +5:50 by the second clock, it having lost one minute every hour. To rectify +this discrepancy we must suppress 10 minutes, calling it 6 p. m., turning +the hands of the clock to coincide with the regulator, making the last +hour to consist of only 50 minutes, too much time having been reckoned in +the preceding hours. It may be seen by this <span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span>illustration, how Gregory +corrected the Julian calendar, the Julian year was too long, consequently +behind true or solar time, so that when the correction was made in 1582, +the ten days gained had to be suppressed to restore the coincidence, +making the year to consist of only 355 days.</p> + +<p>As the solar year consists of 365 days and a fraction, Cæsar intended to +retain the concurrence of the solar and the civil year by intercalating a +day every four years; but this made the year a little too long, by reason +of which it became necessary, in 1582, to rectify the error, and by +adopting the Gregorian rule, three intercalations are suppressed every 400 +years; so that by a series of intercalations and suppressions, our +calendar may be preserved in its present state of perfection.</p> + +<p><a name="appene" id="appene"></a></p> +<p class="center"><br />E.—PAGE <a href="#Page_23">23</a>.</p> + +<p>As the day and the civil year always commence at the same instance, so +they must end at the same instance; and as the solar year always ends with +a fraction, not only of a day, but of an hour, a minute and even a second; +so there is no rule of intercalation by which the solar and the civil year +can be made to coincide exactly. But the discrepancy is only a few hours +in a hundred years, and that is so corrected by the Gregorian rule of +intercalation that it would amount to a little more than a day in 4,000 +years; and by the improved method less than a day in 100,000 years.</p> + +<p><a name="appenf" id="appenf"></a></p> +<p class="center"><br />F.—PAGE <a href="#Page_26">26</a>.</p> + +<p>It has been stated that by adopting the Julian rule of intercalation, time +was gained; it has also been stated that by the same rule time was lost. +Now both<span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span> are true. Time is gained in that there is too much time in a +given year, in other words, the year is too long; but what is gained in a +given year is lost to the following year.</p> + +<p>As an illustration let us take the case of the supposed solar year of 365 +days, and the civil year of 366. The civil year would gain one day every +year, or be too long by one day; but the one day gained is lost to the +following years, and if continued 31 years, when the Earth is in that part +of its orbit marked the 1st day of January 32, the civil year would reckon +the 1st day of December 31; so that in the thirty-one years would reckon +thirty-one days too much, and before the civil year is completed, the +Earth will have passed on in its orbit to a point marked the 1st day of +February.</p> + +<p>Now to reform such a calendar, we would have to suppress or drop the +thirty-one days, by calling the 1st day of December the 1st day of +January, and thus the month of December would disappear from the calendar +in the year 31, making a year of only eleven months, consisting of 334 +days.</p> + +<p>If this method be continued 92 years, there would be gained 92 days, to +the loss of 92 days in the year 92. If the calendar be now reformed by +suppressing 92 days, calling the 1st day of October, 92, the 1st day of +January, 93, then October, November and December would disappear from the +calendar in the year 92; and if continued 365 years there would be crowded +into 364 years, 364 days too much; gained to the 364 years to the total +loss of the year 365, passing from 364 to 366; 365 disappearing from the +calendar.</p> + + +<p><span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span></p> +<p><a name="appeng" id="appeng"></a></p> +<p class="center"><br />G.—PAGE <a href="#Page_50">50</a>.</p> + +<p>An era is a fixed point of time from which a series of years is reckoned. +Among the nations of the Earth there are no less than twenty-five +different eras; but the most of them are not of enough importance to be +mentioned here. Attention is particularly called to the Roman era which +commenced with the building of the city of Rome 753 years before Christ.</p> + +<p>Also the Mahometan era, or the era of the Hegira, employed in Turkey, +Persia and Arabia, which is dated from the flight of Mahomet from Mecca to +Medina, which was Thursday night, the 15th of July, A. D., 622, and it +commenced on Friday, the day following.</p> + +<p>But there is a point from which all computation originally commenced, +namely, the creation of man. Such an era is called the Mundane era. Now +there are different Mundane eras—the common Mundane era 4,004 B. C., the +Grecian Mundane era 5,598 B. C., and the Jewish Mundane era 3,761 B. C. +All these commence computation from the same point, but differ in regard +to the time which has elapsed since their computation commenced. God’s +people used the Mundane era, until the Great Creator appeared among us, as +one of us, in the person of our Lord Jesus Christ, to accomplish the great +work of redemption; then His name was introduced as the turning point of +the ages, the starting point of computation.</p> + +<p>This was done by Dionysius Exiguus in the year of our Lord about 540, +known at that time as the Dionysian, as well as the Christian era, and was +first used in historical works by the venerable Bede early in the<span class="pagenum"><a name="Page_141" id="Page_141">[Pg 141]</a></span> eighth +century. “It was a great thought of the little monk (whether so called +from his humility or littleness of stature is unknown), to view Christ as +the turning point of the ages, and to introduce this view into +chronology.”</p> + +<p>All honor to him who introduced it, and to the nations which have +approved, for thus honoring the Great Redeemer. Dionysius probably did not +know, neither is it now known for a certainty the year of Christ’s birth, +but it is evident, however, from the best authorities, that the era +commenced at least five years too late, and probably more.</p> + +<p><a name="appenh" id="appenh"></a></p> +<p class="center"><br />H.—PAGE <a href="#Page_57">57</a>.</p> + +<p>It is recorded that, in the time of Numa, the vernal equinox fell on the +25th of March, and that Julius Cæsar restored it to the 25th, when he +reformed the ancient Roman calendar in the year 46 B. C. It is also +recorded that in less than 400 years from that time, at the meeting of the +Council of Nice in 325, it had fallen back to the 21st—four days in less +than 400 years.</p> + +<p>Now there is an error somewhere, for it is found by actual computation +that the discrepancy between the solar and the Julian year is about three +days in 400 years. It certainly is true that the vernal equinox fell on +the 21st in 325, and was restored to that place by Gregory in 1582; since +which time it has been made to fall on the 21st by the Gregorian rule of +intercalation. Again it is stated by the same author that the +discrepancies in time from Cæsar to Gregory is thirteen days, from the +Council of Nice to Gregory ten days; now 10 + 4 = 14. While our author +states it is thirteen days, he also states it is fourteen days; a +<span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span>discrepancy of one day. The mistake evidently is in making the 25th +instead of the 24th, the date of the vernal equinox in the time of Cæsar, +consequently a difference of four days instead of three from Cæsar to the +Council of Nice.</p> + +<p><a name="appeni" id="appeni"></a></p> +<p class="center"><br />I.—PAGE <a href="#Page_59">59</a>.</p> + +<p>The concurrence of the solar and the civil year was restored by Gregory in +1582, or 1600 is the same in computation; but the discrepancy between +civil and solar time is 11 minutes and 10.38 seconds every year, which in +100 years will amount to 18 hours, and 37.3 minutes; reckoned in round +numbers 18 hours, and is represented on the chart, hours behind time 18.</p> + +<p>The intercalary day or 24 hours being suppressed in 1700, causes the civil +year to be 6 hours in advance of the solar, and is represented on the +chart 6 hours in advance.</p> + +<p>Now this discrepancy of 18 hours for the next 100 years, will cause the +civil year in 1800 to be 12 hours behind; again suppressing the +intercalation it will be 12 hours in advance. In 1900 it will be 6 hours +behind, but the correction makes 18 hours in advance. The 18 hours gained +the next 100 years restores the coincidence in the year 2000 and so on, +the solar and the civil year being made to coincide very nearly every 400 +years.</p> + +<p>From close examination it will become evident that the solar and the civil +year coincide twice every 400 years, though no account is made of it in +computation. From 6 hours in advance in 1700, the civil year falls back to +12 hours behind the solar in 1800, consequently they must coincide in +1733.</p> + +<p><span class="pagenum"><a name="Page_143" id="Page_143">[Pg 143]</a></span>Again from 12 hours in advance in 1800, it falls back to 6 hours behind +the solar in 1900, consequently they must coincide again in 1867.</p> + +<p>Discrepancy between Julian and solar time in—1 year is (365d. 6h.) - (365d. 5h. 48m. 49.62s.) = (11m. 10.38s.)</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>100</td><td>years is</td><td>(11m. 10.38s.) × 100 = (18h. 37.3.)</td></tr> +<tr><td>400</td><td align="center">"</td><td>(18h. 37.3m.) × 4 = (3d. 2h. 29.2m.)</td></tr> +<tr><td>4,000</td><td align="center">"</td><td>(3d. 2h. 29.2m.) × 10 = (31d. 0h. 52m.)</td></tr> +<tr><td>100,000</td><td align="center">"</td><td>(31d. 0h. 52m.) × 25 = (773d. 21h. 40m.)</td></tr></table> + +<p>Discrepancy between Gregorian and solar time in—</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td>1</td><td>year is</td><td> </td><td align="right">.373m.</td></tr> +<tr><td>100</td><td>years is</td><td>.373m. × 100 =</td><td align="right">37.3m.</td></tr> +<tr><td>400</td><td>years</td><td>37.3m. × 4 =</td><td align="right">2h. 29.2m.</td></tr> +<tr><td>4,000</td><td align="center">"</td><td>(2h. 29.2m.) × 10 =</td><td align="right">1d. 0h. 52m.</td></tr> +<tr><td>100,000</td><td align="center">"</td><td>(1d. 0h. 52m.) × 25 =</td><td align="right">25d. 21h. 40m.</td></tr></table> + +<p>Discrepancy between corrected Gregorian and solar time in—</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td align="right">4,000</td><td>years is</td><td>(1d. 0h. 52m.) - 1 day =</td><td align="right">52m.</td></tr> +<tr><td align="right">100,000</td><td> " "</td><td>(52m. × 25) =</td><td align="right">21h. 40m.</td></tr></table> + +<p><a name="appenj" id="appenj"></a></p> +<p class="center"><br />J.—PAGE <a href="#Page_89">89</a>.</p> + +<p>Lilius, author of the “Extended Table of Epacts,” says, when the full moon +falls on the 10th of March, the following moon, which happens 29 days +later, is the paschal moon, making the 18th of April its latest possible +date. For, says he, because of the double epact that occurs on the 4th and +5th of April that lunation has only 29 days. It may have been very +convenient for Lilius, in his peculiar method of determining the date of +the paschal moon, to give to that lunation only 29 days; but nevertheless, +when he did so, it was at the expense of accuracy, for he makes a +difference of<span class="pagenum"><a name="Page_144" id="Page_144">[Pg 144]</a></span> 12 days in the date of the paschal moon of that year, and +the year preceding, and only 10 days difference between that year and the +succeeding year; whereas the difference is uniformly 11 days from year to +year through the whole cycle of 19 years.</p> + +<p>By referring to the table on the 93d page, it will be seen that, in fixing +the date of the paschal moon, six times in a cycle of 19 years the full +moon falls before the 21st of March, and in every instance except this one +the following moon is reckoned by Lilius 30 days later. By this uniform +method of determining the date of the paschal moon, we make the 19th of +April instead of the 18th, its latest possible date; so it should be borne +in mind that whenever the 19th of April is the date of the paschal moon, +as indicated in the tables commencing with the 93d page, that Lilius, and +probably most, if not all other authors, have the 18th.</p> + +<p>Now it is admitted that notwithstanding the cumbersome apparatus employed +by Lilius in his calculations, the conditions of the problem are not +always satisfied, nor is it possible that they can be always satisfied by +any similar method of proceeding. We admit that none of these calculations +are perfectly exact, but the sum of the solar and lunar inequalities is +compensated in the whole period, or corrections made at the end of certain +periods, not by interrupting the order of a uniform method during the +cycle of 19 years.</p> + +<p>Now the table of epacts was introduced by Lilius himself, making the +excess of the solar year beyond the lunar, in round numbers 11 days. Then +why interrupt this order every 19 years, for a period of 114 years; that +is from 1596 to 1710, by making the epact<span class="pagenum"><a name="Page_145" id="Page_145">[Pg 145]</a></span> 12 days for one year, and the +following year only 10? After which, from 1710 to 1900, a period of 190 +years, according to Lilius’ own calculations, the epact is uniformly 11 +days, coinciding exactly with the calculations made in this work.</p> + +<p>Then again after the year 1900, he gives to that particular lunation, in +every lunar cycle for a period of 304 years, only 29 days; and having done +so, he is under the necessity of giving only 29 days to another lunation +in the same cycle, and also to all the cycles in the period to avoid the +absurdity of making the paschal moon fall twice on the same day in the +course of a lunar cycle.</p> + +<p>By reference to the 101st page, opposite the year 1905, it will be seen +that the date of the paschal moon is the 19th of April. Lilius, by giving +to that lunation only 29 days, makes its date the 18th; and then again in +the year 1916, lest he should make the paschal moon fall twice on the 18th +of April in the course of a lunar cycle, (a thing which cannot really +occur) he for the first time in more than 400 years, gives only 29 days to +a second lunation in the same cycle and of course to all the cycles in the +period of 304 years. Now the epacts for a lunar cycle of 19 years are +represented thus:</p> + +<table border="0" cellpadding="0" cellspacing="5" summary="table"> +<tr><td colspan="10"> </td><td align="center" class="botbor">26</td></tr> +<tr><td align="center">0,</td><td><span class="spacer2"> </span></td> + <td align="center">11,</td><td><span class="spacer2"> </span></td> + <td align="center">22,</td><td><span class="spacer2"> </span></td> + <td align="center">3,</td><td><span class="spacer2"> </span></td> + <td align="center">14,</td><td><span class="spacer2"> </span></td> + <td align="center">25,</td><td><span class="spacer2"> </span></td> + <td align="center">6,</td><td><span class="spacer2"> </span></td> + <td align="center">17,</td><td><span class="spacer2"> </span></td> + <td align="center">28,</td><td><span class="spacer2"> </span></td> + <td align="center">9,</td><td><span class="spacer2"> </span></td> + <td align="center">20</td></tr> +<tr><td colspan="10"> </td><td align="center" class="botbor">27</td></tr> +<tr><td align="center">1,</td><td> </td> + <td align="center">12,</td><td> </td> + <td align="center">23,</td><td> </td> + <td align="center">4,</td><td> </td> + <td align="center">15,</td><td> </td> + <td align="center">26,</td><td> </td> + <td align="center">7,</td><td> </td> + <td align="center">18</td></tr></table> + +<p>The number 26 placed over the 25 shows Lilius’ first error in giving to +that lunation only 29 days. He thereby makes a difference of 12 days +between the<span class="pagenum"><a name="Page_146" id="Page_146">[Pg 146]</a></span> epact 14 and 26, and only 10 between 26 and 6. He now has two +epacts of the same number 26. In order to get out of the dilemma he makes +that 27, by giving to another lunation only 29 days.</p> + +<p><a name="appenk" id="appenk"></a></p> +<p class="center"><br />K.—PAGE <a href="#Page_122">122-3</a>.</p> + +<p>It will probably be noticed that according to the showing in the tables +the ecclesiastical year contains only 364 days. The reason for this is, +that Advent Sunday, which is the first day of the year, happens one day +earlier every year until it occurs on the 27th of November, its earliest +possible date; then the first Sunday after the 26th of November, which is +Advent Sunday, falls on the 3d of December, its latest possible date, so +that the year begins six days later, making a year of 371 days. Then there +is the loss of a day every year until Advent Sunday again falls on the +27th of November and so on. Hence, did the civil year always consist of +365 days, then the ecclesiastical year would always contain either 364 or +371 days. But as every fourth year contains 366 days, this order is so +interrupted that sometimes the first Sunday falls on the 2d instead of the +3d of December; so that the year begins only five days later, making a +year of only 370 days. Hence the ecclesiastical year may consist of either +364, 370 or 371 days. But five times out of six it will contain only 364 +days.</p> + + +<p><span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span></p> +<p><a name="appenl" id="appenl"></a></p> +<p class="center"><br />L.—PAGE <a href="#Page_83">83</a>.</p> + +<p>But why did the Pope, in correcting the Julian calendar in 1582, not +correct the whole error of thirteen days? Why did he leave the three days +uncorrected? This question has been asked an hundred times, but a correct +answer has never yet been given. Some say that the Pope did according to +his best ability, and would make us believe that neither he nor his +astronomers knew what the error was. This is not true, for history records +the fact of the error, and just what that error was. He simply did not +want to correct the three days, and for good reasons, which we shall +endeavor to show; reasons which every churchman ought to know.</p> + +<p>When Cæsar formed his calendar, 46 B. C., the vernal equinox fell on the +24th of March. At the meeting of the Council of Nice, in 325, it had +fallen back to the 21st, the error being three days in about 400 years. +Now it should be borne in mind that the Julian calendar was the only one +in use at that time, and for the next 1257 years, when in 1582, it was +corrected by Pope Gregory XIII. Easter, and all the movable feasts, had +been unsettled during the 1257 years intervening, from the Council of Nice +to Gregory, on account of the errors of the Julian calendar. The Easter +question had been the cause of a good deal of discussion between the +Eastern and Western churches during the second and third centuries, as +they could not agree on the day of the week on which that event should be +celebrated.</p> + +<p>The Western churches observed the nearest Sunday to the full moon of +Nisan. The Asiatics, on the other hand, adopted the 14th of Nisan upon +which to <span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span>commemorate the crucifixion, and observed the festival of Easter +on the third day following, upon whatever day of the week that might fall. +Finally, the Council of Nice was convened, and the matter came before that +council, and a reconciliation was accomplished. It was then and there +agreed by the two parties that Easter should be celebrated on the first +Sunday after the full moon that falls upon or next following the day of +the vernal equinox, and that the 21st of March should be accounted the day +of the vernal equinox.</p> + +<p>It has already been shown that the error in the Julian calendar is three +days in 400 years; so that in 400 years from the Council of Nice the +vernal equinox had fallen back to the 18th of March; in 800 years it had +fallen back to the 15th; in 1257 years, that is in 1582, it fell on the +11th. Still the 21st of March, by the only calendar in use at that time, +was accounted the date of the vernal equinox, by which date Easter was +determined, so that, in 1582, when it was the 21st by the calendar, the +correct date was the 31st. Hence, the error had been increasing at the +rate of three days every 400 years until in 1582 it amounted to ten days.</p> + +<p>Again it should be borne in mind that the Pope was a churchman and wished +to abide by the decision of that council in celebrating the festival of +Easter, so he drops the ten days and restores the vernal equinox to the +21st of March, its date at the meeting of the Council of Nice in 325, the +date by which Easter day was determined. He not only made the correction, +but he so reformed the calendar that the solar and the civil year are now +made to coincide very nearly. Had he dropped the thirteen days, the vernal +equinox would<span class="pagenum"><a name="Page_149" id="Page_149">[Pg 149]</a></span> have been restored to the 24th of March, its date in the +time of Cæsar, and the 24th would still be its date. But the Council of +Nice decided that the 21st should be the date by which Easter day should +be determined. Hence the reason for dropping the ten days instead of the +thirteen is evident; and it is also evident that the Pope acted +understandingly when he made the correction in 1582.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<h2>ERRATA.</h2> + +<div class="note"> +<p>On 51st page, ninth line from the bottom of the page, instead of 1453 ÷ 43 += 63+, should be 1453 ÷ 4 = 363+.</p> + +<p>On 76th page, twelfth line from the top of the page, 356 should be 365.</p></div> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p class="center"><span class="huge">THE COLUMBUS CELEBRATION.</span></p> +<p class="center">THE WELLSBORO MAN WHO BROUGHT ABOUT THE CHANGE IN THE DATE.<br /> +<i>State Superintendent D. J. Waller, in the School Journal.</i></p> + +<p>Who brought about the change in the date? It was down in the books as +October 12th. The Committee of the National Educational Association issued +circulars to the country to observe that day. Congress solemnly resolved +that that day should be celebrated throughout the land. The Commissioners +of the World’s Fair fixed upon October 12, as dedication-day, and sent out +invitations to the exercises. Suddenly there was a change. Heralded by no +newspaper discussion, preceded by no exhaustive treatise, without any +authoritative decree, a change was made to October 21.</p> + +<p>The following facts are indisputable. An aged retired minister in the +Methodist Episcopal Church, living in Wellsboro, Tioga County, Pa., author +of a little book entitled “Our Calendar,” Rev. George Nichols Packer, saw +the error. He possessed the confidence of Judge Henry W. Williams, of the +Supreme Court of Pennsylvania. After laying the facts before him, he +secured through him the approval by the several Justices composing that +body, of an effort to change to the proper date, October 21st. Equipped +with this approval, he secured the endorsement of his project by Governor +Pattison and some of the heads of the Executive departments at Harrisburg. +He then went to Washington, gained an audience with the President, laid +the subject before the member of Congress from his district, and went +before the Congressional Committee.</p> + +<p>The evidence in support of the proposition was so presented that it could +not be successfully disputed. Congressman W. A. Stone skillfully enlisted +influential collegiates in an effort to correct the error already widely +spread. The correction by the National Legislature was in time to have its +influence upon President Harrison, who named October 21 in his +proclamation, as the day to be observed, and Boston and Chicago fell into +line.</p> + +<p>All honor to Rev. George Nichols Packer, of Wellsboro, Tioga County, +Pennsylvania.</p> + + +<p> </p><p> </p> +<hr style="width: 50%;" /> +<p><strong>Transcriber’s Notes:</strong></p> + +<p>Punctuation has been corrected without note.</p> + +<p>Other than the corrections noted by hover information, inconsistencies in +spelling and hyphenation have been retained from the original.</p> + +<p>Errata corrections, noted by red underline, have been made in this text by the transcriber.</p> + + + + + + + + +<pre> + + + + + +End of the Project Gutenberg EBook of Our Calendar, by George Nichols Packer + +*** END OF THIS PROJECT GUTENBERG EBOOK OUR CALENDAR *** + +***** This file should be named 36197-h.htm or 36197-h.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/3/6/1/9/36197/ + +Produced by Bryan Ness and the Online Distributed +Proofreading Team at http://www.pgdp.net (This file was +produced from images generously made available by The +Internet Archive.) + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Our Calendar + +Author: George Nichols Packer + +Release Date: May 23, 2011 [EBook #36197] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK OUR CALENDAR *** + + + + +Produced by Bryan Ness and the Online Distributed +Proofreading Team at http://www.pgdp.net (This file was +produced from images generously made available by The +Internet Archive.) + + + + + + + + + + OUR CALENDAR. + + + The Julian Calendar and Its Errors. + + HOW CORRECTED BY THE GREGORIAN. + + + Rules For Finding the Dominical Letter, + + AND THE DAY OF THE WEEK OF ANY EVENT FROM THE + DAYS OF JULIUS CAESAR 46 B. C. TO THE YEAR OF + OUR LORD FOUR THOUSAND--A NEW AND EASY + METHOD OF FIXING THE DATE OF EASTER. + + + HEBREW CALENDAR; + + SHOWING THE CORRESPONDENCE IN THE DATE OF + EVENTS RECORDED IN THE BIBLE WITH OUR + PRESENT GREGORIAN CALENDAR. + + + ILLUSTRATED BY VALUABLE TABLES AND CHARTS. + + + BY REV. GEORGE NICHOLS PACKER, + CORNING, N. Y. + + + + + Entered according to Act of Congress, in 1890, 1892 and 1893, + BY REV. GEORGE NICHOLS PACKER, + In the Office of the Librarian of Congress, Washington, D. C. + ALL RIGHTS RESERVED. + + + WILLIAMSPORT, PA.: + FRED R. MILLER BLANK BOOK CO. + 1893. + + + + +TO HON. HENRY W. WILLIAMS, JUSTICE OF THE SUPREME COURT OF PENNSYLVANIA +WHOM I HAVE FOUND A TRUE FRIEND IN POVERTY AND IN SICKNESS, AND FROM WHOM +I HAVE RECEIVED WORDS OF ENCOURAGEMENT AND COMFORT DURING MANY YEARS OF +ADVERSITY, AND AT WHOSE SUGGESTION THIS LITTLE VOLUME HAS BEEN WRITTEN, +AND BY WHOSE ASSISTANCE IT IS NOW PUBLISHED, THIS HUMBLE VOLUME IS +DEDICATED AS A TRIBUTE OF RESPECT BY THE AUTHOR. + + + + +PREFACE. + + +Many years ago, while engaged in teaching, the writer of this little +volume was in the habit of bringing to the attention of his pupils a few +simple rules for finding the dominical letter and the day of the week of +any given event within the past and the present centuries; further than +this he gave the subject no special attention. + +A few years ago, having occasion to learn the day of the week of certain +events that were transpiring at regular intervals on the same day of the +same month, but in different years, he was led to investigate the subject +more thoroughly, so that he is now able to give rules for finding the +dominical letter and the day of the week of any event that has transpired +or will transpire, from the commencement of the Christian era to the year +of our Lord 4,000, and to explain the principles on which these rules +rest. When the investigations were entered upon he had no thought of +writing a book; but having been laid aside from active labor by ill +health, he found relief from the despondency in which sickness and poverty +plunged him by pursuing the study of the calendar, its history, and the +method of disposing of the fraction of a day found in the time required +for the revolution of the Earth in its orbit about the Sun. + +He became so much interested in the study of this subject that he +frequently spoke of it to friends and acquaintances whom he met. On one +occasion, while speaking to Hon. H. W. Williams about some of the curious +results of the process by which the coincidence of the solar and the civil +year is preserved, it was suggested to him that he should put the story of +the calendar, its correction by Gregory, and the theory and results of +intercalation, in writing. It was urged that this would give increased +interest to the study, help the writer to forget his pains, and probably +enable him to realize a little money from the sale of his work to meet +pressing wants. Acting upon this suggestion, an effort has been made to +put into this little volume some of the most interesting facts relating to +the origin, condition, and practical operation of the calendar now in use; +together with rules for finding the day of the week on which any given day +of any month has fallen or will fall during four thousand years from the +beginning of our era. + +The writer does not claim absolute originality for all that appears in the +following pages; on the contrary, he has made free use of all the +materials that came within his reach relating to the history of the +calendar and the work of its correction by Gregory. These materials, +together with his own calculations, he has arranged in accordance with a +plan of his own devising, so that the outline and the execution of the +work may be truly said to be original. Of its value the world must judge. +It has been prepared in weakness of body and in suffering, which have been +to some extent relieved by the mental occupation thus afforded, but which +may have nevertheless left their impress on the work. But let it be read +before pronouncing judgment upon it. Cicero could infer the littleness of +the Hebrew God from the smallness of the territory he had given his +people. To whom Kitto replies: "The interest and importance of a country +arise, not from its territorial extent, but from the men who form its +living soul; from its institutions bearing the impress of mind and spirit, +and from the events which grow out of the character and condition of its +inhabitants." So the value of a book does not consist in the size and +number of its pages, but from the knowledge that may be gained by its +perusal. + +THE AUTHOR. + + + + +PREFACE + +TO THE REVISED EDITION. + + +Soon after the publication of the former edition of this work, it was +suggested that a chapter be added on Easter; rules for fixing its date, +and also church festivals that depended upon the date of Easter. It was +suggested that this would add very much to the value of the work, if so +presented as to be brought within the comprehension of ordinary minds. +Knowing that the determination of Easter was an affair of considerable +nicety and complication, and had had the attention of our best minds, and +they had failed so to present it, that even among scholarly men, probably +not one in a hundred was able to determine its date without referring to +tables prepared for that purpose the author of this work felt as though he +was hardly competent for the task. Nevertheless it was undertaken, and the +work has been revised and enlarged by a Chapter on the Peculiarities of +the Roman Calendar, another on fixing the date of events prior to the +Christian era, and a third part on Easter, church festivals, and the +Hebrew Calendar. In the opinion of the author, the rules for determining +the date of Easter are so simplified by his new method that any person of +ordinary intelligence may understand them. How well he has succeeded the +public will decide. + +G. N. P. + + + + +CONTENTS. + + + PART FIRST. + + DEFINITIONS--HISTORY. + + _Pages._ + + CHAPTER I.--Definitions 11 + + CHAPTER II.--History of the divisions of time, and the old + Roman Calendar 12 + + CHAPTER III--History of the reformation of the Calendar by + Julius Caesar 18 + + CHAPTER IV.--History of the reformation of the Julian Calendar + by Pope Gregory XIII 20 + + CHAPTER V.--Peculiarities of the Roman Calendar 26 + + + PART SECOND. + + MATHEMATICAL. + + CHAPTER I.--Errors of the Julian Calendar 36 + + CHAPTER II.--Errors of the Gregorian Calendar 38 + + CHAPTER III.--Dominical Letter 39 + + CHAPTER IV.--Rule for finding the Dominical Letter 44 + + CHAPTER V.--Rule for finding the day of the week of any given + date, for both Old and New Styles 50 + + CHAPTER VI.--A simple method of finding the day of the week of + events, which occur quadrennially; the inaugural of + the Presidents, the day of the week on which they + have occurred and on which they will occur for the + next one hundred years 61 + + Some peculiarities concerning events which fall on + the 29th of February 64 + + CHAPTER VII.--Rule for finding the day of the week of events + prior to the Christian era 68 + + + PART THIRD. + + CYCLES--JULIAN PERIOD--EASTER. + + CHAPTER I.--The Solar Cycle 73 + + CHAPTER II.--The Lunar Cycle 75 + + CHAPTER III.--The Lunar Cycle and Golden Number 77 + + CHAPTER IV.--Cycle of Indiction, and the Julian Period 79 + + CHAPTER V.--Easter 82 + + CHAPTER VI.--A new and easy method of fixing the date of Easter 88 + + CHAPTER VII.--Church feasts and fasts whose date depend on the + date of Easter 108 + + CHAPTER VIII.--Hebrew Calendar 124 + + APPENDIX 134 + + ERRATA 149 + + + + +OUR CALENDAR. + +PART FIRST. + +DEFINITIONS. HISTORY. + + + + +CHAPTER I. + +DEFINITIONS. + + +_a_--A Calendar is a method of distributing time into certain periods +adapted to the purposes of civil life, as hours, days, weeks, months, +years, etc. + +_b_--The only natural divisions of time are the solar day, the solar year, +and the lunar month. + +_c_--An hour is one of the subdivisions of the day into twenty-four equal +parts. + +_d_--The true solar day is the interval of time which elapses between two +consecutive returns of the same terrestrial meridian to the Sun, the mean +length of which is twenty-four hours. + +_e_--The week is a period of seven days, having no reference whatever to +the celestial motions, a circumstance to which it owes its unalterable +uniformity. + +_f_--The lunar month is the time which elapses between two consecutive new +or full moons, and was used in the Roman calendar until the time of Julius +Caesar, and consists of 29d, 12h, 44m, 2.87s. + +_g_--The calendar month is usually employed to denote an arbitrary number +of days approaching a twelfth part of a year, and has now its place in the +calendar of nearly all nations. + +_h_--The year is either astronomical or civil. The solar astronomical year +is the period of time in which the Earth performs a revolution in its +orbit about the sun or passes from any point of the ecliptic to the same +point again, and consists of 365 days, 5 hours, 48 minutes and 49.62 +seconds of mean solar time. Appendix A. + +_i_--The civil year is that which is employed in chronology, and varies +among different nations, both in respect of the seasons at which it +commences and of its subdivisions. + + + + +CHAPTER II. + +HISTORY OF THE DIVISIONS OF TIME AND THE OLD ROMAN CALENDAR. + + +_Day_--The subdivision of the day into twenty-four parts or hours has +prevailed since the remotest ages, though different nations have not +agreed either with respect to the epoch of its commencement or the manner +of distributing the hours. Europeans in general, like the ancient +Egyptians, place the commencement of the civil day at midnight; and reckon +twelve morning hours from midnight to midday and twelve evening hours from +midday to midnight. Astronomers, after the example of Ptolemy, regarded +the day as commencing with the Sun's culmination, or noon, and find it +most convenient for the purpose of computation to reckon through the whole +twenty-four hours. Hipparchus reckoned the twenty-four hours from midnight +to midnight. + +The Roman day, from sunrise to sunset, and the night, from sunset to +sunrise, were each divided at all seasons of the year into twelve hours, +the hour being uniformly one-twelfth of the day or the night, of course, +varied in length with the length of the day or night at different seasons +of the year. + +_Week_--Although the week did not enter into the calendar of the Greeks, +and was not introduced at Rome till after the reign of Theodosius, A. D. +292, it has been employed from time immemorial in almost all Eastern +countries; and as it forms neither an aliquot part of a year nor of the +lunar months, those who reject the Mosaic recital will be at a loss to +assign to it an origin having much semblance of probability. In the +Egyptian astronomy the order of the planets, beginning with the most +remote, is Saturn, Jupiter, Mars, the Sun, Venus, Mercury, the Moon. Now, +the day being divided into twenty-four hours, each hour was consecrated to +a particular planet, namely: One to Saturn, the following to Jupiter, +third to Mars, and so on according to the above order; and the day +received the name of the planet which presided over its first hour. If, +then, the first hour of a day was consecrated to Saturn, that planet would +also have the 8th, the 5th and the 22d hours; the 23d would fall to +Jupiter, the 24th to Mars, and the 25th or the first hour of the second +day would belong to the Sun. In like manner the first hour of the third +day would fall to the Moon, the first hour of the fourth to Mars, of the +fifth to Mercury, of the sixth to Jupiter and the seventh to Venus. The +cycle being completed, the first hour of the eighth day would again return +to Saturn and all the others succeed in the same order. See table on the +17th page. + +It will be seen by the table, and it is also recorded by Dio Cassius, of +the second Century, that the Egyptian week commenced with Saturday. On +their flight from Egypt the Jews, from hatred to their ancient oppressors, +made Saturday the last day of the week. It is stated that the ancient +Saxons borrowed the week from some Eastern nation, and substituted the +names of their own divinities for those of the gods of Greece. The names +of the days are here given in Latin, Saxon and English. It will be seen +that the English names of the days are derived from the Saxon. + + LATIN. SAXON. ENGLISH. + _Dies Solis._ Sun's Day. SUNDAY. + _Dies Lunae._ Moon's Day. MONDAY. + _Dies Martis._ Tiw's Day. TUESDAY. + _Dies Mercurii._ Woden's Day. WEDNESDAY. + _Dies Jovis._ Thor's Day. THURSDAY. + _Dies Veneris._ Friga's Day. FRIDAY. + _Dies Saturni._ Seterne's Day. SATURDAY. + +_Month_--The ancient Roman year contained but ten months and is indicated +by the names of the last four. September from Septem, seven; October from +Octo, eight; November from Novem, nine, and December from Decem, ten; July +and August were also denominated Quintilis and Sextilis, from Quintus +five, and Sex, six. + +Quintilis was changed to July in honor of Julius Caesar, who was born on +the 12th of that month 98 B. C. Sextilis was changed to August by the +Roman Senate to flatter Augustus on his victories about 8 B. C. In the +reign of Numa Pompilius, about 700 B. C., two months were added to the +year, January at the beginning, and February at the end of the year. This +arrangement continued till 450 B. C., when the Decemvirs (ten magistrates) +changed the order, placing February after January, making March the third +instead of the first month of the Roman year. + +_Year_--If the civil year correspond with the solar the seasons of the +year will always come at the same period. But if the civil year is +supposed to be too long (as is the case in the Julian year) the seasons +will go back proportionately; but if too short they will advance in the +same proportion. Now, as the ancient Egyptians reckoned thirty days to the +month invariably, and to complete the year, added five days, called +supplementary days, their year consisted of 365 days. + +They made use of no intercalation, and by losing one-fourth of a day every +year, the commencement of the year went back one day in every period of +four years, and consequently made a revolution of the seasons in 1460 +years. Hence the Egyptian year was called a vague or erratic year because +the first day of the year in the course of 1460 years wandered, as it +were, over all the seasons. Therefore 1460 Julian years of 365-1/4 days +each are equal to 1461 Egyptian years of 365 days each. + +The ancient Roman year consisted of twelve lunar months, of twenty-nine +and thirty days alternately, which equals 354 days; but a day was added +to make the number odd, which was considered more fortunate, so that the +year consisted of 355 days. + +This differed from the solar year by ten whole days and a fraction; but to +restore the coincidence, Numa ordered an additional or intercalary month +to be inserted every second year between the 23d and 24th of February, +consisting of twenty-two and twenty-three days alternately, so that four +years contained 1465 days, and the mean length of the year was +consequently 366-1/4 days, so that the year was then too long by one day. + +As the error amounted to twenty-four days in as many years, it was ordered +that every third period of eight years, instead of containing four +intercalary months, two of twenty-two and two of twenty-three days, +amounting in all to ninety days, should contain only three of those months +of twenty-two days each, amounting to sixty-six days, thereby suppressing +twenty-four days in as many years, reducing the mean length of the year to +365-1/4 days. + +Had the intercalations been regularly made the concurrence of the solar +and the civil year would have been preserved very nearly. But its +regulation was left to the pontiffs, who, to prolong the term of a +magistracy or hasten an annual election, would give to the intercalary +month a greater or less number of days, and consequently the calendar was +thrown into confusion, so that in the time of Julius Caesar there was a +discrepancy between the solar and the civil year of about three months; +the winter months being carried back into autumn and the autumnal into +summer. + +A table of the order and the names of the planets in the Egyptian +astronomy illustrating the origin of the names of the days of the week: + + ---------+---------+--------+-------+-------+----------+------- + Saturn, |Jupiter, |Mars, |Sun, |Venus, |Mercury, |Moon, + Saturday.|Thursday.|Tuesday.|Sunday.|Friday.|Wednesday.|Monday. + ---------+---------+--------+-------+-------+----------+------- + 1 | 2 | 3 | 4 | 5 | 6 | 7 + 8 | 9 | 10 | 11 | 12 | 13 | 14 + 15 | 16 | 17 | 18 | 19 | 20 | 21 + 22 | 23 | 24 | 1 | 2 | 3 | 4 + 5 | 6 | 7 | 8 | 9 | 10 | 11 + 12 | 13 | 14 | 15 | 16 | 17 | 18 + 19 | 20 | 21 | 22 | 23 | 24 | 1 + 2 | 3 | 4 | 5 | 6 | 7 | 8 + 9 | 10 | 11 | 12 | 13 | 14 | 15 + 16 | 17 | 18 | 19 | 20 | 21 | 22 + 23 | 24 | 1 | 2 | 3 | 4 | 5 + 6 | 7 | 8 | 9 | 10 | 11 | 12 + 13 | 14 | 15 | 16 | 17 | 18 | 19 + 20 | 21 | 22 | 23 | 24 | 1 | 2 + 3 | 4 | 5 | 6 | 7 | 8 | 9 + 10 | 11 | 12 | 13 | 14 | 15 | 16 + 17 | 18 | 19 | 20 | 21 | 22 | 23 + 24 | 1 | 2 | 3 | 4 | 5 | 6 + 7 | 8 | 9 | 10 | 11 | 12 | 13 + 14 | 15 | 16 | 17 | 18 | 19 | 20 + 21 | 22 | 23 | 24 | 1 | 2 | 3 + 4 | 5 | 6 | 7 | 8 | 9 | 10 + 11 | 12 | 13 | 14 | 15 | 16 | 17 + 18 | 19 | 20 | 21 | 22 | 23 | 24 + ---------+---------+--------+-------+-------+----------+------- + + + + +CHAPTER III. + +HISTORY OF THE REFORMATION OF THE CALENDAR BY JULIUS CAESAR. + + +In order to put an end to the disorders arising from the negligence or +ignorance of the pontiffs, Julius Caesar, 46 B. C., abolished the use of +the lunar year and the intercalary month, and regulated the civil year +entirely by the Sun. With the advice and assistance of the astronomers, +especially Sosigenes of Alexandria, he fixed the mean length of the year +at 365-1/4 days, and decided that there should be three consecutive years +of 365 days, and a fourth of 366. + +In order to restore the vernal equinox to the 24th of March, the place it +occupied in the time of Numa, two months, together consisting of 67 days, +were inserted between the last day of November and the first day of +December of that year. An intercalary month of 23 days had already been +added to February of the same year according to the old method, so that +the first Julian year commenced with the first day of January, 45 years +before Christ, and 709 from the foundation of Rome, making the year A. U. +C. 708 to consist of the prodigious number of 445 days, (i. e. 355 + 23 + +67 = 445). Hence it was called by some the year of confusion; Macrobius +said it should be named the last year of confusion. + +There was also adopted at the same time a more commodious arrangement in +the distribution of the days throughout the several months. It was decided +to give to January, March, May, July, September and November each +thirty-one days; and the other months thirty, excepting February, which +in common years should have but twenty-nine days, but every fourth year +thirty; so that the average length of the Julian year was 365-1/4 days. + +Augustus Caesar interrupted this order by taking one day from February, +reducing it to twenty-eight and giving it to August, that the month +bearing his name should have as many days as July, which was named in +honor of his great-uncle, Julius. In order that three months of thirty-one +days might not come together, September and November were reduced to +thirty days, and thirty-one given to October and December. + +In the Julian calendar a day was added to February every fourth year, it +being the shortest month, which was called the additional or intercalary +day, and was inserted in the calendar between the 23d and 24th of that +month. In the ancient Roman calendar the first day of every month was +invariably called the calends. The 24th of February then was the 6th of +the calends of March--Sexto calendas; the preceding, which was the +additional or intercalary day, was called bis-sexto calendas (from _bis_, +twice, and _sextus_, six), twice the sixth day. Hence the term bis-sextile +as applied to every fourth year, commonly called leap-year. Appendix B. + + + + +CHAPTER IV. + +HISTORY OF THE REFORMATION OF THE JULIAN CALENDAR BY POPE GREGORY XIII. + + +True enough, the year in which Julius Caesar reformed the ancient Roman +calendar was the last year of confusion, and the method adopted by him a +commodious one, and answered a very good purpose for a short time; but as +the years rolled on and century after century had passed away, astronomers +began to discover the discrepancy between the solar and the civil year; +that the vernal equinox did not occupy the place it occupied in the time +of Caesar, namely, the 24th of March, but was gradually retrograding +towards the beginning of the year, so that at the meeting of the Council +of Nice in 325 it fell on the 21st. Appendix C. + +The venerable Bede, in the 8th century, observed that these phenomena took +place three or four days earlier than at the meeting of that council. +Roger Bacon, in the 13th century, wrote a treatise on this subject and +sent it to the Pope, setting forth the errors of the Julian calendar. The +discrepancy at that time amounted to seven or eight days. + +Thus the errors of the calendar continued to increase until 1582, when the +vernal equinox fell on the 11th instead of the 21st of March. Gregory, +perceiving that the measure (of reforming the calendar) was likely to +confer great eclat on his pontificate, undertook the long desired +reformation; and having found the governments of the principal Catholic +states ready to adopt his views, he issued a brief in the month of March, +1582, in which he abolished the use of the ancient calendar, and +substituted that which has since been received in almost all Christian +countries under the name of the Gregorian calendar or New Style. + +The edict of the Pope took effect in October of that year, causing the 5th +to be called the 15th of that month, thus suppressing ten days and making +the year 1582 to consist of only 355 days. So we see that the ten days +that had been gained by incorrect computation during the past 1257 years, +were deducted from 1582, restoring the concurrence of the solar and the +civil year, and consequently the vernal equinox to the place it occupied +in 325, namely, the 21st of March. + +The Pope was promptly obeyed in Spain, Portugal, and Italy. The change +took place the same year in France, by calling the 10th the 20th of +December. Many other Catholic countries made the change the same year, and +the Catholic states of Germany the year following; but most of the +Protestant countries adhered to the Old Style until after the year 1700. +Among the last was Great Britain; she, after having suffered a great deal +of inconvenience for nearly two hundred years by using a different date +from the most of Europe, at length, by an act of Parliament, fixed on +September, 1752, as the time for making the much desired change, which was +done by calling the 3d of that month the 14th (as the error now amounted +to eleven days), adopting at the same time the Gregorian rule of +intercalation. + +Russia is the only Christian country that still adheres to the Old Style, +and by using a different date from the rest of Europe is now twelve days +behind the true time. The discrepancy between solar and civil time does +not effect the day, for, as has already been shown, the mean length of the +day is twenty-four hours, and is marked by one revolution of the earth +upon its axis. + +Nor does it effect the week, for the week is uniformly seven of those +days. But it effects the year, the month and the day of the month. + +Russia, by adhering to the Old Style, has reckoned as many days and as +many weeks, and events have transpired on the same day of the week as they +have with us who have adopted the New Style; as Christian nations we are +observing the same day as the Sabbath. + +When it was Tuesday, the 20th day of December, 1888, in Russia, it was +Tuesday, the 1st day of January, 1889, in those countries which have +adopted the New Style. Columbus sailed from Palos, in Spain, on Friday, +August 3d, 1492, Old Style, which was Friday, August 12th, New Style. +Washington was born on Friday, February 11th, 1732, Old Style, which was +Friday, February 22d, New Style. + +Now, the difference in styles during the 15th century is nine days; during +the 16th and 17th centuries, ten days; the 18th century, eleven days, and +the 19th, twelve days. In regard to the sailing of Columbus, the change is +made by suppressing nine days, calling the 3d the 12th of August. In +regard to the birth of Washington, the change is effected by suppressing +eleven days, calling the 11th of February the 22d. As regards Russia, she +could have made the change last year by calling the 20th of December, +1888, the 1st day of January, 1889, thereby suppressing twelve days, and +making the year 1888 to consist of only 354 days, and the month of +December twenty days. The methods of computation, both Old and New Styles, +will be explained in another chapter. + +To persons unacquainted with astronomy, the difference between Old and New +Styles would probably be better understood by the diagram on the 25th +page. The figures represent the ecliptic, which is the apparent path of +the Sun, or the real path of the Earth as seen from the Sun, in her annual +or yearly revolution around the Sun in the order of the months, as marked +on the ecliptic. + +Attention is called to four points on the ecliptic, namely, the vernal +equinox, the autumnal equinox, the winter solstice, and the summer +solstice. These occur, in the order given above, on the 21st of March, the +21st of September, the 21st of December and the 21st of June. It has +already been stated that if the civil year correspond with the solar, the +seasons of the year will always come at the same period. Julius Caesar +found the ancient Roman year in advance of the solar; Gregory found the +Julian behind the solar year; so one reforms the calendar by +intercalation, the other by suppression. Appendix D. + +Caesar restored the coincidence of the solar and the civil year, but failed +to retain it by allowing what probably appeared to him at the time a +trifling error in his calendar. The error, which was 11 minutes and 10.38 +seconds every year, was hardly perceptable for a short period, but still +amounted to three days every 400 years. Hence the necessity in 1582 of +reforming the reformed calendar of Julius Caesar to restore the +coincidence. Appendix E. + +From the meeting of the Council of Nice, in 325, to 1582, a period of 1257 +years, there was found to be an error in the Julian calendar of ten days. +Now, in 1257 years the Earth performs 1257 annual and 459,109 daily +revolutions, after which the vernal equinox was found to occur on the 21st +of March, true or solar time; thus concurring with the vernal equinox of +325. But the erroneous Julian calendar would make the Earth perform +459,119 daily revolutions to complete the 1257 years, a discrepancy of ten +days, making the vernal equinox to fall on the 11th instead of the 21st. +It will be seen by the diagram that the ten days were deducted from +October, in 1582, making it a short month, consisting of only twenty-one +days. + +The discrepancy between the Julian and Gregorian calendar amounts to +thirty days in 4000 years; three months in 12,175 years. Hence, in 12,175 +years the equinoxes would take the place of the solstices, and the +solstices the place of the equinoxes. In 24,350 years, the vernal equinox +would take the place of the autumnal equinox, and the winter solstice the +place of the summer solstice. + +And in 48,700 years, according to the Julian rule of intercalation, there +would be gained nearly 365-1/4 days, or one entire revolution of the +Earth. So, to restore the concurrence of the Julian and Gregorian years, +there would have to be suppressed 365-1/4 days, calling the 1st day of +January, 48,699, the 1st day of January, 48,700. + +Thus would disappear from the Julian calendar twelve months, or one whole +year, it having been divided among the thousands of the preceding years. + + +[Illustration: The Julian calendar, reformed by Gregory XIII, Oct. 5th, +1582, by suppressing ten days, calling the 5th of Oct. the 15th, making it +a short month of 21 days, and the year to consist of 355 days. + +The Roman calendar, reformed by Julius Caesar, 46 B. C., by intercalating +90 days, making that year to consist of 445 days, that is, 355 + 23 + 67 = +445 days, and "the last year of confusion."] + + +To make this subject better understood, let us suppose the solar year to +consist in round numbers of 365 days, and the civil year 366. It is +evident that at the end of the year of 365 days, there would still be +wanting one day to complete the civil year of 366 days, so one day must be +added to that year, and to every succeeding year, to complete the years of +366 days each, which would be the loss of one year of 365 days in 365 +years. Hence, 364 years of 366 days each are equal to 365 years of 365 +days each, wanting one day. + +Again, let us suppose the civil year to consist of 364 days. It is evident +that at the end of the supposed solar year of 365 days, there would be an +advance or gain of one day in that year and every succeeding year, so that +in 365 years there would be a gain of 365 days or one whole year. Hence, +366 years of 364 days each are equal to 365 years of 365 days each, +wanting one day. Appendix F. + + + + +CHAPTER V. + +PECULIARITIES OF THE ROMAN CALENDAR. + + +The Romans, instead of distinguishing the days of the month by the ordinal +numbers, first, second, third, etc., counted backwards from three fixed +points, namely, the Calends, the Nones, and the Ides. + +Calends (Latin _Calandae_, from _Calare_, to call,) was so denominated +because it had been an ancient custom of the pontiffs to call the people +together on that day to apprise them of the festivals, or days that were +to be kept sacred during the month. + +Nones (Latin _nonae_, from _nonus_, the ninth,) the ninth day before the +Ides. + +Ides (Latin _idus_, supposed to be derived from an obsolete verb _iduare_, +to divide,) was near the middle of the month, either the 13th or the 15th +day. + +The first day of each month was invariably called the Calends. The Nones +were the fifth, and the Ides the thirteenth, except in March, May, July, +and October, in which the Nones occurred on the seventh day and the Ides +on the fifteenth. + +From these three points the days of the month were numbered--not forward, +but backward--as so many days before the Nones, the Ides, or the Calends, +the point of departure being counted in the reckoning, so that the last +day of every month was the second of the Calends of the following month. + +It will be seen by the Roman and English calendar found on the following +pages, that there are six days of Nones in March, May, July and October, +and four of all the other months; also that all the months have eight days +of Ides. The number of days of Calends depend upon the number of days in +the month, and the day of the month on which the Ides fall. + +If the month has thirty-one days and the Ides fall on the thirteenth, +there are nineteen days of Calends; but if the Ides fall on the fifteenth, +there are only seventeen days of Calends. As the Ides fall on the +thirteenth of all the months of thirty days, they have eighteen days of +Calends. February, the month of twenty-eight days, has only sixteen, +except in leap-year, when the sixth of the Calends is reckoned twice. + +It may also be seen from the calendar that the Romans, after the first +day of the month, began to reckon so many days before the Nones, as 4th, +3d, 2d, then Nones; after the Nones, so many days before the Ides, as 8th, +7th, 6th, etc., and after the Ides, so many before the Calends of the next +month, the highest numbers being reckoned first. + +In reducing the Roman calendar to our own, it should be remembered that in +reckoning backward from a fixed point, that the point of departure is +counted; also, that the last day of the month is not the point from which +the Calends are reckoned, but the first day of the following month. We +have then this rule for finding the English expression for any Latin date: + + +RULE. + +If the given date be Calends, add two to the number of days in the month, +from which subtract the given date; if the date be Nones, or Ides, add one +to that of the day on which the Nones or Ides fall, from which subtract +the given date, and you will have the day of the month in our calendar. To +find the Latin expression for any English date, the preceding method is to +be reversed, upon the principle that if 5 - 3 = 2, then 5 - 2 = 3. + +But in reducing a Roman date to a date of February in leap-year, for the +first twenty-four days, proceed according to the preceding rule as if the +month had only twenty-eight days, and to obtain the proper expression for +the remaining five days, regard the month as having twenty-nine days, +taking the Roman date from 31 instead of 30. Thus 31 - 6 = 25, while 30 -6 += 24; the former corresponding with sexto calendas, the latter with +bis-sexto calendas of the Julian calendar. By referring to the table on +the 35th page, one may easily learn how to find the English expression for +any Latin date, or the Latin expression for any English date. + +It has already been stated that in January the Nones fall on the 5th, and +the Ides on the 13th, January then having thirty one days, the number from +which to subtract the Roman date to obtain the corresponding day of the +month is, for Nones, 5 + 1 = 6; for Ides, 13 + 1 = 14; for Calends, 31 + 2 += 33. Hence the first column in the table under January are the numbers 6, +14 and 33. February is the same as January for Nones and Ides. For Calends +in leap-year, for the first 24 days, it is 28 + 2 = 30; for the remaining +5 days it is 29 + 2 = 31. Hence for the first column under February are +the numbers 6, 14, 30 and 31. March is the same as January, except that +the Nones fall on the 7th and the Ides on the 15th, consequently we have +for Nones, 7 + 1 = 8, and for Ides, 15 + 1 = 16; hence, for the first +column under March we have the numbers 8, 16, and 33. + +In the table the three months are taken to illustrate how easily the +change may be made from Roman to English, or from English to Roman date. A +complete calendar for 1892, both in Roman and English, which will be very +convenient for reference, may be found on the four following pages. + +The first seven letters of the alphabet, used to represent the days of the +week, are placed in the calendar beside the days of the week. The letter +that represents Sunday is called the dominical or Sunday letter. The +letter that represents the first Sunday in any given year represents all +the Sundays in that year, unless it be leap-year, when two Sunday letters +are used. The first represents all the Sundays in January and February, +while the letter that precedes it represents all the Sundays for the rest +of the year. + +The reason of this is, the day intercalated, or thrust in, between the +28th day of February and the 1st day of March so interrupts the order of +the letters that D, which always represents the 1st day of March, now +represents the 29th day of February, so that in 1892 it represents Monday, +the 29th day of February, also Tuesday the 1st day of March. As it +represented all the Mondays in January and February, it will now represent +all the Tuesdays for the rest of the year, while C, the letter preceding, +represented all the Sundays, will now represent all the Mondays, and B all +the Sundays. For January and February we have then C, Sunday; D, Monday; +E, Tuesday; F, Wednesday; G, Thursday; A, Friday, and B, Saturday. For the +rest of the year we have B, Sunday; C, Monday; D, Tuesday; E, Wednesday; +F, Thursday; G, Friday, and A, Saturday. See Part Second, chapters IV and +V. + + ------------------++------------------++------------------ + JAN., 1892. || FEB., 1892. || MARCH, 1892. + ------------------++------------------++------------------ + 1|_Cal._ |a|Fri. || 1|_Cal._ |d|Mon. || 1|_Cal._ |d|Tues. + 2| 4 |b|Sat. || 2| 4 |e|Tues.|| 2| 6 |e|Wed. + 3| 3 |c|Sun. || 3| 3 |f|Wed. || 3| 5 |f|Thur. + 4| 2 |d|Mon. || 4| 2 |g|Thur.|| 4| 4 |g|Fri. + 5|_Non._ |e|Tues.|| 5|_Non._ |a|Fri. || 5| 3 |a|Sat. + 6| 8 |f|Wed. || 6| 8 |b|Sat. || 6| 2 |b|Sun. + 7| 7 |g|Thur.|| 7| 7 |c|Sun. || 7|_Non._ |c|Mon. + 8| 6 |a|Fri. || 8| 6 |d|Mon. || 8| 8 |d|Tues. + 9| 5 |b|Sat. || 9| 5 |e|Tues.|| 9| 7 |e|Wed. + 10| 4 |c|Sun. ||10| 4 |f|Wed. ||10| 6 |f|Thur. + 11| 3 |d|Mon. ||11| 3 |g|Thur.||11| 5 |g|Fri. + 12| 2 |e|Tues.||12| 2 |a|Fri. ||12| 4 |a|Sat. + 13|_Ides._|f|Wed. ||13|_Ides._|b|Sat. ||13| 3 |b|Sun. + 14| 19 |g|Thur.||14| 16 |c|Sun. ||14| 2 |c|Mon. + 15| 18 |a|Fri. ||15| 15 |d|Mon. ||15|_Ides._|d|Tues. + 16| 17 |b|Sat. ||16| 14 |e|Tues.||16| 17 |e|Wed. + 17| 16 |c|Sun. ||17| 13 |f|Wed. ||17| 16 |f|Thur. + 18| 15 |d|Mon. ||18| 12 |g|Thur.||18| 15 |g|Fri. + 19| 14 |e|Tues.||19| 11 |a|Fri. ||19| 14 |a|Sat. + 20| 13 |f|Wed. ||20| 10 |b|Sat. ||20| 13 |b|Sun. + 21| 12 |g|Thur.||21| 9 |c|Sun. ||21| 12 |c|Mon. + 22| 11 |a|Fri. ||22| 8 |d|Mon. ||22| 11 |d|Tues. + 23| 10 |b|Sat. ||23| 7 |e|Tues.||23| 10 |e|Wed. + 24| 9 |c|Sun. ||24| 6 |f|Wed. ||24| 9 |f|Thur. + 25| 8 |d|Mon. ||25| 6 |g|Thur.||25| 8 |g|Fri. + 26| 7 |e|Tues.||26| 5 |a|Fri. ||26| 7 |a|Sat. + 27| 6 |f|Wed. ||27| 4 |b|Sat. ||27| 6 |b|Sun. + 28| 5 |g|Thur.||28| 3 |c|Sun. ||28| 5 |c|Mon. + 29| 4 |a|Fri. ||29| 2 |d|Mon. ||29| 4 |d|Tues. + 30| 3 |b|Sat. || | | | ||30| 3 |e|Wed. + 31| 2 |c|Sun. || | | | ||31| 2 |f|Thur. + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + + ------------------++------------------++------------------ + APRIL, 1892. || MAY, 1892. || JUNE, 1892. + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + 1|_Cal._ |g|Fri. || 1|_Cal._ |b|Sun. || 1|_Cal._ |e|Wed. + 2| 4 |a|Sat. || 2| 6 |c|Mon. || 2| 4 |f|Thur. + 3| 3 |b|Sun. || 3| 5 |d|Tues.|| 3| 3 |g|Fri. + 4| 2 |c|Mon. || 4| 4 |e|Wed. || 4| 2 |a|Sat. + 5|_Non._ |d|Tues.|| 5| 3 |f|Thur.|| 5|_Non._ |b|Sun. + 6| 8 |e|Wed. || 6| 2 |g|Fri. || 6| 8 |c|Mon. + 7| 7 |f|Thur.|| 7|_Non._ |a|Sat. || 7| 7 |d|Tues. + 8| 6 |g|Fri. || 8| 8 |b|Sun. || 8| 6 |e|Wed. + 9| 5 |a|Sat. || 9| 7 |c|Mon. || 9| 5 |f|Thur. + 10| 4 |b|Sun. ||10| 6 |d|Tues.||10| 4 |g|Fri. + 11| 3 |c|Mon. ||11| 5 |e|Wed. ||11| 3 |a|Sat. + 12| 2 |d|Tues.||12| 4 |f|Thur.||12| 2 |b|Sun. + 13|_Ides._|e|Wed. ||13| 3 |g|Fri. ||13|_Ides._|c|Mon. + 14| 18 |f|Thur.||14| 2 |a|Sat. ||14| 18 |d|Tues. + 15| 17 |g|Fri. ||15|_Ides._|b|Sun. ||15| 17 |e|Wed. + 16| 16 |a|Sat. ||16| 17 |c|Mon. ||16| 16 |f|Thur. + 17| 15 |b|Sun. ||17| 16 |d|Tues.||17| 15 |g|Fri. + 18| 14 |c|Mon. ||18| 15 |e|Wed. ||18| 14 |a|Sat. + 19| 13 |d|Tues.||19| 14 |f|Thur.||19| 13 |b|Sun. + 20| 12 |e|Wed. ||20| 13 |g|Fri. ||20| 12 |c|Mon. + 21| 11 |f|Thur.||21| 12 |a|Sat. ||21| 11 |d|Tues. + 22| 10 |g|Fri. ||22| 11 |b|Sun. ||22| 10 |e|Wed. + 23| 9 |a|Sat. ||23| 10 |c|Mon. ||23| 9 |f|Thur. + 24| 8 |b|Sun. ||24| 9 |d|Tues.||24| 8 |g|Fri. + 25| 7 |c|Mon. ||25| 8 |e|Wed. ||25| 7 |a|Sat. + 26| 6 |d|Tues.||26| 7 |f|Thur.||26| 6 |b|Sun. + 27| 5 |e|Wed. ||27| 6 |g|Fri. ||27| 5 |c|Mon. + 28| 4 |f|Thur.||28| 5 |a|Sat. ||28| 4 |d|Tues. + 29| 3 |g|Fri. ||29| 4 |b|Sun. ||29| 3 |e|Wed. + 30| 2 |a|Sat. ||30| 3 |c|Mon. ||30| 2 |f|Thur. + | | | ||31| 2 |d|Tues.|| | | | + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + + --+---------------++------------------++------------------ + JULY, 1892. || AUG., 1892. || SEPT., 1892. + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + 1|_Cal._ |g|Fri. || 1|_Cal._ |c|Mon. || 1|_Cal._ |f|Thur. + 2| 6 |a|Sat. || 2| 4 |d|Tues.|| 2| 4 |g|Fri. + 3| 5 |b|Sun. || 3| 3 |e|Wed. || 3| 3 |a|Sat. + 4| 4 |c|Mon. || 4| 2 |f|Thur.|| 4| 2 |b|Sun. + 5| 3 |d|Tues.|| 5|_Non._ |g|Fri. || 5|_Non._ |c|Mon. + 6| 2 |e|Wed. || 6| 8 |a|Sat. || 6| 8 |d|Tues. + 7|_Non._ |f|Thur.|| 7| 7 |b|Sun. || 7| 7 |e|Wed. + 8| 8 |g|Fri. || 8| 6 |c|Mon. || 8| 6 |f|Thur. + 9| 7 |a|Sat. || 9| 5 |d|Tues.|| 9| 5 |g|Fri. + 10| 6 |b|Sun. ||10| 4 |e|Wed. ||10| 4 |a|Sat. + 11| 5 |c|Mon. ||11| 3 |f|Thur.||11| 3 |b|Sun. + 12| 4 |d|Tues.||12| 2 |g|Fri. ||12| 2 |c|Mon. + 13| 3 |e|Wed. ||13|_Ides._|a|Sat. ||13|_Ides._|d|Tues. + 14| 2 |f|Thur.||14| 19 |b|Sun. ||14| 18 |e|Wed. + 15|_Ides._|g|Fri. ||15| 18 |c|Mon. ||15| 17 |f|Thur. + 16| 17 |a|Sat. ||16| 17 |d|Tues.||16| 16 |g|Fri. + 17| 16 |b|Sun. ||17| 16 |e|Wed. ||17| 15 |a|Sat. + 18| 15 |c|Mon. ||18| 15 |f|Thur.||18| 14 |b|Sun. + 19| 14 |d|Tues.||19| 14 |g|Fri. ||19| 13 |c|Mon. + 20| 13 |e|Wed. ||20| 13 |a|Sat. ||20| 12 |d|Tues. + 21| 12 |f|Thur.||21| 12 |b|Sun. ||21| 11 |e|Wed. + 22| 11 |g|Fri. ||22| 11 |c|Mon. ||22| 10 |f|Thur. + 23| 10 |a|Sat. ||23| 10 |d|Tues.||23| 9 |g|Fri. + 24| 9 |b|Sun. ||24| 9 |e|Wed. ||24| 8 |a|Sat. + 25| 8 |c|Mon. ||25| 8 |f|Thur.||25| 7 |b|Sun. + 26| 7 |d|Tues.||26| 7 |g|Fri. ||26| 6 |c|Mon. + 27| 6 |e|Wed. ||27| 6 |a|Sat. ||27| 5 |d|Tues. + 28| 5 |f|Thur.||28| 5 |b|Sun. ||28| 4 |e|Wed. + 29| 4 |g|Fri. ||29| 4 |c|Mon. ||29| 3 |f|Thur. + 30| 3 |a|Sat. ||30| 3 |d|Tues.||30| 2 |g|Fri. + 31| 2 |b|Sun. ||31| 2 |e|Wed. || | | | + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + + ------------------++------------------++------------------ + OCT., 1892. || NOV., 1892. || DEC., 1892. + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + 1|_Cal._ |a|Sat. || 1|_Cal._ |d|Tues.|| 1|_Cal._ |f|Thur. + 2| 6 |b|Sun. || 2| 4 |e|Wed. || 2| 4 |g|Fri. + 3| 5 |c|Mon. || 3| 3 |f|Thur.|| 3| 3 |a|Sat. + 4| 4 |d|Tues.|| 4| 2 |g|Fri. || 4| 2 |b|Sun. + 5| 3 |e|Wed. || 5|_Non._ |a|Sat. || 5|_Non._ |c|Mon. + 6| 2 |f|Thur.|| 6| 8 |b|Sun. || 6| 8 |d|Tues. + 7|_Non._ |g|Fri. || 7| 7 |c|Mon. || 7| 7 |e|Wed. + 8| 8 |a|Sat. || 8| 6 |d|Tues.|| 8| 6 |f|Thur. + 9| 7 |b|Sun. || 9| 5 |e|Wed. || 9| 5 |g|Fri. + 10| 6 |c|Mon. ||10| 4 |f|Thur.||10| 4 |a|Sat. + 11| 5 |d|Tues.||11| 3 |g|Fri. ||11| 3 |b|Sun. + 12| 4 |e|Wed. ||12| 2 |a|Sat. ||12| 2 |c|Mon. + 13| 3 |f|Thur.||13|_Ides._|b|Sun. ||13|_Ides._|d|Tues. + 14| 2 |g|Fri. ||14| 18 |c|Mon. ||14| 19 |e|Wed. + 15|_Ides._|a|Sat. ||15| 17 |d|Tues.||15| 18 |f|Thur. + 16| 17 |b|Sun. ||16| 16 |e|Wed. ||16| 17 |g|Fri. + 17| 16 |c|Mon. ||17| 15 |f|Thur.||17| 16 |a|Sat. + 18| 15 |d|Tues.||18| 14 |g|Fri. ||18| 15 |b|Sun. + 19| 14 |e|Wed. ||19| 13 |a|Sat. ||19| 14 |c|Mon. + 20| 13 |f|Thur.||20| 12 |b|Sun. ||20| 13 |d|Tues. + 21| 12 |g|Fri. ||21| 11 |c|Mon. ||21| 12 |e|Wed. + 22| 11 |a|Sat. ||22| 10 |d|Tues.||22| 11 |f|Thur. + 23| 10 |b|Sun. ||23| 9 |e|Wed. ||23| 10 |g|Fri. + 24| 9 |c|Mon. ||24| 8 |f|Thur.||24| 9 |a|Sat. + 25| 8 |d|Tues.||25| 7 |g|Fri. ||25| 8 |b|Sun. + 26| 7 |e|Wed. ||26| 6 |a|Sat. ||26| 7 |c|Mon. + 27| 6 |f|Thur.||27| 5 |b|Sun. ||27| 6 |d|Tues. + 28| 5 |g|Fri. ||28| 4 |c|Mon. ||28| 5 |e|Wed. + 29| 4 |a|Sat. ||29| 3 |d|Tues.||29| 4 |f|Thur. + 30| 3 |b|Sun. ||30| 2 |e|Wed. ||30| 3 |g|Fri. + 31| 2 |c|Mon. || | | | ||31| 2 |a|Sat. + --+-------+-+-----++--+-------+-+-----++--+-------+-+----- + + --------------++----------------++---------------- + JANUARY. || FEBRUARY. || MARCH. + --------------++----------------++---------------- + _Cal._ 1 || _Cal._ 1 || _Cal._ 1 + 6 - 4 = 2 || 6 - 4 = 2 || 8 - 6 = 2 + 6 - 3 = 3 || 6 - 3 = 3 || 8 - 5 = 3 + 6 - 2 = 4 || 6 - 2 = 4 || 8 - 4 = 4 + _Nones_ 5 || _Nones_ 5 || 8 - 3 = 5 + 14 - 8 = 6 || 14 - 8 = 6 || 8 - 2 = 6 + 14 - 7 = 7 || 14 - 7 = 7 || _Nones_ 7 + 14 - 6 = 8 || 14 - 6 = 8 || 16 - 8 = 8 + 14 - 5 = 9 || 14 - 5 = 9 || 16 - 7 = 9 + 14 - 4 = 10 || 14 - 4 = 10 || 16 - 6 = 10 + 14 - 3 = 11 || 14 - 3 = 11 || 16 - 5 = 11 + 14 - 2 = 12 || 14 - 2 = 12 || 16 - 4 = 12 + _Ides_ 13 || _Ides_ 13 || 16 - 3 = 13 + 33 - 19 = 14 || 30 - 16 = 14 || 16 - 2 = 14 + 33 - 18 = 15 || 30 - 15 = 15 || _Ides_ 15 + 33 - 17 = 16 || 30 - 14 = 16 || 33 - 17 = 16 + 33 - 16 = 17 || 30 - 13 = 17 || 33 - 16 = 17 + 33 - 15 = 18 || 30 - 12 = 18 || 33 - 15 = 18 + 33 - 14 = 19 || 30 - 11 = 19 || 33 - 14 = 19 + 33 - 13 = 20 || 30 - 10 = 20 || 33 - 13 = 20 + 33 - 12 = 21 || 30 - 9 = 21 || 33 - 12 = 21 + 33 - 11 = 22 || 30 - 8 = 22 || 33 - 11 = 22 + 33 - 10 = 23 || 30 - 7 = 23 || 33 - 10 = 23 + 33 - 9 = 24 || 30 - 6 = 24 || 33 - 9 = 24 + 33 - 8 = 25 || 31 - 6 = 25 || 33 - 8 = 25 + 33 - 7 = 26 || 31 - 5 = 26 || 33 - 7 = 26 + 33 - 6 = 27 || 31 - 4 = 27 || 33 - 6 = 27 + 33 - 5 = 28 || 31 - 3 = 28 || 33 - 5 = 28 + 33 - 4 = 29 || 31 - 2 = 29 || 33 - 4 = 29 + 33 - 3 = 30 || || 33 - 3 = 30 + 33 - 2 = 31 || || 33 - 2 = 31 + --------------++----------------++---------------- + + + + +PART SECOND. + +MATHEMATICAL. + + + + +CHAPTER I. + +ERRORS OF THE JULIAN CALENDAR. + + +It will be necessary in the first place to understand the difference +between the Julian and Gregorian rule of intercalation. If the number of +any year be exactly divisible by four it is leap year; if the remainder be +1, it is the first year after leap-year; if 2, the second; if 3, the +third; thus: + + 1888 / 4 = 472, no remainder. + 1889 / 4 = 472, remainder, 1. + 1890 / 4 = 472, remainder, 2. + 1891 / 4 = 472, remainder, 3. + 1892 / 4 = 473, no remainder. + +And so on, every fourth year being leap-year of 366 days. + +This is the Julian rule of intercalation, which is corrected by the +Gregorian by making every centurial year, or the year that completes the +century, a common year, if not exactly divisible by 400; so that only +every fourth centurial year is leap-year; thus, 1,700, 1,800, and 1,900 +are common years, but 2,000, the fourth centurial year, is leap year, and +so on. + +By the Julian rule three-fourths of a day is gained every century, which +in 400 years amounts to three days. This is corrected by the Gregorian, by +making three consecutive centurial years common years, thus suppressing +three days in 400 years. + + +RULE. + +Multiply the difference between the Julian and the solar year by 100, and +we have the error in 100 years. Multiply this product by 4 and we have the +error in 400 years. Now, 400 is the tenth of 4,000; therefore, multiply +the last product by 10, and we have the error in 4,000 years. Now, as the +discrepancy between the Julian and Gregorian year is three days in 400 +years, making 3-400 of a day every year, so by dividing 365-1/4, the +number of days in a year, by 3-400, we have the time it would take to make +a revolution of the seasons. + + +SOLUTION. + +(365 d, 6 h.) - (365 d, 5 h, 48 m, 49.62 s.) = (11 m, 10.38 s.) Now, (11 +m, 10.38 s.) x 100 = 18 h, 37.3 m, the gain in 100 years. This is, +reckoned in round numbers, 18 hours, or three-fourths of a day. Now, (3/4 +x 4) = (1 x 3) = 3: the Julian rule gaining three days, the Gregorian +suppressing three days in 400 years. (3 x 10) = 30, the number of days +gained by the Julian rule in 4,000 years. 365-1/4 / 3 400 = 48,700, so +that in this long period of time, this falling back 3/4 of a day every +century would amount to 365-1/4 days; therefore, 48,699 Julian years are +equal to 48,700 Gregorian years. + + + + +CHAPTER II. + +ERRORS OF THE GREGORIAN CALENDAR. + + +By reference to the preceding chapter it will be seen that there is an +error of 37.3 minutes in every 100 years not corrected by the Gregorian +calendar; this amounts to only .373 of a minute a year, or one day in +3,861 years, and one day and fifty-two minutes in 4,000 years. + + +RULE. + +To find how long it would take to gain one day: Divide the number of +minutes in a day by the decimal .373, that being the fraction of a minute +gained every year. To find how much time would be gained in 4,000 years, +multiply the decimal .373 by 4,000, and you will have the answer in +minutes, which must be reduced to hours. + + +SOLUTION. + +(24 x 60) / .373 = 3,861, nearly; hence the error would amount to only one +day in 3,861 years. + +(.373 x 4,000) / 60 = (24 h, 52 m,) = (1 d, 0 h, 52 m), the error in 4,000 +years. + +This trifling error in the Gregorian calendar may be corrected by +suppressing the intercalations in the year 4,000, and its multiples, +8,000, 12,000, 16,000, etc., so that it will not amount to a day in +100,000 years. + + +RULE. + +Divide 100,000 by 4,000 and you will have the number of intercalations +suppressed in 100,000 years. Multiply 1 d, 52 m, (that being the error in +4,000 years) by this quotient, and you will have the discrepancy between +the Gregorian and solar year for 100,000 years. By this improved method we +suppress 25 days, so that the error will only amount to 25 times 52 +minutes. + + +SOLUTION. + +100,000 / 4,000 x (1 d, 52 m,) = (25d, 21 h, 40 m.) Now, (25d, 21 h, 40 +m,) - 25 d = (21 h, 40 m,) the error in 100,000. + + + + +CHAPTER III. + +DOMINICAL LETTER. + + +Dominical (from the Latin _Dominus_, Lord,) indicating the Lord's day or +Sunday. Dominical letter, one of the first seven letters of the alphabet +used to denote the Sabbath or Lord's day. + +For the sake of greater generality, the days of the week are denoted by +the first seven letters of the alphabet, A, B, C, D, E, F, G, which are +placed in the calendar beside the days of the year, so that A stands +opposite the first day of January, B opposite the second, C opposite the +third, and so on to G, which stands opposite the seventh; after which A +returns to the eighth, and so on through the 365 days of the year. + +Now, if one of the days of the week, Sunday for example, is represented by +F, Monday will be represented by G, Tuesday by A, Wednesday by B, Thursday +by C, Friday by D, and Saturday by E; and every Sunday throughout the year +will have the same character, F, every Monday G, every Tuesday A, and so +with regard to the rest. + +The letter which denotes Sunday is called the Dominical or Sunday letter +for that year; and when the dominical letter of the year is known, the +letters which respectively correspond to the other days of the week become +known also. Did the year consist of 364 days, or 52 weeks invariably, the +first day of the year and the first day of the month, and in fact any day +of any year, or any month, would always commence on the same day of the +week. But every common year consists of 365 days, or 52 weeks and 1 day, +so that the following year will begin one day later in the week than the +year preceding. Thus the year 1837 commenced on Sunday, the following +year, 1838, on Monday, 1839 on Tuesday, and so on. + +As the year consists of 52 weeks and 1 day, it is evident that the day +which begins and ends the year must occur 53 times; thus the year 1837 +begins on Sunday and ends on Sunday; so the following year, 1838, must +begin on Monday. As A represented all the Sundays in 1837 and as A always +stands for the first day of January, so in 1838 it will represent all the +Mondays, and the dominical letter goes back from A to G; so that G +represents all the Sundays in 1838, A all the Mondays, B all the Tuesdays, +and so on, the dominical letter going back one place in every year of 365 +days. + +While the following year commences one day later in the week than the year +preceding, the dominical letter goes back one place from the preceding +year; thus while the year 1865 commenced on Sunday, 1866 on Monday, 1867 +on Tuesday, the dominical letters are A, G and F, respectively. Therefore, +if every year consisted of 365 days, the dominical cycle would be +completed in seven years, so that after seven years the first day of the +year would again occur on the same day of the week. + +But this order is interrupted every four years by giving February 29 days, +thereby making the year to consist of 366 days, which is 52 weeks and two +days, so that the following year would commence two days later in the week +than the year preceding, thus the year 1888 being leap-year, had two +dominical letters, A and G; A for January and February, and G for the rest +of the year. The year commenced on Sunday and ended on Monday, making 53 +Sundays and 53 Mondays, and the following year, 1889, to commence on +Tuesday. It now becomes evident that if the years all consisted of 364 +days, or 52 weeks, they would all commence on the same day of the week; if +they all consisted of 365 days, or 52 weeks and one day, they would all +commence one day later in the week than the year preceding; if they all +consisted of 366 days, or 52 weeks and two days, they would commence two +days later in the week; if 367 days or 52 weeks and three days, then three +days later, and so on, one day later for every additional day. It is also +evident that every additional day causes the dominical letter to go back +one place. Now in leap-year the 29th day of February is the additional or +intercalary day. So one letter for January and February, and another for +the rest of the year. If the number of years in the intercalary period +were two, and seven being the number of days in the week, their product +would be 2 x 7 = 14; fourteen, then, would be the number of years in the +cycle. Again, if the number of years in the intercalary period were three, +and the number of days in the week being seven, their product would be 3 x +7 = 21; twenty-one would then be the number of years in the cycle. But the +number of years in the intercalary period is four, and the number of days +in the week is seven, therefore their product is 4 x 7 = 28; twenty-eight +is then the number of years in the cycle. + +This period is called the dominical or solar cycle, and restores the first +day of the year to the same day of the week. At the end of the cycle the +dominical letters return again in the same order, on the same days of the +month. Thus, for the year 1801, the dominical letter is D; 1802, C; 1803, +B; 1804, A and G; and so on, going back five places every four years for +twenty-eight years, when the cycle, being ended, D is again dominical +letter for 1829, C for 1830, and so on every 28 years forever, according +to the Julian rule of intercalation. + +But this order is interrupted in the Gregorian calendar at the end of the +century by the secular suppression of the leap-year. It is not +interrupted, however, at the end of every century, for the leap-year is +not suppressed in every fourth centurial year; consequently the cycle will +then be continued for two hundred years. It should be here stated that +this order continued without interruption from the commencement of the era +until the reformation of the calendar in 1582, during which time the +Julian calendar, or Old Style was used. + +It has already been shown that if the number of years in the intercalary +period be multiplied by seven, the number of days in the week, their +product will be the number of years in the cycle. Now, in the Gregorian +calendar, the intercalary period is 400 years; this number being +multiplied by seven, their product would be 2,800 years, as the interval +in which the coincidence is restored between the days of the year and the +days of the week. + +This long period, however, may be reduced to 400 years; for since the +dominical letter goes back five places every four years, in 400 years it +will go back 500 places in the Julian and 497 in the Gregorian calendar, +three intercalations being suppressed in the Gregorian every 400 years. +Now 497 is exactly divisible by seven, the number of days in the week, +therefore, after 400 years the cycle will be completed, and the dominical +letters will return again in the same order, on the same days of the +month. + +In answer to the question, "Why two dominical letters for leap-year?" we +reply, because of the additional or intercalary day after the 28th of +February. It has already been shown that every additional day causes the +dominical letter to go back one place. As there are 366 days in leap-year, +the letter must go back two places, one being used for January and +February, and the other for the rest of the year. Did we continue one +letter through the year and then go back two places, it would cause +confusion in computation, unless the intercalation be made at the end of +the year. Whenever the intercalation is made there must necessarily be a +change in the dominical letter. Had it been so arranged that the +additional day was placed after the 30th of June or September, then the +first letter would be used until the intercalation is made in June or +September, and the second to the end of the year. Or suppose that the end +of the year had been fixed as the time and place for the intercalation, +(which would have been much more convenient for computation,) then there +would have been no use whatever for the second dominical letter, but at +the end of the year we would go back two places; thus, in the year 1888, +instead of A being dominical letter for two months merely, it would be +continued through the year, and then passing back to F, no use whatever +being made of G, and so on at the end of every leap-year. Hence it is +evident that this arrangement would have been much more convenient, but we +have this order of the months, and the number of days in the months as +Augustus Caesar left them eight years before Christ. The dominical letter +probably was not known until the Council of Nice, in the year of our Lord +325, where, in all probability, it had its origin. + + + + +CHAPTER IV. + +RULE FOR FINDING THE DOMINICAL LETTER. + + +Divide the number of the given year by 4, neglecting the remainders, and +add the quotient to the given number. Divide this amount by 7, and if the +remainder be less than three, take it from 3; but if it be 3 or more than +3, take it from 10 and the remainder will be the number of the letter +calling A, 1; B, 2; C, 3, etc. + +By this rule the dominical letter is found from the commencement of the +era to October 5th, 1582. O. S. From October 15th, 1582, till the year +1700, take the remainder as found by the rule from 6, if it be less than +6, but if the remainder be 6, take it from 13, and so on according to +instructions given in the table on 49th page. It should be understood +here, that in leap-years the letter found by the preceding rule will be +the dominical letter for that part of the year that follows the 29th of +February, while the letter which follows it will be the one for January +and February. + + +EXAMPLES. + +To find the dominical letter for 1365, we have 1365 / 4 = 341 +; 1365 + +341 = 1706; 1706 / 7 = 243, remainder 5. Then 10 - 5 = 5; therefore E +being the fifth letter is the dominical letter for 1365. + +To find the dominical letter for 1620, we have 1620 / 4 = 405; 1620 + 405 += 2025; 2025 / 7 = 289, remainder 2. Then 6 - 2 = 4; therefore, D and E +are the dominical letters for 1620; E for January and February, and D for +the rest of the year. The process of finding the dominical letter is very +simple and easily understood, if we observe the following order: + +1st. Divide by 4. + +2d. Add to the given number. + +3d. Divide by 7. + +4th. Take the remainder from 3 or 10, from the commencement of the era to +October 5th, 1582. From October 15th, 1582 to 1700, from 6 or 13. From +1700 to 1800, from 7, and so on. See table on 49th page. + +We divide by 4 because the intercalary period is four years; and as every +fourth year contains the divisor 4 once more than any of the three +preceding years, so there is one more added to the fourth year than there +is to any of the three preceding years; and as every year consists of 52 +weeks and one day, this additional year gives an additional day to the +remainder after dividing by 7. For example, the year + + 1 of the era consists of 52 w. 1 d. + 2 years consist of 104 w. 2 d. + 3 years consist of 156 w. 3 d. + (4 / 4) + 4 = 5 years consist of 260 w. 5 d. + +Hence the numbers thus formed will be 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, +15, and so on. + +We divide by 7, because there are seven days in the week, and the +remainders show how many days more than an even number of weeks there are +in the given year. Take, for example, the first twelve years of the era +after being increased by one-fourth, and we have + + 1 / 7 = 0 remainder 1 Then 3 - 1 = 2 = B + 2 / 7 = 0 " 2 " 3 - 2 = 1 = A + 3 / 7 = 0 " 3 " 10 - 3 = 7 = G + 5 / 7 = 0 " 5 " 10 - 5 = 5 = F E + 6 / 7 = 0 " 6 " 10 - 6 = 4 = D + 7 / 7 = 1 " 0 " 3 - 0 = 3 = C + 8 / 7 = 1 " 1 " 3 - 1 = 2 = B + 10 / 7 = 1 " 3 " 10 - 3 = 7 = A G + 11 / 7 = 1 " 4 " 10 - 4 = 6 = F + 12 / 7 = 1 " 5 " 10 - 5 = 5 = E + 13 / 7 = 1 " 6 " 10 - 6 = 4 = D + 15 / 7 = 2 " 1 " 3 - 1 = 2 = C B + +From this table it may be seen that it is these remainders representing +the number of days more than an even number of weeks in the given year, +that we have to deal with in finding the dominical letter. + +Did the year consist of 364 days, or 52 weeks, invariably, there would be +no change in the dominical letter from year to year, but the letter that +represents Sunday in any given year would represent Sunday in every year. +Did the year consist of only 363 days, thus wanting one day of an even +number of weeks, then these remainders, instead of being taken from a +given remainder, would be added to that number, thus removing the +dominical letter forward one place, and the beginning of the year, instead +of being one day later, would be one day earlier in the week than in the +preceding year. + +Thus, if the year 1 of the era be taken from 3, we would have 3 - 1 = 2; +therefore, B being the second letter, is dominical letter for the year 1. +But if the year consist of only 363 days, then the 1 instead of being +taken from 3 would be added to 3; then we would have 3 + 1 = 4; therefore, +D being the fourth letter would be dominical letter for the year 1. The +former going back from C to B, the latter forward from C to D; or which +amounts to the same thing, make the year to consist of 51 weeks and 6 +days; then 10 - 6 = 4, making D the dominical letter as before. + +As seven is the number of days in the week, and the object of these +subtractions is to remove the dominical letter back one place every common +year, and two in leap-year, why not take these remainders from 7? We +answer, all depends upon the day of the week on which the era commenced. +Had G, the seventh letter been dominical letter for the year preceding the +era, then these remainders would be taken from 7; and 7 would be used +until change of style in 1582. But we know from computation that C, the +third letter, is dominical letter for the year preceding the era; so we +commence with three, and take the smaller remainders, 1 and 2 from 3; that +brings us to A. We take the larger remainders, from 3 to 6, from 3 + 7 = +10. We add the 7 because there are seven days in the week. We use the +number 10 until we get back to C, the third letter, the place from whence +we started. For example, we have + + 3 - 1 = 2 = B + 3 - 2 = 1 = A + 10 - 3 = 7 = G + 10 - 4 = 6 = F + 10 - 5 = 5 = E + 10 - 6 = 4 = D + 3 - 0 = 3 = C + +The cycle of seven days being completed, we commence with the number three +again, and so on until 1582, when on account of the errors of the Julian +calendar, ten days were suppressed to restore the coincidence of the solar +and civil year. Now every day suppressed removes the dominical letter +forward one place; so counting from C to C again is seven, D is eight, E +is nine, and F is ten. As F is the sixth letter, we take the remainders +from 1 to 5, from 6; if the remainder be 6, take it from 6 + 7 = 13. Then +6 or 13 is used till 1700, when, another day being suppressed, the number +is increased to 7. And again in 1800, for the same reason, a change is +made to 1 or 8; in 1900 to 2 or 9, and so on. It will be seen by the table +on the 49th page that the smaller numbers run from 1 to 7; the larger ones +from 8 to 13. + +From the commencement of the Christian era to October 5th, 1582, take the +remainders, after dividing by 7, from 3 or 10; from October 15th, + + 1582 to 1700 from 6 or 13 + 1700 to 1800 " 7 + 1800 to 1900 " 1 or 8 + 1900 to 2100 " 2 or 9 + 2100 to 2200 " 3 or 10 + 2200 to 2300 " 4 or 11 + 2300 to 2500 " 5 or 12 + 2500 to 2600 " 6 or 13 + 2600 to 2700 " 7 + 2700 to 2900 " 1 or 8 + 2900 to 3000 " 2 or 9 + 3000 to 3100 " 3 or 10 + 3100 to 3300 " 4 or 11 + 3300 to 3400 " 5 or 12 + 3400 to 3500 " 6 or 13 + 3500 to 3700 " 7 + 3700 to 3800 " 1 or 8 + 3800 to 3900 " 2 or 9 + 3900 to 4000 " 3 or 10 + 4000 to 4100 " 4 or 11 + 4100 to 4200 " 5 or 12 + 4200 to 4300 " 6 or 13 + 4300 to 4500 " 7 + 4500 to 4600 " 1 or 8 + 4600 to 4700 " 2 or 9 + 4700 to 4900 " 3 or 10 + 4900 to 5000 " 4 or 11 + 5000 to 5100 " 5 or 12 + + + + +CHAPTER V. + +RULE FOR FINDING THE DAY OF THE WEEK OF ANY GIVEN DATE, FOR BOTH OLD AND +NEW STYLES. + + +By arranging the dominical letters in the order in which the different +months commence, the day of the week on which any month of any year, or +day of the month has fallen or will fall, from the commencement of the +Christian era to the year of our Lord 4000, may be calculated. (Appendix +G.) They have been arranged thus in the following couplet, in which At +stands for January, Dover for February, Dwells for March, etc. + + At Dover Dwells George Brown, Esquire, + Good Carlos Finch, and David Fryer. + +Now if A be dominical or Sunday letter for a given year, then January and +October being represented by the same letter, begin on Sunday; February, +March and November, for the same reason, begin on Wednesday; April and +July on Saturday; May on Monday, June on Thursday, August on Tuesday, +September and December on Friday. It is evident that every month in the +year must commence on some one day of the week represented by one of the +first seven letters of the alphabet. Now let + + January 1st be represented by A, Sun. + Feb. 1st (4 w. 3 d. from the preceding date) by D, Wed. + Mar. 1st 4 w. 0 d. " " " by D, Wed. + Apr. 1st 4 w. 3 d. " " " by G, Sat. + May 1st 4 w. 2 d. " " " by B, Mon. + June 1st 4 w. 3 d. " " " by E, Thur. + July 1st 4 w. 2 d. " " " by G, Sat. + Aug. 1st 4 w. 3 d. " " " by C, Tues. + Sept. 1st 4 w. 3 d. " " " by F, Fri. + Oct. 1st 4 w. 2 d. " " " by A, Sun. + Nov. 1st 4 w. 3 d. " " " by D, Wed. + Dec. 1st 4 w. 2 d. " " " by F, Fri. + +Now each of these letters placed opposite the months respectively +represents the day of the week on which the month commences, and they are +the first letters of each word in the preceding couplet. + +To find the day of the week on which a given day of any year will occur, +we have the following + + +RULE. + +Find the dominical letter for the year. Read from this to the letter which +begins the given month, always reading from A toward G, calling the +dominical letter Sunday, the next Monday, etc. This will show on what day +of the week the month commenced; then reckoning the number of days from +this will give the day required. + + +EXAMPLES. + +History records the fall of Constantinople on May 29th, 1453. On what day +of the week did it occur? We have then 1453 / 4 = 363 +; 1453 + 363 = +1816; 1816 / 7 = 259, remainder 3. Then 10 - 3 = 7; therefore, G being the +seventh letter is dominical letter for 1453. Now reading from G to B, the +letter for May, we have G Sunday, A Monday, and B Tuesday; hence May +commenced on Tuesday and the 29th was Tuesday. + +The change from Old to New Style was made by Pope Gregory XIII, October +5th, 1582. On what day of the week did it occur? We have then 1582 / 4 = +395+; 1582 + 395 = 1977; 1977 / 7 = 282, remainder 3. Then 10 - 3 = 7; +therefore, G being the seventh letter, is dominical letter for 1582. Now +reading from G to A, the letter for October, we have G Sunday, A Monday, +etc. Hence October commenced on Monday, and the 5th was Friday. + +On what day of the week did the 15th of the same month fall in 1582? We +have then 1582 / 4 = 395+; 1582 + 395 = 1977; 1977 / 7 = 282, remainder 3. +Then 6 - 3 = 3; therefore, C being the third letter, is the dominical +letter for 1582. Now reading from C to A, the letter for October, we have +C Sunday, D Monday, E Tuesday, etc. Hence October commenced on Friday, and +the 15th was Friday. + +How is this, says one? You have just shown by computation that October, +1582, commenced on Monday, you now say that it occurred on Friday. You +also stated that the 5th was Friday; you now say that the 15th was Friday. +This is absurd; ten is not a multiple of seven. There is nothing absurd +about it. The former computation was Old Style, the latter New Style, the +Old being ten days behind the new. + +As regards an interval of ten days between the two Fridays, there was +none; Friday, the 5th, and Friday, the 15th, was one and the same day; +there was no interval, nothing ever occurred, there was no time for +anything to occur; the edict of the Pope decided it; he said the 5th +should be called the 15th, and it was so. + +Hence to October the 5th, 1582, the computation should be Old Style; from +the 15th to the end of the year New Style. + +On what day of the week did the years 1, 2 and 3, of the era commence? +None of these numbers can be divided by 4; neither are they divisible by +7; but they may be treated as remainders after dividing by 7. Now each of +these numbers of years consists of an even number of weeks with remainders +of 1, 2 and 3 days respectively. Hence we have then for the year 1, 3 - 1 += 2; therefore, B being the second letter, is the dominical letter for the +year 1. Now reading from B to A, the letter for January, we have B Sunday, +C Monday, D Tuesday, etc. Hence January commenced on Saturday. + +Then we have for the year 2, 3 - 2 = 1; therefore A being the first +letter, is dominical letter for the year 2; hence it is evident that +January commenced on Sunday. Again we have for the year 3, 10 - 3 = 7; +therefore, G being the seventh letter, is dominical letter for the year 3. +Now reading from G to A, the letter for January, we have G Sunday, A +Monday; hence January commenced on Monday. + +On what day of the week did the year 4 commence? Now we have a number that +is divisible by 4, it being the first leap-year in the era, so we have 4 / +4 = 1; 4 + 1 = 5; 5 / 7 = 0, remainder 5. Then 10 - 5 = 5; therefore, E +being the 5th letter, is dominical letter for that part of the year which +follows the 29th of February, while F, the letter that follows it, is +dominical letter for January and February. Now reading from F to A, the +letter for January, we have F Sunday, G Monday, A Tuesday; hence January +commenced on Tuesday. + +Now we have disposed of the first four years of the era; the dominical +letters being B, A, G, and F, E. Hence it is evident, while one year +consists of an even number of weeks and one day, two years of an even +number of weeks and two days, three years of an even number of weeks and +three days, that every fourth year, by intercalation, is made to consist +of 366 days; so that four years consist of an even number of weeks and +five days; for we have (4 / 4) + 4 = 5, the dominical letter going back +from G in the year 3, to F, for January and February in the year 4, and +from F to E for the rest of the year, causing the following year to +commence two days later in the week than the year preceding. + +The year 1 had 53 Saturdays; the year 2, 53 Sundays; the year 3, 53 +Mondays, and the year 4, 53 Tuesdays and 53 Wednesdays, causing the year 5 +to commence on Thursday, two days later in the week than the preceding +year. Now what is true concerning the first four years of the era, is true +concerning all the future years, and the reason for the divisions, +additions and subtractions in finding the dominical letter is evident. + +The Declaration of Independence was signed July 4, 1776. On what day of +the week did it occur? We have then 1776 / 4 = 444; 1776 + 444 = 2220; +2220 / 7 = 317, remainder 1. Then 7 - 1 = 6, therefore F and G are the +dominical letters for 1776, G for January and February, and F for the rest +of the year. Now reading from F to G, the letter for July, we have F +Sunday, G Monday; hence July commenced on Monday, and the fourth was +Thursday. On what day of the week did Lee surrender to Grant, which +occurred on April 9th, 1865? We have then 1865 / 4 = 466+; 1865 + 466 = +2331; 2331 / 7 = 333, remainder 0. Then 1 - 0 = 1; therefore, A being the +first letter, is dominical letter for 1865. Now reading from A to G, the +letter for April, we have A Sunday, B Monday, C Tuesday, etc. Hence April +commenced on Saturday, and the 9th was Sunday. + +Benjamin Harrison was inaugurated President of the United States on +Monday, March 4, 1889. On what day of the week will the 4th of March fall +in 1989? We have then 1989 / 4 = 497+; 1989 + 497 = 2486; 2486 / 7 = 355, +remainder 1. Then 2 - 1 = 1; therefore, A being the first letter, is +dominical letter for 1989. Now, reading from A to D, the letter for March, +we have A Sunday, B Monday, C Tuesday, and D Wednesday; hence March will +commence on Wednesday, and the 4th will fall on Saturday. Columbus landed +on the island of San Salvador on Friday, October 12, 1492. On what day of +the month and on what day of the week will the four hundredth anniversary +fall in 1892? + +The day of the month on which Columbus landed is, of course, the day to be +observed in commemoration of that event. The Julian calendar, which was +then in use throughout Europe, and the very best that had ever been given +to the world, made the year too long by more than eleven minutes. Those +eleven minutes a year had accumulated, from the council of Nice, in 325, +to the discovery of America, in 1492, to nine days, so that the civil year +was nine days behind the true or solar time; that is, when the Earth, in +her annual revolution, had arrived at that point of the ecliptic +coinciding with the 21st of October, the civil year, according to the +Julian calendar, was the 12th. + +Now, to restore the coincidence, the nine days must be dropped, or +suppressed, calling what was erroneously called the 12th of October, the +21st. Since the Julian calendar was corrected by Gregory, in 1582, we have +so intercalated as to retain, very nearly, the coincidence of the solar +and the civil year. It has already been shown in Chapter III, (q. v.) that +in the Gregorian calendar, the cycle which restores the coincidence of the +day of the month and the day of the week, is completed in 400 years; so +that after 400 years, events will again transpire in the same order, on +the same day of the week. Now, as Columbus landed on Friday, October 21st, +1492, so Friday, October 21st, 1892, is the day of the month and also the +day of the week to be observed in commemoration of that event. We have +then 1892 / 4 = 473; 1892 + 473 = 2365; 2365 / 7 = 337, remainder 6. Then +8 - 6 = 2; therefore, B and C are dominical letters for 1892, C for +January and February, and B for the rest of the year. Now, reading from B +to A, the letter for October, we have B Sunday, C Monday, etc. Hence +October will commence on Saturday and the 21st will be Friday. + +Although there was an error of thirteen days in the Julian calendar when +it was reformed by Gregory, in 1582, there was a correction made of only +ten days. There was still an error of three days from the time of Julius +Caesar to the Council of Nice, which remained uncorrected. Gregory restored +the vernal equinox to the 21st of March, its date at the meeting of that +council, not to the place it occupied in the time of Caesar, namely, the +24th of March. Had he done so it would now fall on the 24th, by adopting +the Gregorian rule of intercalation. Appendix H. + +If desirable calculations may be made in both Old and New Styles from the +year of our Lord 300. There is no perceptible discrepancy in the +calendars, however, until the close of the 4th century, when it amounts to +nearly one day, reckoned in round numbers one day. Now in order to make +the calculation, proceed according to rule already given for finding the +dominical letter, and for New Style take the remainders after dividing by +seven from the numbers in the following table: + + From 400 to 500 From 4 or 11 + " 500 " 600 " 5 " 12 + " 600 " 700 " 6 " 13 + " 700 " 900 " 7 + " 900 " 1000 " 1 " 8 + " 1000 " 1100 " 2 " 9 + " 1100 " 1300 " 3 " 10 + " 1300 " 1400 " 4 " 11 + " 1400 " 1500 " 5 " 12 + " 1500 " 1700 " 6 " 13 + +It will be found by calculation that from the year + + 400 to 500 the discrepancy is 1 day + 500 " 600 " " " 2 " + 600 " 700 " " " 3 " + 700 " 900 " " " 4 " + 900 " 1000 " " " 5 " + 1000 " 1100 " " " 6 " + 1100 " 1300 " " " 7 " + 1300 " 1400 " " " 8 " + 1400 " 1500 " " " 9 " + 1500 " 1700 " " " 10 " + +Hence the necessity, in reforming the calendar in 1582, of suppressing ten +days. (See table on 59th page.) On what day of the week did January +commence in 450? We have then 450 / 4 = 112+; 450 + 112 = 562; 562 / 7 = +80, remainder 2. Then 3 - 2 = 1; therefore, A being the first letter, is +dominical letter for 450, Old Style, and January commenced on Sunday. For +New Style we have 4 - 2 = 2; therefore, B being the second letter, is +dominical letter for the year 450. Now reading from B to A, the letter for +January, we have B Sunday, C Monday, D Tuesday, etc. + +Hence, January commenced on Saturday. Old Style makes Sunday the first +day; New Style makes Saturday the first and Sunday the second. On what day +of the week did January commence in the year 1250? We have then 1250 / 4 = +312+; 1250 + 312 = 1562; 1562 / 7 = 223, remainder 1. Then 3 - 1 = 2; +therefore, B being the second letter, is dominical letter for the year +1250, Old Style. Now, reading from B to A, the letter for January, we have +B Sunday, C Monday, etc. Hence January commenced on Saturday. B is also +dominical letter, New Style; for we take the remainder after dividing by +7, from the same number. + +As both Old and New Styles have the same dominical letter, so both make +January to commence on the same day of the week; but Old Style, during +this century, is seven days behind the true time, so that when it is the +first day of January by the Old, it is the eighth by the New. + + Vernal equinox in the time of Numa, about 700 B. C. + + It is here seen by the errors of the Julian Calendar + the Vernal Equinox is made to occur + three days earlier every 400 years, so + that in 1582 it fell on the + 11th instead of the + 21st of March. 18 + + 17 + + 16 + + 15 + + 14 + + 13 + + 12 + + 11 By suppressing 10 d + + Hou + + " + + " + + + + Hou + + " + + " + + + + By the Gregorian rule of intercalation the coincidence of + years. + + + March 24, 46 B. C. + + 23 | | 1 A. D. + | Restored | + 22 | | 100 " " + | by | + 21 | | 300 " " + | | | | Julius | + 20 | | | | | 400 " " + | | | | Caesar, | + 19 | Vernal | | | 500 " " + | equinox | | 46 B. C., | + | at the | | | 600 " " + | Council | | to the | + | of | | | 800 " " + | Nice, | | place it | + | 325 | | | 900 " " + | A. D. | | occupied | + | | | | | 1000 " " + | | | | in the | + | | | | | 1200 " " + | | | | time of | + | | | | | 1300 " " + | | | | Numa. | + | | | | | 1400 " " + | | | | | + ays, Coincidence 0 Restored in | | 1600 " " + | | | + rs behind time, 18 | 6 in advance. | | 1700 " " + | | | + " " 12 | 12 " " | | 1800 " " + | | | + " " 6 | 18 " " | | 1900 " " + | | | + Coincidence 0 Restored. | | 2000 " " + | | | + rs behind time, 18 | 6 in advance. | | 2100 " " + | | | + " " 12 | 12 " " | | 2200 " " + | | | + " " 6 | 18 " " | | 2300 " " + | | | + Coincidence 0 Restored. | | 2400 " " + + the solar and civil year is restored very nearly every 400 + +Appendix I. + + + + +CHAPTER VI. + +A SIMPLE METHOD FOR FINDING THE DAY OF THE WEEK OF EVENTS WHICH OCCUR +QUADRENNIALLY. + + +The inaugural of the Presidents. The day of the week on which they have +occurred, and on which they will occur for the next one hundred years: + + April 30th, 1789, Thursday, George Washington. + March 4th, 1793, Monday, " " + " " 1797, Saturday, John Adams + " " 1801, Wednesday, Thomas Jefferson. + " " 1805, Monday, " " + " " 1809, Saturday, James Madison. + " " 1813, Thursday, " " + " " 1817, Tuesday, James Monroe. + " " 1821, Sunday, " " + " " 1825, Friday, John Q. Adams. + " " 1829, Wednesday, Andrew Jackson. + " " 1833, Monday, " " + " " 1837, Saturday, Martin Van Buren. + " " 1841, Thursday, Wm. H. Harrison. + " " 1845, Tuesday, James K. Polk. + " " 1849, Sunday, Zachary Taylor. + " " 1853, Friday, Franklin Pierce. + " " 1857, Wednesday, James Buchanan. + " " 1861, Monday, Abraham Lincoln. + " " 1865, Saturday, " " + " " 1869, Thursday, Ulysses S. Grant. + " " 1873, Tuesday, " " + " " 1877, Sunday, Rutherford B. Hays. + " " 1881, Friday, James A. Garfield. + " " 1885, Wednesday, Grover Cleveland. + " " 1889, Monday, Benjamin Harrison. + " " 1893, Saturday, Grover Cleveland. + " " 1897, Thursday, + " " 1901, Monday, + " " 1905, Saturday, + " " 1909, Thursday, + " " 1913, Tuesday, + " " 1917, Sunday, + " " 1921, Friday, + " " 1925, Wednesday, + " " 1929, Monday, + " " 1933, Saturday, + " " 1937, Thursday, + " " 1941, Tuesday, + " " 1945, Sunday, + " " 1949, Friday, + " " 1953, Wednesday, + " " 1957, Monday, + " " 1961, Saturday, + " " 1965, Thursday, + " " 1969, Tuesday, + " " 1973, Sunday, + " " 1977, Friday, + " " 1981, Wednesday, + " " 1985, Monday, + " " 1989, Saturday, + " " 1993, Thursday. + +Any one understanding what has been said in a preceding chapter concerning +the dominical letter, can very easily make out such a table without going +through the process of making calculations for every year. As every +succeeding year, or any day of the year, commences one day later in the +week than the year preceding, and two days later in leap-year, which makes +five days every four years, and as the Presidential term is four years, so +every inaugural occurs five days later in the week than it did in the +preceding term. + +Now, as counting forward five days is equivalent to counting back two, it +will be much more convenient to count back two days every term. There is +one exception, however, to this rule; the year which completes the century +is reckoned as a common year (that is, three centuries out of four), +consequently we count forward only four days or back three. + +Commencing, then, with the second inaugural of Washington, which occurred +on Monday, March 4, 1793, and counting back two days to Saturday in 1797, +three days to Wednesday in 1801 and two days to 1805, and so on two days +every term till 1901, when, for reasons already given, we count back three +days again for one term only, after which it will be two days for the next +two hundred years; hence anyone can make his calculations as he writes, +and as fast as he can write. See table on 61st page. + + +SOME PECULIARITIES CONCERNING EVENTS WHICH FALL ON THE TWENTY-NINTH DAY OF +FEBRUARY. + +The civil year and the day must be regarded as commencing at the same +instant. We cannot well reckon a fraction of a day, giving to February 28 +days and 6 hours, making the following month to commence six hours later +every year; if so, then March, for example, in + + 1888 would commence at 12 m. night. + 1889 " " " 6 a. m. + 1890 " " " 12 m. + 1891 " " " 6 p. m. + 1892 " " " 12 m. night, + +again, and so on. + +Instead of doing so, we wait until the fraction accumulates to a whole +day; then give to February 29 days, and the year 366. Therefore, events +which fall on the 29th of February cannot be celebrated annually, but only +quadrennially; and at the close of those centuries in which the +intercalations are suppressed only octennially. For example: From the year +1696 to 1704, 1796 to 1804, and 1896 to 1904, there is no 29th day of +February; consequently no day of the month in the civil year on which an +event falling on the 29th of February could be celebrated. Therefore, a +person born on the 29th of February, 1896, could celebrate no birthday +till 1904, a period of eight years. + +In every common year February has 28 days, each day of the week being +contained in the number of days in the month four times; but in leap-year, +when February has 29 days, the day which begins and ends the month is +contained five times. Let us suppose that in a certain year, when February +has 29 days, the month comes in on Friday; it also must necessarily end on +Friday. + +After four years it will commence on Wednesday, and end on Wednesday, and +so on, going back two days in the week every four years, until after 28 +years we come back to Friday again. This, as has already been explained, +is the dominical or solar cycle. For example: February in + + The year 4 has five Fridays. + " " 8 " " Wednesdays. + " " 12 " " Mondays. + " " 16 " " Saturdays. + " " 20 " " Thursdays. + " " 24 " " Tuesdays. + " " 28 " " Sundays. + " " 32 " " Fridays. + +So that after 28 years we come back to Friday again; and so on every 28 +years, until change of style in 1582, when the Gregorian rule of +intercalation being adopted by suppressing the intercalations in three +centurial years out of four interrupts this order at the close of these +three centuries. For example--1700, 1800 and 1900, after which the cycle +of 28 years will be continued until 2100, and so on. The cycle being +interrupted by the Gregorian rule of intercalation, causes all events +which occur between 28 and 12 years of the close of the centuries to fall +on the same day of the week again in 40 years; and those events that fall +within 12 years of the close of these centuries, to fall on the same day +of the week again in 12 years; after which the cycle of 28 years will be +continued during the century. See following table: + + 1804 February has five Wednesdays. + 1808 " " " Mondays. + 1812 " " " Saturdays. + 1816 " " " Thursdays. + 1820 " " " Tuesdays. + 1824 " " " Sundays. + 1828 " " " Fridays. + 1832 " " " Wednesdays. + 1836 " " " Mondays. + 1840 " " " Saturdays. + 1844 " " " Thursdays. + 1848 " " " Tuesdays. + 1852 " " " Sundays. + 1856 " " " Fridays. + 1860 " " " Wednesdays. + 1864 " " " Mondays. + 1868 " " " Saturdays. + 1872 " " " Thursdays. + 1876 " " " Tuesdays. + 1880 " " " Sundays. + 1884 " " " Fridays. + 1888 " " " Wednesdays. + 1892 " " " Mondays. + 1896 " " " Saturdays. + 1900 + 1904 " " " Mondays. + 1908 " " " Saturdays. + 1912 " " " Thursdays. + 1916 " " " Tuesdays. + 1920 " " " Sundays. + 1924 " " " Fridays. + 1928 " " " Wednesdays. + +It will be seen from this table that in 1804 February had five Wednesdays; +and then again in 1832, 1860 and 1888; then suppressing the intercalation +in the year 1900 suppresses the 29th of February; so opposite 1900 in the +table is blank, and the 29th of February does not occur again till 1904, +and the five Wednesdays do not occur again till 1928--that is, 40 years +from 1888, when it last occurred. + +Again taking the five Mondays which occurred first in this century, in +1808, and then again in 1836, 1864 and in 1892, you will see, for reasons +already given, that it will occur again in 12 years, that is, in 1904; and +so on with all the days of the week, when it will be seen what is peculiar +concerning the 29th of February. + +But attention is particularly called to the five Thursdays, which occur +first in this century 1816, and then again in 1844 and 1872, the last date +being within 28 years of the close of the century. Suppressing the +intercalation suppresses the 29th of February; consequently the five +Thursdays do not occur again till 1912, that is 40 years from the +preceding date, after which the cycle will be continued for two hundred +years. + +Hence it may be seen that the dominical or solar cycle of 28 years is so +interrupted at the close of these centuries by the suppression of the +leap-year, that certain events do not occur again on the same day of the +week under 40 years, while others are repeated again on the same day of +the week in 12 years; also the number of years in the cycle, that is 28 + +12 = 40. + +And again the change of style in 1582, causes all events which occur +between 28 and 8 years of that change, to fall again on the same day of +the week in 36 years, and all that occur within 8 years of that change to +be repeated again on the same day of the week in 8 years, after which the +cycle of 28 years is continued for 100 years; also that the number of +years in the cycle, that is, 28 + 8 = 36. + + + + +CHAPTER VII. + +RULES FOR FINDING THE DAY OF THE WEEK OF EVENTS THAT TRANSPIRED PRIOR TO +THE CHRISTIAN ERA. + + +First, it should be understood that the year 4 is the first leap year in +our era, reckoning from the year 1 B. C., which must necessarily be leap +year; so that the odd numbers 1, 5, 9, 13, etc., are leap years. Hence +every year that is divisible by four and one remainder, is leap year; if +no remainder, it is the first year after leap-year; if 3, the second; if +2, the third, thus: + + 45 / 4 = 11, remainder, 1, + 44 / 4 = 11, no remainder, + 43 / 4 = 10, remainder, 3, + 42 / 4 = 10, remainder, 2, + 41 / 4 = 10, remainder, 1, + +and so on, every year being divided by four and 1 remainder is leap-year +of 366 days. It should be borne in mind that the same calendar was in use +without any correction from the days of Julius Caesar 46 B. C. to Pope +Gregory XIII in 1582; consequently the method of finding the dominical +letter is, in some respects, similar to the one already given on the 44th +page. But in some respects the one is the reverse of the other, for we +reckon backward and forward from a fixed point--the era; that is the +numbers increase each way from the era. Also the dominical letters occur +in the natural order of the letters in reckoning backward, but exactly the +reverse in reckoning forward. See table on the 73d page, where the +dominical letter is placed opposite each year from 45 B. C. to 45 A. D. +Now we use the same number 3, because C, the third letter is dominical +letter for the year 1 B. C., the point from which we reckon. But instead +of taking the remainder, after dividing by 7, _from_ 3 or 10, to find the +number of the letter, as in Part Second, Chapter IV, (q. v.) we add the +remainder _to_ 3; hence we have the following: + + +RULE. + +Divide the number of the given year by 4, neglecting the remainders, and +add the quotient to the given number, divide this amount by 7, and add the +remainder to 3, and that amount will give the number of the letter, +calling A, 1; B, 2; C, 3, etc.; except the first year after leap-year, +(which is the year exactly divisible by 4), the number of the letter is +one less than is indicated by the rule. + +This rule gives the dominical letter for January and February only, in +leap-year, while the letter that precedes it, is the letter for the rest +of the year. If the amount be greater than seven, we should reckon from A +to A or B again. + +It has already been stated in Part First, Chapter III, (q. v.), that a +change was made by Augustus Caesar about 8 B. C., in the number of days in +the month; and, as this change effects the day of the week on which +certain events fall, it becomes necessary that they should be presented as +they were arranged by Julius Caesar, and as corrected by Augustus. Julius +Caesar gave to February 29 days in common years, and in leap-year 30. This +arrangement was the very best that could possibly be made, but, as has +already been shown, it was interrupted to gratify the vanity of Augustus. + +The left hand column in the table on the 72d page represents the number of +days in each month from the days of Julius Caesar to Augustus, a period of +37 years. The right hand column represents the number of days in the +months as they now are, and have been since the change was made by +Augustus, 8 B. C. Consequently the rule for finding the day of the week on +which events have fallen for the 37 years prior to the last mentioned +date, is not perfectly exact, and needs a little explanation here. + +The rule itself is given, and fully explained in Part Second, Chapter V, +(q. v.) but cannot be applied to the 37 years without some correction. In +all the months marked with a star, events fall one day later in the week +than that which is indicated by the rule. This should be borne in mind, +and make the event one day later in the week than that which is found by +the rule. For example, Julius Caesar was assassinated on the 15th of March, +44 B. C. By giving to February 28 days the first day of March would fall +on Wednesday, and, of course, the 15th would be Wednesday. But Caesar gave +to February 29 days, so that the first day of March fell on Thursday, and +the 15th was Thursday. + +Hence, every event from March to September will fall one day later in the +week than the rule indicates. But the rule is applicable to September, for +it will make no difference whether there are 29 days in February or 31 in +August, there are the same number of days from February to September. But +the 31 days in September will cause all events to fall one day later in +the week during the month of October, but they coincide again during the +month of November. The order is interrupted again in December by giving 31 +days to November. See following table: + + _As Arranged by Julius_ | _As Corrected by Augustus,_ + _Caesar._ | _8 B. C._ + | + January, 31 | January, 31 + February, 29 | February, 28 + March, 31* | March, 31 + April, 30* | April, 30 + May, 31* | May, 31 + June, 30* | June, 30 + July, 31* | July, 31 + August, 30* | August, 31 + September, 31 | September, 30 + October, 30* | October, 31 + November, 31 | November, 30 + December, 30* | December, 31 + + + ---------+-----+---------+-----+---------+-----+---------+----- + Dominical|Year.|Dominical|Year.|Dominical|Year.|Dominical|Year. + Letter. | | Letter. | | Letter. | | Letter. | + ---------+-----+---------+-----+---------+-----+---------+----- + |B. C.| |B. C.| |A. D.| |A. D. + cb | 45 | b | 22 | b | 1 | c | 23 + a | 44 | ag | 21 | a | 2 | ba | 24 + g | 43 | f | 20 | g | 3 | g | 25 + f | 42 | e | 19 | fe | 4 | f | 26 + ed | 41 | d | 18 | d | 5 | e | 27 + c | 40 | cb | 17 | c | 6 | dc | 28 + b | 39 | a | 16 | b | 7 | b | 29 + a | 38 | g | 15 | ag | 8 | a | 30 + gf | 37 | f | 14 | f | 9 | g | 31 + e | 36 | ed | 13 | e | 10 | fe | 32 + d | 35 | c | 12 | d | 11 | d | 33 + c | 34 | b | 11 | cb | 12 | c | 34 + ba | 33 | a | 10 | a | 13 | b | 35 + g | 32 | gf | 9 | g | 14 | ag | 36 + f | 31 | e | 8 | f | 15 | f | 37 + e | 30 | d | 7 | ed | 16 | e | 38 + dc | 29 | c | 6 | c | 17 | d | 39 + b | 28 | ba | 5 | b | 18 | cb | 40 + a | 27 | g | 4 | a | 19 | a | 41 + g | 26 | f | 3 | gf | 20 | g | 42 + fe | 25 | e | 2 | e | 21 | f | 43 + d | 24 | dc | 1 | d | 22 | ed | 44 + c | 23 | | | | | c | 45 + ---------+-----+---------+-----+---------+-----+---------+----- + + + + +PART THIRD. + +CYCLES--JULIAN PERIOD--EASTER. + +HEBREW CALENDAR. + + + + +CHAPTER I. + +THE SOLAR CYCLE. + + +Cycle, (Latin _Cyclus_, ring or circle). The revolution of a certain +period of time which finishes and re-commences perpetually. Cycles were +invented for the purpose of chronology, and for marking the intervals in +which two or more periods of unequal length are each completed a certain +number of times, so that both begin exactly in the same circumstance as at +first. Cycles used in chronology are three: The solar cycle, the lunar +cycle, and the cycle of indiction. + +The solar cycle is a period of time after which the same days of the year +recur on the same days of the week. If every year contained 365 days, then +every year would commence one day later in the week than the year +preceding, and the cycle would be completed in seven years. For if the +first day of January, in any given year, fall on Sunday, then the +following year on Monday, the third on Tuesday, and so on to Sunday again +in seven years. + +But this order is interrupted in the Julian calendar every four years by +giving to February 29 days, and consequently the year 366. Now the number +of years in the intercalary period being four and the days of the week +being seven, their product is 4 x 7 = 28; twenty-eight years then is a +period after which the first day of the year and the first day of every +month recur again in the same order on the same day of the week. This +period is called the solar cycle or the cycle of the sun, the origin of +which is unknown; but is supposed to have been invented about the time of +the Council of Nice, in the year of our Lord 325; but the first year of +the cycle is placed by chronologists nine years before the commencement of +the Christian era. + +Hence the year of the cycle corresponding to any given year in the Julian +calendar is found by the following rule: Add nine to the date and divide +the sum by twenty-eight; the quotient is the number of cycles elapsed, and +the remainder is the year of the cycle. Should there be no remainder, the +proposed year is the twenty-eighth, or last of the cycle. Thus, for the +year 1892, we have (1892 + 9) / 28 = 67, remainder 25. Therefore, 67 is +the number of cycles, and 25 the number in the cycle. + + + + +CHAPTER II. + +THE LUNAR CYCLE. + + +The Lunar cycle, or the cycle of the moon, is a period of nineteen years, +after which the new and full moons fall on the same days of the year as +they did nineteen years before. This cycle was invented by Meton, a +celebrated astronomer of Athens, and may be regarded as the masterpiece of +ancient astronomy. In nineteen solar years there are 235 lunations, a +number which, on being divided by nineteen, gives twelve lunations, with +seven of a remainder, to be distributed among the years of the period. + +The period of Meton, therefore, consisted of twelve years containing +twelve months each, and seven years containing thirteen mouths each, and +these last formed the third, fifth, eighth, eleventh, thirteenth, +sixteenth, and nineteenth years of the cycle. As it had now been +discovered that the exact length of the lunation is a little more than +twenty-nine and a half days, it became necessary to abandon the alternate +succession of full and deficient months; and, in order to preserve a more +accurate correspondence between the civil month and the lunation, Meton +divided the cycle into 125 full months of 30 days, and 110 deficient +months of 29 days each. The number of days in the period was, therefore, +6940; for (125 x 30) + (110 x 29) = 6940. + +In order to distribute the deficient months through the period in the most +equable manner, the whole period may be regarded as consisting of 235 full +months of thirty days, or 7050 days, from which 110 days are to be +deducted; for (235 x 30) = 7050; 7050 - 110 = 6940, as before. This gives +one day to be suppressed in sixty-four, so that if we suppose the months +to contain each thirty days, and then omit every sixty-fourth day in +reckoning from the beginning of the period, those months in which the +omission takes place will, of course, be the deficient months. + +The number of days in the period being known, it is easy to ascertain its +accuracy both in respect of the solar and lunar motions. The exact length +of nineteen solar years is (365d, 5h, 48m, 49.62s.) x 19 = 6939d, 14h, +27m, 42.78s.; hence, the period, which is exactly 6940 days, exceeds +nineteen annual revolutions of the earth by a little more than nine and a +half hours. On the other hand, the exact time of the synodic revolution of +the moon is 29d, 12h, 44m, 2.87s.; 235 lunations, therefore, contain 235 x +(29d, 12h, 44m, 2.87s.) = (6939d, 16h, 31m, 14.45s.), so that the period +exceeds 235 lunations by nearly seven and a half hours. + +At the end of four cycles, or seventy-six years, the accumulation of the +seven and a half hours of difference between the cycle and 235 lunations +amounts to thirty hours, or one whole day and six hours. Calippus, +therefore, in order to make a correction of the Metonic cycle, proposed to +quadruple the period of Meton, and deduct one day at the end of that time +by changing one of the full months into a deficient month. The period of +Calippus, therefore, consisted of three Metonic cycles of 6940 days each, +and a period of 6939 days; and its error in respect to the moon, +consequently, amounted to only six hours, or to one day in 304 years. +This period exceeds seventy-six true solar years by 14h, 9m, 8.88s., but +coincides exactly with seventy-six Julian years; and in the time of +Calippus the length of the solar year was almost universally supposed to +be exactly 365-1/4 days. + + + + +CHAPTER III. + +THE LUNAR CYCLE AND GOLDEN NUMBER. + + +In connecting the lunar month with the solar year, the framers of the +ecclesiastical calendar adopted the period of Meton, or lunar cycle, which +they supposed to be exact. A different arrangement has, however, been +followed with respect to the distribution of the months. The lunations are +supposed to consist of twenty-nine and thirty days alternately, or the +lunar year of 354 days; and in order to make up nineteen solar years, six +embolismic or intercalary months, of thirty days each, are introduced in +the course of the cycle, and one of twenty-nine days is added at the end. +This gives (19 x 354) + (6 x 30) + 29 = 6935 days, to be distributed among +235 lunar months. + +But every leap-year one day must be added to the lunar month in which the +29th of February is included. Now if leap-year happened on the first, +second or third year of the period, there will be five leap-years in the +period, but only four when the first leap-year falls on the fourth. In the +former case the number of days in the period becomes 6940, and in the +latter 6939. The mean length of the cycle is, therefore, 6939-3/4 days, +agreeing exactly with nineteen Julian years. By means of the lunar cycle +the new moons of the calendar were indicated before the reformation in +1582. As the cycle restores these phenomena to the same days of the civil +month, they will fall on the same days in any two years which occupy the +same place in the cycle; consequently a table of the moon's phases for +nineteen years will serve for any year whatever when we know its number in +the cycle. + +The number of the year in the cycle is called the Golden Number; either +because it was so termed by the Greeks, who, on account of its utility, +ordered it to be inscribed in letters of gold in their temples, or more +probably because it was usual to distinguish it by red letters in the +calendar. The Golden Numbers were introduced into the calendar about the +year 530, but disposed as they would have been if they had been inserted +at the time of the Council of Nice. The cycle is supposed to commence with +the year in which the new moon falls on the first day of January, which +took place the year preceding the commencement of our era. + +Hence to find the Golden Number for any year, we have the following rule: +Add one to the date, divide the sum by nineteen; the quotient is the +number of cycles elapsed, and the remainder is the Golden Number. Should +there be no remainder, the proposed year is, of course, the last or +nineteenth of the cycle. Thus, for the year 1892, we have (1892 + 1) / 19 += 99, remainder 12; therefore, 99 is the number of cycles, and 12 the +number in the cycle, or the Golden number. + +It ought to be remarked that the new moons determined in this manner, may +differ from the astronomical new moons sometimes as much as two days. The +reason is, that the sum of the solar and lunar inequalities which are +compensated in the whole period, may amount in certain cases to 10 degrees +and thereby cause the new moon to arrive on the second day before or after +its mean time. + +The cycle of the sun brings back the days of the month to the same day of +the week; the cycle of the moon restores the new moons to the same day of +the month; therefore, 28 x 19 = 532 years, includes all the variations in +respect of the new moons and the dominical letter, and is consequently a +period after which the new moons again occur on the same day of the month +and the same day of the week. This is called the Dionysian or Great +Paschal Period, from its having been employed by Dionysius Exiguus in +determining Easter Sunday. + + + + +CHAPTER IV. + +CYCLE OF INDICTION, AND THE JULIAN PERIOD. + + +The cycle of Indiction or Roman Indiction, is a period of fifteen years; +not astronomical like the two former, but entirely arbitrary. Its origin +and the purpose for which it was established are alike uncertain; but it +is conjectured that it was introduced by Constantine the Great, about the +year 312 of the common era, and had reference to certain judicial acts +that took place under the Greek emperors at stated intervals of fifteen +years. In chronological reckoning, it is considered as having commenced on +the first day of January of the year 313. + +By extending it backward, it will be found that the cycle commenced three +years before the beginning of our era. In order, therefore, to find the +number of any year in the cycle of indiction, we have this rule: Add three +to the date, divide the number by fifteen; and the remainder is the year +of the indiction. Should there be no remainder, the proposed year is the +fifteenth or last of the cycle. Thus, for the year 1892, we have (1892 + +3) / 15 = 126, remainder 5. Therefore, 5 is the number in the cycle. + +The Julian period, proposed by the celebrated Joseph Scaliger, as an +universal measure of chronology, is a period of 7980 years, and is formed +by the continual multiplication of the three numbers, 28, 19 and 15; that +is, of the cycle of the sun, the cycle of the moon, and the cycle of +indiction. Thus, (28 x 19 x 15) = 7980. In the course of this long period +no two years can be expressed by the same numbers in all the three cycles. + +The first year of the Christian era had 10 for its number in the cycle of +the sun, 2 in the cycle of the moon, and 4 in the cycle of the indiction. +Now, it is found by actual calculation, that the only number less than +7980 which, on being divided successively by 28, 19, and 15, leaves the +respective remainders 10, 2 and 4, is 4714. Hence, the first year of the +Christian era corresponded with the year 4714 of the Julian period, which +period coincides with the 710th before the common mundane era 4004 B. C.; +for 4004 + 710 = 4714. Hence, also, the year of our era corresponding to +any other year of the period, or _vice versa_, is found by the following +rule: + +When the given year is anterior to the commencement of the era, subtract +the number of the year of the Julian period from 4714, and the remainder +is the year before Christ; or, subtract the year before Christ from 4714, +and the remainder is the corresponding year in the Julian period. Thus, +Rome was founded in the year 3960 of the Julian period. What was the year +before Christ? We have then 4714 - 3960 = 754. Julius Caesar was +assassinated 44 years before Christ, what was the corresponding year of +the Julian period? We have then, 4714 - 44 = 4670. + +When the given year is after Christ, subtract 4713 from the year of the +period, and the remainder is the year of the era; or add 4713 to the year +of the era, and the sum is the corresponding year in the Julian period. +Thus, the Council of Nice was convened in the year 5038 of the Julian +period, what was the year of our era? We have then, 5038 - 4713 = 325. +What year of the Julian period corresponds with the present year, 1892? We +have then, 4713 + 1892 = 6605. + + + + +CHAPTER V. + +EASTER. + + +Easter (Germ. _Ostern_, Old Saxon _Oster_, from _Osten_, signifying +rising). The English name is probably derived from Ostera or Eostre, the +Teutonic goddess of spring, whose festival occurred about the same time of +the year as the celebration of Easter. The Hebrew-Greek word Pascha has +passed into the name given to this feast by most Christian nations. This +festival is held in commemoration of our Lord's resurrection. + +The Jews celebrated their passover, in conformity with the directions +given them by Moses, on the 14th day of the month Nisan, being the lunar +month of which the 14th day either falls on or next follows the day of the +vernal equinox. In the year of our Lord's crucifixion this fell on a +Friday; the resurrection, therefore, took place on the first day of the +week, which from thence is denominated the Lord's Day. + +The primitive Christians, in celebrating this anniversary, fell into two +different systems. The Western churches observed the nearest Sunday to the +full moon of Nisan, taking no account of the day on which the passover +would be celebrated. The Asiatics, on the other hand, following the Jewish +calendar, adopted the 14th of Nisan upon which to commemorate the +crucifixion, and observed the festival of Easter on the third day +following, upon whatever day of the week that might fall, hence they +obtained the name of Quartodecimans, (from quarto, four, and decem, ten,) +the fourteenth day men. The former appealed to the authority of St. Peter +and St. Paul, the latter to that of St. John. + +The dispute which took place upon this point in the second and third +centuries of our era is remarkable, as connected with perhaps the first +event which can be brought to bear upon the question of the primacy of the +Roman bishop; and it is the more interesting as both parties are +accustomed to claim it as a testimony in favor of their own views. Victor, +bishop of Rome, wrote an imperious letter to the Asiatic bishops, +requiring their conformity to the Western rule; which was answered by +Polycrates, bishop of Ephesus, in the name of the rest, expressing their +resolution to maintain the custom handed down to them by their ancestors. +The Roman bishop thereupon broke off communion with them; but he was +rebuked by Irenaeus, of Lyons, and it was agreed by his mediation that +each party should retain its customs. Such continued to be the practice +till the time of Constantine, when the Council of Nice determined the +matter by the following Canons: + +_a_--Easter must be celebrated on a Sunday. + +_b_--This Sunday must follow the 14th day of the paschal moon, so that if +the 14th day of the paschal moon fall on a Sunday, then Easter must be +celebrated on the Sunday following. + +_c_--The paschal moon is that moon of which the 14th day either falls on +or next follows the day of the vernal equinox. + +_d_--The 21st of March is to be accounted the day of the vernal equinox. +(Appendix L.) + +Sometimes a misunderstanding has arisen from not observing that this +regulation is to be construed according to the tabular full moon as +determined from the epact, and not by the true full moon, which in +general, occurs one or two days earlier. From these conditions it follows, +that if the paschal full moon fall on Saturday, the 21st of March, then +Easter will happen on the 22d, its earliest possible date. For if the full +moon arrive on the 20th, it would not be the paschal full moon, which +cannot happen before the 21st, consequently the following moon is the +paschal full moon, which happens 30 days after the 20th of March, which is +the 19th of April. Now, if in this case the 19th of April is Sunday, then +Easter must be celebrated the following Sunday, or the 26th of April. +Hence, Easter Sunday cannot happen earlier than the 22d of March, or later +than the 26th of April. + +The observance of these rules renders it necessary to reconcile three +periods which have no common measure, namely, the week, the lunar month, +and the solar year; and as this can be done only approximately, and within +certain limits, the determination of Easter is an affair of considerable +nicety and complication. It has already been shown that the lunar cycle +contained 6939 days and 18 hours; also, that the exact time of 235 +lunations is 6939d, 16h, 31m, 14.45s. The difference, which is 1h, 28m, +45.55s., amounts to a day in 308 years, so that at the end of this time +the new moons occur one day earlier than they are indicated by the Golden +Numbers. During the 1257 years that elapsed between the Council of Nice +and the reformation, the error had accumulated to four days, so that the +new moons, which were marked in the calendar as happening, for example, on +the 5th of the month, actually fell on the 1st. + +It would have been easy to correct this error by placing the Golden +Numbers four lines higher in the new calendar, but the suppression of ten +days had already rendered it necessary to place them ten lines lower, and +to carry those which belonged, for example, to the 5th and 6th of the +month, to the 15th and 16th. But supposing this correction to have been +made, it would have become necessary, at the end of 308 years, to place +them one line higher, in consequence of the accumulation of the error of +the cycle to a whole day. On the other hand, as the Golden Numbers were +only adapted to the Julian calendar, every omission of the centenary +intercalation would require them to be placed one line lower, opposite the +6th, for example, instead of the 5th of the month, so that, generally +speaking, the places of the Golden Numbers would have to be changed every +century. On this account Lilius thought fit to reject the Golden Numbers +from the Calendar, and supply their places by another set of numbers +called Epacts, the use of which we shall now proceed to explain. + +Epact, (Greek _epaktos_, added or introduced). The excess of the solar +year beyond the lunar, employed in the calendar to signify the moon's age +at the beginning of the year. The common solar year consisted of 365 days +and the lunar year only 354 days, the difference is eleven; whence, if a +new moon fall on the first day of January in any year, the moon will be +eleven days old on the first day of the following year, and twenty-two +days old on the first of the third year. The numbers eleven and twenty-two +are therefore the epacts of those years respectively. Another addition of +eleven gives thirty-three for the epact of the fourth year; but in +consequence of the insertion of the intercalary month in each third year +of the lunar cycle, this epact is reduced to three; for 33 - 30 = 3. In +like manner the epacts of all the following years of the cycle are +obtained by successively adding eleven to the epact of the former year, +and rejecting thirty as often as the sum exceeds or equals that number. + +In order to show how the epacts are connected with the Golden Numbers, let +a cypher represent the new moon on the first day of January in any year, +then the epacts and Golden Numbers for a whole lunar cycle would be +represented thus: + + 1 2 3 4 5 6 7 8 9 + 0 11 22 3 14 25 6 17 28 + + 10 11 12 13 14 15 16 17 18 19 + 9 20 1 12 23 4 15 26 7 18 + +But the order is interrupted at the end of the cycle; for the epact of the +following year found in the same manner would be 18 + 11 = 29, whereas it +ought to be a cipher to correspond with the moon's age and the Golden +Number 1. The reason for this is, that the intercalary month, inserted at +the end of the cycle, contains only twenty-nine days instead of thirty; +whence, after 11 has been added to the epact of the year corresponding to +the Golden Number 19, we must reject twenty-nine instead of thirty, in +order to have the epact of the succeeding year; or, which comes to the +same thing, we must add twelve to the epact of the last year of the cycle, +and then reject thirty as before. Thus, 18 + 12 = 30; 30 - 30 = 0; the +cipher corresponding with the Golden Number 1. + +This method of forming the epacts might have been continued indefinitely +if the Julian intercalation had been followed without correction and the +cycle had been perfectly exact; but as neither of these suppositions is +true, two equations or corrections must be applied, one depending on the +error of the Julian year, which is called the solar equation; the other on +the errors of the lunar cycle, which is called the lunar equation. The +solar equation occurs three times in 400 years, namely, in every secular +year which is not a leap-year; for in this case the omission of the +intercalary day causes the new moons to arrive one day later in all the +following months, so that the moon's age at the end of the month is one +day less than it would have been if the intercalation had been made, and +the epacts must accordingly be all diminished by unity. Thus, the epacts +11, 22, 3, 14, etc., become 10, 21, 2, 13, etc. + +On the other hand, when the time by which the new moons anticipate the +lunar cycle amounts to a whole day, which, as we have seen, it does in 308 +years, the new moons will arrive one day earlier and the epacts must, +consequently, be increased by unity. Thus, the epacts 11, 22, 3, 14, etc., +in consequence of the lunar equation, becomes 12, 23, 4, 15, etc. In order +to preserve the uniformity of the calendar, the epacts are changed only at +the commencement of the century; the correction of the error of the lunar +cycle is therefore made at the end of 300 years. In the Gregorian calendar +this error is assumed to amount to a day in 312-1/2 years, or eight days +in 2500 years, an assumption which requires the line of epacts to be +changed seven times successively at the end of each period of 300 years, +and once at the end of 400 years; and from the manner in which the epacts +were disposed at the reformation, it was found most correct to suppose one +of the periods of 2500 years to terminate with the year 1800. + +The years in which the solar equation occurs, counting from the +reformation, are 1700, 1800, 1900, 2100, 2200, 2300, 2500, etc. Those in +which the lunar equation occurs are 1800, 2100, 2400, 2700, 3000, 3300, +3600, 3900, after which 4300, 4600, and so on. When the solar equation +occurs, the epacts are diminished by unity; when the lunar equation +occurs, the epacts are augmented by unity; and when both equations occur +together, as in 1800, 2100, 2700, etc., they compensate each other, and +the epacts are not changed. + + + + +CHAPTER VI. + +A NEW AND EASY METHOD OF FIXING THE DATE OF EASTER. + + +In determining the date of Easter, we make use of the numbers called +epacts; and, as these numbers have already been explained in the preceding +chapter, (q. v.) it will be necessary to give them only a brief notice +here. Epact, as has already been defined, is the excess of the solar year +beyond the lunar, employed in the calendar to signify the moon's age at +the beginning of the year; that is, if a new moon fall on the first day +of January in any year, it will be eleven days old on the first day of +the following year, and twenty-two days old on the first day of the third +year, and so on. + +Now, in this work, in fixing the date of Easter, we abandon the use of the +new moons altogether, and make calculations wholly from the paschal full +moons, which cannot happen earlier than the 21st of March, nor later than +the 19th of April. Appendix J. The epacts are here used to show the day of +the month on which the paschal full moons fall; that is, if the paschal +moon fall on a given day of the month in any year, it will happen eleven +days earlier the following year, and twenty-two days earlier the third +year, and so on. To illustrate, suppose the paschal moon fall on the 18th +of April in any given year, on the following year it would fall on the +7th, in the third year on the 27th of March; and in the fourth year the +moon would full on the 16th of March, but that would not be the paschal +moon, which cannot happen earlier than the 21st; so the following moon +would be the paschal moon, which happens thirty days later, or the 15th of +April; then the fifth year it would fall on the 4th of April, and so on. + +The solar and lunar equations or corrections are not made by change of +epacts, for only one line of epacts is used in this work, but these +corrections are made by a change of the day of the month on which the +cycle commences. This change is made at the beginning of a century, and, +of course, does not occur but once in a hundred years, and frequently no +change is made for two, and even three hundred years. The reason for +making these changes has been given in the preceding chapter, (q. v.), +and will again be noticed in the proper place. The line of epacts used are +thus represented, commencing with a cipher as the point of departure: 0, +11, 22, 3, 14, 25, 6, 17, 28, 9, 20, 1, 12, 23, 4, 15, 26, 7, 18. It +should be borne in mind that the epacts are obtained by successively +adding eleven to the epact of the former year, and rejecting thirty as +often as the sum exceeds or equals that number. But, as the intercalary +month inserted at the end of the cycle contains only 29 days, add twelve +instead of eleven, to eighteen, the last of the cycle, and then reject +thirty as before; thus, 18 + 12 = 30; then 30 - 30 = 0. The cycle being +completed, we again commence with the cipher as the point of departure. + +After having found the paschal full moons for one lunar cycle, a period of +nineteen years, then the paschal moons again occur in the same order, on +the same days of the month, as they did nineteen years before. Now, as has +also been shown in the preceding chapter, this cycle might have been +continued indefinitely had the Julian intercalation been followed without +correction, and the cycle been perfectly exact; but neither of these being +true, two equations or corrections must be made, one depending on the +error of the Julian calendar, which is called the solar-equation; the +other on the error of the lunar cycle, which is called the lunar equation. + +Every omission of the intercalary day, which occurs three times in 400 +years, will cause the full moons to fall one day later; for example, on +the 13th of the month instead of the 12th. On the other hand, as has also +been shown in the preceding chapter, the error of the lunar cycle is one +day in 300 years; so that at the end of every 300 years the full moons +will fall one day earlier, for example, on the 11th of the month instead +of the 12th. Now, when both equations occur together, they compensate each +other; that is, while the solar equation would cause the full moon to fall +on the 13th, the lunar equation would make it fall on the 11th; therefore, +no correction is to be made--there is nothing to correct. Had they +occurred singly, the full moon, at the beginning of the cycle, would have +fallen either on the 13th or the 11th; but as they occur together, no +change is made; and the full moons of the calendar will remain as they are +for the next one hundred years. + +Hence, the date of Easter may very easily be determined, as indicated in +the following tables (q. v.). It is known by actual calculation that the +paschal full moon fell on the 12th of April in the year 1596, which moon +was the first of a cycle after the reformation of the calendar by Gregory. +Now, by taking the epact of the following years of the cycle, which are +11, 22, 3, 14, 25, etc., from 12, the date of the first paschal moon, and +you will have all the moons of the cycle. Of course, the epacts 22, 25, +etc., cannot be taken from 12, but being carried back from the 12th of +April, they will show on what day in March the full moons fall. When the +epacts are greater than 12, it would be more convenient to take them from +43, as the number of days in March being 31, so 12 + 31 = 43. + +To find the paschal moons of the cycle, we have then this rule: If the +epact is less than 12, take it from 12; if greater, take it from 43, and +the remainder will be the date of the paschal moon; unless the full moon +fall before the 21st of March, in which case the following moon will be +the paschal moon, which happens thirty days later. But when the solar +equation occurs in 1710, causing the cycle to commence with the 13th of +April, then the epacts must be taken from 13, or 13 + 31 = 44. And again +in 1900, the correction makes the cycle commence on the 14th of April; so +the number from which the epacts are taken is 14, or 14 + 31 = 45, and so +on. Whenever there is a change of date of the paschal moon in the +beginning of the cycle, as there is again in 2204, 2318 and 2413, etc., as +may be seen in the following tables, then the epacts must be taken from +that date, or that date plus 31, the number of days in March. + +Or the date of the paschal moons may very easily be determined by taking +eleven successively from the date of every preceding full moon, and that +will give the date of the paschal moons; only it should be borne in mind +that, whenever the full moon falls before the 21st of March, the following +moon is the paschal moon, which happens thirty days later. + +As Easter Sunday is the first Sunday after the paschal full moon, so all +that remains to be done in fixing the date of Easter, is to find the day +of the month on which that Sunday falls; and as this can easily be done by +the use of the dominical letter, which letter and its use in fixing dates +having been fully explained in Part Second, Chapters IV and V, (q. v.), a +repetition seems to be unnecessary here. + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + gf | 1596 | April 12 | 14 | 0 | 1 + e | 1597 | " 1 | 6 | 11 | 2 + d | 1598 | March 21 | 22 | 22 | 3 + c | 1599 | April 9 | 11 | 3 | 4 + ba | 1600 | March 29 | 2 | 14 | 5 + g | 1601 | April 17 | 22 | 25 | 6 + f | 1602 | " 6 | 7 | 6 | 7 + e | 1603 | March 26 | 30 | 17 | 8 + dc | 1604 | April 14 | 18 | 28 | 9 + b | 1605 | " 3 | 10 | 9 | 10 + a | 1606 | March 23 | 26 | 20 | 11 + g | 1607 | April 11 | 15 | 1 | 12 + fe | 1608 | March 31 | 6 | 12 | 13 + d | 1609 | April 19 | 26 | 23 | 14 + c | 1610 | " 8 | 11 | 4 | 15 + b | 1611 | March 28 | 3 | 15 | 16 + ag | 1612 | April 16 | 22 | 26 | 17 + f | 1613 | " 5 | 7 | 7 | 18 + e | 1614 | March 25 | 30 | 18 | 19 + d | 1615 | April 12 | 19 | 0 | 1 + cb | 1616 | " 1 | 3 | 11 | 2 + a | 1617 | March 21 | 26 | 22 | 3 + g | 1618 | April 9 | 15 | 3 | 4 + f | 1619 | March 29 | 31 | 14 | 5 + ed | 1620 | April 17 | 19 | 25 | 6 + c | 1621 | " 6 | 11 | 6 | 7 + b | 1622 | March 26 | 27 | 17 | 8 + a | 1623 | April 14 | 16 | 28 | 9 + gf | 1624 | " 3 | 7 | 9 | 10 + e | 1625 | March 23 | 30 | 20 | 11 + d | 1626 | April 11 | 12 | 1 | 12 + c | 1627 | March 31 | 4 | 12 | 13 + ba | 1628 | April 19 | 23 | 23 | 14 + g | 1629 | " 8 | 15 | 4 | 15 + f | 1630 | March 28 | 31 | 15 | 16 + e | 1631 | April 16 | 20 | 26 | 17 + dc | 1632 | " 5 | 11 | 7 | 18 + b | 1633 | March 25 | 27 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +By close examination of the above tables, it will be seen that there is +just eleven days difference in the date of these paschal moons, from year +to year, through the whole lunar cycle, and through all lunar cycles. In +determining the date of Easter, it will also be seen, that whenever the +full moon falls before the 21st of March, then the following moon, which +happens thirty days later, is the paschal moon, as the 21st of March is +its earliest possible date. Also when the cycle is + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + a | 1634 | April 12 | 16 | 0 | 1 + g | 1635 | " 1 | 8 | 11 | 2 + fe | 1636 | March 21 | 23 | 22 | 3 + d | 1637 | April 9 | 12 | 3 | 4 + c | 1638 | March 29 | 4 | 14 | 5 + b | 1639 | April 17 | 24 | 25 | 6 + ag | 1640 | " 6 | 8 | 6 | 7 + f | 1641 | March 26 | 31 | 17 | 8 + e | 1642 | April 24 | 20 | 28 | 9 + d | 1643 | " 3 | 5 | 9 | 10 + cb | 1644 | March 23 | 27 | 20 | 11 + a | 1645 | April 11 | 16 | 1 | 12 + g | 1646 | March 31 | 1 | 12 | 13 + f | 1647 | April 19 | 21 | 23 | 14 + ed | 1648 | " 8 | 12 | 4 | 15 + c | 1649 | March 28 | 4 | 15 | 16 + b | 1650 | April 16 | 17 | 26 | 17 + a | 1651 | " 5 | 9 | 7 | 18 + gf | 1652 | March 25 | 31 | 18 | 19 + e | 1653 | April 12 | 13 | 0 | 1 + d | 1654 | " 1 | 5 | 11 | 2 + c | 1655 | March 21 | 28 | 22 | 3 + ba | 1656 | April 9 | 16 | 3 | 4 + g | 1657 | March 29 | 1 | 14 | 5 + f | 1658 | April 17 | 21 | 25 | 6 + e | 1659 | " 6 | 13 | 6 | 7 + dc | 1660 | March 26 | 28 | 17 | 8 + b | 1661 | April 14 | 17 | 28 | 9 + a | 1662 | " 3 | 9 | 9 | 10 + g | 1663 | March 23 | 25 | 20 | 11 + fe | 1664 | April 11 | 13 | 1 | 12 + d | 1665 | March 31 | 5 | 12 | 13 + c | 1666 | April 19 | 25 | 23 | 14 + b | 1667 | " 8 | 10 | 4 | 15 + ag | 1668 | March 28 | 1 | 15 | 16 + f | 1669 | April 16 | 21 | 26 | 17 + e | 1670 | " 5 | 6 | 7 | 18 + d | 1671 | March 25 | 29 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +completed, then the paschal moons again occur in the same order, on the +same day of the month as they did nineteen years before. Now this cycle is +six times repeated in a period of 114 years, when the intercalary day +being suppressed in 1700, causes the first paschal moon of the cycle to +fall on the 13th of April instead of the 12th, and all the moons of the +cycle to fall one day later than they would had the correction not been +made. The cycle is now repeated ten times without + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + cb | 1672 | April 12 | 17 | 0 | 1 + a | 1673 | " 1 | 2 | 11 | 2 + g | 1674 | March 21 | 25 | 22 | 3 + f | 1675 | April 9 | 14 | 3 | 4 + ed | 1676 | March 29 | 5 | 14 | 5 + c | 1677 | April 17 | 18 | 25 | 6 + b | 1678 | " 6 | 10 | 6 | 7 + a | 1679 | March 26 | 2 | 17 | 8 + gf | 1680 | April 24 | 21 | 28 | 9 + e | 1681 | " 3 | 6 | 9 | 10 + d | 1682 | March 23 | 29 | 20 | 11 + c | 1683 | April 11 | 18 | 1 | 12 + ba | 1684 | March 31 | 2 | 12 | 13 + g | 1685 | April 19 | 22 | 23 | 14 + f | 1686 | " 8 | 14 | 4 | 15 + e | 1687 | March 28 | 30 | 15 | 16 + dc | 1688 | April 16 | 18 | 26 | 17 + b | 1689 | " 5 | 10 | 7 | 18 + a | 1690 | March 25 | 26 | 18 | 19 + g | 1691 | April 12 | 15 | 0 | 1 + fe | 1692 | " 1 | 6 | 11 | 2 + d | 1693 | March 21 | 22 | 22 | 3 + c | 1694 | April 9 | 11 | 3 | 4 + b | 1695 | March 29 | 3 | 14 | 5 + ag | 1696 | April 17 | 22 | 25 | 6 + f | 1697 | " 6 | 7 | 6 | 7 + e | 1698 | March 26 | 30 | 17 | 8 + d | 1699 | April 14 | 19 | 28 | 9 + c | 1700 | " 3 | 4 | 9 | 10 + b | 1701 | March 23 | 27 | 20 | 11 + a | 1702 | April 11 | 16 | 1 | 12 + g | 1703 | March 31 | 1 | 12 | 13 + fe | 1704 | April 19 | 20 | 23 | 14 + d | 1705 | " 8 | 12 | 4 | 15 + c | 1706 | March 28 | 4 | 15 | 16 + b | 1707 | April 16 | 17 | 26 | 17 + ag | 1708 | " 5 | 8 | 7 | 18 + f | 1709 | March 25 | 31 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +correction, that is, till the year 1900, a period of 190 years, when the +intercalation being again suppressed, causes the first paschal moon of the +cycle to fall on the 14th of April, and, of course, all the other moons of +the cycle to fall one day later. The reason the correction is not made the +first year of the century is, the lunar cycle must first be completed, and +that did not occur until 1710. As 100 is not a multiple of 19, the number +of years in the cycle, and, as the corrections + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + e | 1710 | April 13 | 20 | 0 | 1 + d | 1711 | " 2 | 5 | 11 | 2 + cb | 1712 | March 22 | 27 | 22 | 3 + a | 1713 | April 10 | 16 | 3 | 4 + g | 1714 | March 30 | 1 | 14 | 5 + f | 1715 | April 18 | 21 | 25 | 6 + ed | 1716 | " 7 | 12 | 6 | 7 + c | 1717 | March 27 | 28 | 17 | 8 + b | 1718 | April 15 | 17 | 28 | 9 + a | 1719 | " 4 | 9 | 9 | 10 + gf | 1720 | March 24 | 31 | 20 | 11 + e | 1721 | April 12 | 13 | 1 | 12 + d | 1722 | " 1 | 5 | 12 | 13 + c | 1723 | March 21 | 28 | 23 | 14 + ba | 1724 | April 9 | 16 | 4 | 15 + g | 1725 | March 29 | 1 | 15 | 16 + f | 1726 | April 17 | 21 | 26 | 17 + e | 1727 | " 6 | 13 | 7 | 18 + dc | 1728 | March 26 | 28 | 18 | 19 + b | 1729 | April 13 | 17 | 0 | 1 + a | 1730 | " 2 | 9 | 11 | 2 + g | 1731 | March 22 | 25 | 22 | 3 + fe | 1732 | April 10 | 13 | 3 | 4 + d | 1733 | March 30 | 5 | 14 | 5 + c | 1734 | April 18 | 25 | 25 | 6 + b | 1735 | " 7 | 10 | 6 | 7 + ag | 1736 | March 27 | 1 | 17 | 8 + f | 1737 | April 15 | 21 | 28 | 9 + e | 1738 | " 4 | 6 | 9 | 10 + d | 1739 | March 24 | 29 | 20 | 11 + cb | 1740 | April 12 | 17 | 1 | 12 + a | 1741 | " 1 | 2 | 12 | 13 + g | 1742 | March 21 | 25 | 23 | 14 + f | 1743 | April 9 | 14 | 4 | 15 + ed | 1744 | March 29 | 5 | 15 | 16 + c | 1745 | April 17 | 18 | 26 | 17 + b | 1746 | " 6 | 10 | 7 | 18 + a | 1747 | March 26 | 2 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +cannot be made only at the beginning of the cycle, so they cannot be made +the first year of the century only once in 1900 years. It may be seen from +one of the above tables that the correction is made in the year 1900, for +the reason that that is the first century which is a multiple of 19. The +next centurial year that is exactly divisible by 19, is 3800. Therefore, +none of the corrections for the next 1900 years, will occur on the first +year of the century. It may also be seen from + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + gf | 1748 | April 13 | 14 | 0 | 1 + e | 1749 | " 2 | 6 | 11 | 2 + d | 1750 | March 22 | 29 | 22 | 3 + c | 1751 | April 10 | 11 | 3 | 4 + ba | 1752 | March 30 | 2 | 14 | 5 + g | 1753 | April 18 | 22 | 25 | 6 + f | 1754 | " 7 | 14 | 6 | 7 + e | 1755 | March 27 | 30 | 17 | 8 + dc | 1756 | April 15 | 18 | 28 | 9 + b | 1757 | " 4 | 10 | 9 | 10 + a | 1758 | March 24 | 26 | 20 | 11 + g | 1759 | April 12 | 15 | 1 | 12 + fe | 1760 | " 1 | 6 | 12 | 13 + d | 1761 | March 21 | 22 | 23 | 14 + c | 1762 | April 9 | 11 | 4 | 15 + b | 1763 | March 29 | 3 | 15 | 16 + ag | 1764 | April 17 | 22 | 26 | 17 + f | 1765 | " 6 | 7 | 7 | 18 + e | 1766 | March 26 | 30 | 18 | 19 + d | 1767 | April 13 | 19 | 0 | 1 + cb | 1768 | " 2 | 3 | 11 | 2 + a | 1769 | March 22 | 26 | 22 | 3 + g | 1770 | April 10 | 15 | 3 | 4 + f | 1771 | March 30 | 31 | 14 | 5 + ed | 1772 | April 18 | 19 | 25 | 6 + c | 1773 | " 7 | 11 | 6 | 7 + b | 1774 | March 27 | 3 | 17 | 8 + a | 1775 | April 15 | 16 | 28 | 9 + gf | 1776 | " 4 | 7 | 9 | 10 + e | 1777 | March 24 | 30 | 20 | 11 + d | 1778 | April 12 | 19 | 1 | 12 + c | 1779 | " 1 | 4 | 12 | 13 + ba | 1780 | March 21 | 26 | 23 | 14 + g | 1781 | April 9 | 15 | 4 | 15 + f | 1782 | March 29 | 31 | 15 | 16 + e | 1783 | April 17 | 20 | 26 | 17 + dc | 1784 | " 6 | 11 | 7 | 18 + b | 1785 | March 26 | 27 | 18 | 19 + ----------+-------+----------+---------+--------+---------- + +the above tables, that, though the intercalary day was suppressed in the +year 1800, no change is made in the date of the paschal moon. The reason +is, the lunar equation also occurred; while the former correction would +cause the paschal moon to fall one day later, that is on the 14th day of +April, the latter would make it fall one day earlier, that is on the 12th; +so they compensate each other, and there is no correction to be made until +the year 1900, when the solar equation + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + a | 1786 | April 13 | 16 | 0 | 1 + g | 1787 | " 2 | 8 | 11 | 2 + fe | 1788 | March 22 | 23 | 22 | 3 + d | 1789 | April 10 | 12 | 3 | 4 + c | 1790 | March 30 | 4 | 14 | 5 + b | 1791 | April 18 | 24 | 25 | 6 + ag | 1792 | " 7 | 8 | 6 | 7 + f | 1793 | March 27 | 31 | 17 | 8 + e | 1794 | April 15 | 20 | 28 | 9 + d | 1795 | " 4 | 5 | 9 | 10 + cb | 1796 | March 24 | 27 | 20 | 11 + a | 1797 | April 12 | 16 | 1 | 12 + g | 1798 | " 1 | 8 | 12 | 13 + f | 1799 | March 21 | 24 | 23 | 14 + e | 1800 | April 9 | 13 | 4 | 15 + d | 1801 | March 29 | 5 | 15 | 16 + c | 1802 | April 17 | 18 | 26 | 17 + b | 1803 | " 6 | 10 | 7 | 18 + ag | 1804 | March 26 | 1 | 18 | 19 + f | 1805 | April 13 | 14 | 0 | 1 + e | 1806 | " 2 | 6 | 11 | 2 + d | 1807 | March 22 | 29 | 22 | 3 + cb | 1808 | April 10 | 17 | 3 | 4 + a | 1809 | March 30 | 2 | 14 | 5 + g | 1810 | April 18 | 22 | 25 | 6 + f | 1811 | " 7 | 14 | 6 | 7 + ed | 1812 | March 27 | 29 | 17 | 8 + c | 1813 | April 15 | 18 | 28 | 9 + b | 1814 | " 4 | 10 | 9 | 10 + a | 1815 | March 24 | 26 | 20 | 11 + gf | 1816 | April 12 | 14 | 1 | 12 + e | 1817 | " 1 | 6 | 12 | 13 + d | 1818 | March 21 | 22 | 23 | 14 + c | 1819 | April 9 | 11 | 4 | 15 + ba | 1820 | March 29 | 2 | 15 | 16 + g | 1821 | April 17 | 22 | 26 | 17 + f | 1822 | " 6 | 7 | 7 | 18 + e | 1823 | March 26 | 30 | 18 | 19 + ----------+-------+----------+---------+--------+---------- + +again occurs, and the first paschal moon of the cycle falls on the 14th; +which cycle is repeated sixteen times in a period of 304 years, after +which, in 2204, the date of the first paschal moon is the 15th of April. +The reason there is no correction to make in this long period is, first, +the year 2000 is a common year in the Gregorian calendar; second, in the +year 2100 both the solar and the lunar equations again occur, and +occurring together, they compensate each other; consequently + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + dc | 1824 | April 13 | 17 | 0 | 1 + b | 1825 | " 2 | 2 | 11 | 2 + a | 1826 | March 22 | 25 | 22 | 3 + g | 1827 | April 10 | 14 | 3 | 4 + fe | 1828 | March 30 | 5 | 14 | 5 + d | 1829 | April 18 | 18 | 25 | 6 + c | 1830 | " 7 | 10 | 6 | 7 + b | 1831 | March 27 | 2 | 17 | 8 + ag | 1832 | April 15 | 21 | 28 | 9 + f | 1833 | " 4 | 6 | 9 | 10 + e | 1834 | March 24 | 29 | 20 | 11 + d | 1835 | April 12 | 18 | 1 | 12 + cb | 1836 | " 1 | 2 | 12 | 13 + a | 1837 | March 21 | 22 | 23 | 14 + g | 1838 | " 9 | 14 | 4 | 15 + f | 1839 | March 29 | 30 | 15 | 16 + ed | 1840 | April 17 | 18 | 26 | 17 + c | 1841 | " 6 | 10 | 7 | 18 + b | 1842 | March 26 | 26 | 18 | 19 + a | 1843 | April 13 | 15 | 0 | 1 + gf | 1844 | " 2 | 6 | 11 | 2 + e | 1845 | March 22 | 22 | 22 | 3 + d | 1846 | April 10 | 11 | 3 | 4 + c | 1847 | March 30 | 3 | 14 | 5 + ba | 1848 | April 18 | 22 | 25 | 6 + g | 1849 | " 7 | 7 | 6 | 7 + f | 1850 | March 27 | 30 | 17 | 8 + e | 1851 | April 15 | 19 | 28 | 9 + dc | 1852 | " 4 | 4 | 9 | 10 + b | 1853 | March 24 | 27 | 20 | 11 + a | 1854 | April 12 | 16 | 1 | 12 + g | 1855 | " 1 | 1 | 12 | 13 + fe | 1856 | March 21 | 20 | 23 | 14 + d | 1857 | " 9 | 12 | 4 | 15 + c | 1858 | March 29 | 4 | 15 | 16 + b | 1859 | April 17 | 17 | 26 | 17 + ag | 1860 | " 6 | 8 | 7 | 18 + f | 1861 | March 26 | 31 | 18 | 19 + ----------+-------+----------+---------+--------+---------- + +the cycle is continued until 2204, after which, as has already been +stated, the date of the first paschal moon is the 15th of April. This +cycle is repeated six times in a period of 114 years, when in 2318, for +reasons already given, the date of the first paschal moon of the next +cycle falls on the 16th, and is repeated five times in a period of 95 +years, when, in 2413, the lunar equation occurs alone, and the date of the +first paschal moon for the next 95 years, that is till the year 2508, + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + e | 1862 | April 13 | 20 | 0 | 1 + d | 1863 | " 2 | 5 | 11 | 2 + cb | 1864 | March 22 | 27 | 22 | 3 + a | 1865 | April 10 | 16 | 3 | 4 + g | 1866 | March 30 | 1 | 14 | 5 + f | 1867 | April 18 | 21 | 25 | 6 + ed | 1868 | " 7 | 12 | 6 | 7 + c | 1869 | March 27 | 28 | 17 | 8 + b | 1870 | April 15 | 17 | 28 | 9 + a | 1871 | " 4 | 9 | 9 | 10 + gf | 1872 | March 24 | 31 | 20 | 11 + e | 1873 | April 12 | 13 | 1 | 12 + d | 1874 | " 1 | 5 | 12 | 13 + c | 1875 | March 21 | 28 | 23 | 14 + ba | 1876 | April 9 | 16 | 4 | 15 + g | 1877 | March 29 | 1 | 15 | 16 + f | 1878 | April 17 | 21 | 26 | 17 + e | 1879 | " 6 | 13 | 7 | 18 + dc | 1880 | March 26 | 28 | 18 | 19 + b | 1881 | April 13 | 17 | 0 | 1 + a | 1882 | " 2 | 9 | 11 | 2 + g | 1883 | March 22 | 25 | 22 | 3 + fe | 1884 | April 10 | 13 | 3 | 4 + d | 1885 | March 30 | 5 | 14 | 5 + c | 1886 | April 18 | 25 | 25 | 6 + b | 1887 | " 7 | 10 | 6 | 7 + ag | 1888 | March 27 | 1 | 17 | 8 + f | 1889 | April 15 | 21 | 28 | 9 + e | 1890 | " 4 | 6 | 9 | 10 + d | 1891 | March 24 | 29 | 20 | 11 + cb | 1892 | April 12 | 17 | 1 | 12 + a | 1893 | " 1 | 2 | 12 | 13 + g | 1894 | March 21 | 25 | 23 | 14 + f | 1895 | April 9 | 14 | 4 | 15 + ed | 1896 | March 29 | 5 | 15 | 16 + c | 1897 | April 17 | 18 | 26 | 17 + b | 1898 | " 6 | 10 | 7 | 18 + a | 1899 | March 26 | 2 | 18 | 19 + ----------+-------+----------+---------+--------+---------- + +falls back to the 15th of April. After which the 16th, on account of the +solar equation, is again the date of the first paschal moon of the cycle +for another period of 95 years; that is till the year 2603, when the solar +equation causes the first paschal moon to fall on the 17th, which cycle is +repeated sixteen times during another period of 304 years, after which, in +2907, the correction makes the date of the first paschal moon of the + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + g | 1900 | April 14 | 15 | 0 | 1 + f | 1901 | " 3 | 7 | 11 | 2 + e | 1902 | March 23 | 30 | 22 | 3 + d | 1903 | April 11 | 12 | 3 | 4 + cb | 1904 | March 31 | 3 | 14 | 5 + a | 1905 | April 19 | 23 | 25 | 6 + g | 1906 | " 8 | 15 | 6 | 7 + f | 1907 | March 28 | 31 | 17 | 8 + ed | 1908 | April 16 | 19 | 28 | 9 + c | 1909 | " 5 | 11 | 9 | 10 + b | 1910 | March 25 | 27 | 20 | 11 + a | 1911 | April 13 | 16 | 1 | 12 + gf | 1912 | " 2 | 7 | 12 | 13 + e | 1913 | March 22 | 23 | 23 | 14 + d | 1914 | April 10 | 12 | 4 | 15 + c | 1915 | March 30 | 4 | 15 | 16 + ba | 1916 | April 18 | 23 | 26 | 17 + g | 1917 | " 7 | 8 | 7 | 18 + f | 1918 | March 27 | 31 | 18 | 19 + e | 1919 | April 14 | 20 | 0 | 1 + dc | 1920 | " 3 | 4 | 11 | 2 + b | 1921 | March 23 | 27 | 22 | 3 + a | 1922 | April 11 | 16 | 3 | 4 + g | 1923 | March 31 | 1 | 14 | 5 + fe | 1924 | April 19 | 20 | 25 | 6 + d | 1925 | " 8 | 12 | 6 | 7 + c | 1926 | March 28 | 4 | 17 | 8 + b | 1927 | April 16 | 17 | 28 | 9 + ag | 1928 | " 5 | 8 | 9 | 10 + f | 1929 | March 25 | 31 | 20 | 11 + e | 1930 | April 13 | 20 | 1 | 12 + d | 1931 | " 2 | 5 | 12 | 13 + cb | 1932 | March 22 | 27 | 23 | 14 + a | 1933 | April 10 | 16 | 4 | 15 + g | 1934 | March 30 | 1 | 15 | 16 + f | 1935 | April 18 | 21 | 26 | 17 + ed | 1936 | " 7 | 12 | 7 | 18 + c | 1937 | March 27 | 28 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +cycle, the 18th of April, which cycle is continued without correction till +the year 3116, a period of 209 years. By reference to the above tables, it +will be seen that the solar and lunar equations occur together in the year +2700 and compensate each other; also, that the year 2800 is a common year +in the Gregorian calendar; consequently there is no correction to make +from 2603 to 2907; also the two equations occur together + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + b | 1938 | April 14 | 17 | 0 | 1 + a | 1939 | " 3 | 9 | 11 | 2 + gf | 1940 | March 23 | 24 | 22 | 3 + e | 1941 | April 11 | 13 | 3 | 4 + d | 1942 | March 31 | 5 | 14 | 5 + c | 1943 | April 19 | 25 | 25 | 6 + ba | 1944 | " 8 | 9 | 6 | 7 + g | 1945 | March 28 | 1 | 17 | 8 + f | 1946 | April 16 | 21 | 28 | 9 + e | 1947 | " 5 | 6 | 9 | 10 + dc | 1948 | March 25 | 28 | 20 | 11 + b | 1949 | April 13 | 17 | 1 | 12 + a | 1950 | " 2 | 9 | 12 | 13 + g | 1951 | March 22 | 25 | 23 | 14 + fe | 1952 | April 10 | 13 | 4 | 15 + d | 1953 | March 30 | 5 | 15 | 16 + c | 1954 | April 18 | 25 | 26 | 17 + b | 1955 | " 7 | 10 | 7 | 18 + ag | 1956 | March 27 | 1 | 18 | 19 + f | 1957 | April 14 | 21 | 0 | 1 + e | 1958 | " 3 | 6 | 11 | 2 + d | 1959 | March 23 | 29 | 22 | 3 + cb | 1960 | April 11 | 17 | 3 | 4 + a | 1961 | March 31 | 2 | 14 | 5 + g | 1962 | April 19 | 22 | 25 | 6 + f | 1963 | " 8 | 14 | 6 | 7 + ed | 1964 | March 28 | 29 | 17 | 8 + c | 1965 | April 16 | 18 | 28 | 9 + b | 1966 | " 5 | 10 | 9 | 10 + a | 1967 | March 25 | 26 | 20 | 11 + gf | 1968 | April 13 | 14 | 1 | 12 + e | 1969 | " 2 | 6 | 12 | 13 + d | 1970 | March 22 | 29 | 23 | 14 + c | 1971 | April 10 | 11 | 4 | 15 + ba | 1972 | March 30 | 2 | 15 | 16 + g | 1973 | April 18 | 22 | 26 | 17 + f | 1974 | " 7 | 14 | 7 | 18 + e | 1975 | March 27 | 30 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +again in the year 3000 and compensate each other, is the reason there is +no correction to make from 2907 to 3116, after which the first paschal +moon falls on the 19th, and is repeated fifteen times in a period of 285 +years, that is till the year 3401, when the correction makes the 20th of +April, the date of the full moon, but that cannot be the paschal moon, +which cannot happen later than the 19th; consequently the + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + dc | 1976 | April 14 | 18 | 0 | 1 + b | 1977 | " 3 | 10 | 11 | 2 + a | 1978 | March 23 | 26 | 22 | 3 + g | 1979 | April 11 | 15 | 3 | 4 + fe | 1980 | March 31 | 6 | 14 | 5 + d | 1981 | April 19 | 26 | 25 | 6 + c | 1982 | " 8 | 11 | 6 | 7 + b | 1983 | March 28 | 3 | 17 | 8 + ag | 1984 | April 16 | 22 | 28 | 9 + f | 1985 | " 5 | 7 | 9 | 10 + e | 1986 | March 25 | 30 | 20 | 11 + d | 1987 | April 13 | 19 | 1 | 12 + cb | 1988 | " 2 | 3 | 12 | 13 + a | 1989 | March 22 | 26 | 23 | 14 + g | 1990 | April 10 | 15 | 4 | 15 + f | 1991 | March 30 | 31 | 15 | 16 + ed | 1992 | April 18 | 19 | 26 | 17 + c | 1993 | " 7 | 11 | 7 | 18 + b | 1994 | March 27 | 3 | 18 | 19 + a | 1995 | April 14 | 16 | 0 | 1 + gf | 1996 | " 3 | 7 | 11 | 2 + e | 1997 | March 23 | 30 | 22 | 3 + d | 1998 | April 11 | 12 | 3 | 4 + c | 1999 | March 31 | 4 | 14 | 5 + ba | 2000 | April 19 | 23 | 25 | 6 + g | 2001 | " 8 | 15 | 6 | 7 + f | 2002 | March 28 | 31 | 17 | 8 + e | 2003 | April 16 | 20 | 28 | 9 + dc | 2004 | " 5 | 11 | 9 | 10 + b | 2005 | March 25 | 27 | 20 | 11 + a | 2006 | April 13 | 16 | 1 | 12 + g | 2007 | " 2 | 8 | 12 | 13 + fe | 2008 | March 22 | 23 | 23 | 14 + d | 2009 | April 10 | 12 | 4 | 15 + c | 2010 | March 30 | 4 | 15 | 16 + b | 2011 | April 18 | 24 | 26 | 17 + ag | 2012 | " 7 | 8 | 7 | 18 + f | 2013 | March 27 | 31 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +moon that precedes it by thirty days, and which falls on the 21st of +March, is the date of the first paschal moon of the cycle which commences +with the year 3401. The day of the month on which Easter Sunday has fallen +or will fall, from the year 1596 to 2013, is already determined, and may +be seen by reference to the above tables. From 2013 to 3401, the date of +Easter is determined for one lunar cycle only, at the + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + ag | 2204 | April 15 | 22 | 0 | 1 + f | 2205 | " 4 | 7 | 11 | 2 + e | 2206 | March 24 | 30 | 22 | 3 + d | 2207 | April 12 | 19 | 3 | 4 + cb | 2208 | " 1 | 3 | 14 | 5 + a | 2209 | March 21 | 26 | 25 | 6 + g | 2210 | April 9 | 15 | 6 | 7 + f | 2211 | March 29 | 31 | 17 | 8 + ed | 2212 | April 17 | 19 | 28 | 9 + c | 2213 | " 6 | 11 | 9 | 10 + b | 2214 | March 26 | 27 | 20 | 11 + a | 2215 | April 14 | 16 | 1 | 12 + gf | 2216 | " 3 | 7 | 12 | 13 + e | 2217 | March 23 | 30 | 23 | 14 + d | 2218 | April 11 | 12 | 4 | 15 + c | 2219 | March 31 | 4 | 15 | 16 + ba | 2220 | April 19 | 23 | 26 | 17 + g | 2221 | " 8 | 15 | 7 | 18 + f | 2222 | March 28 | 31 | 18 | 19 + f | 2318 | April 16 | 21 | 0 | 1 + e | 2319 | " 5 | 6 | 11 | 2 + dc | 2320 | March 25 | 28 | 22 | 3 + b | 2321 | April 13 | 17 | 3 | 4 + a | 2322 | " 2 | 9 | 14 | 5 + g | 2323 | March 22 | 25 | 25 | 6 + fe | 2324 | April 10 | 13 | 6 | 7 + d | 2325 | March 30 | 5 | 17 | 8 + c | 2326 | April 18 | 25 | 28 | 9 + b | 2327 | " 7 | 10 | 9 | 10 + ag | 2328 | March 27 | 1 | 20 | 11 + f | 2329 | April 15 | 21 | 1 | 12 + e | 2330 | " 4 | 6 | 12 | 13 + d | 2331 | March 24 | 29 | 23 | 14 + cb | 2332 | April 12 | 17 | 4 | 15 + a | 2333 | " 1 | 2 | 15 | 16 + g | 2334 | March 21 | 25 | 26 | 17 + f | 2335 | April 9 | 14 | 7 | 18 + ed | 2336 | March 29 | 5 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +beginning of each period; for the reason that it was deemed unnecessary, +because the paschal moons, the epacts, and the Golden Numbers are the same +for every cycle in the period. Therefore, all that remains to be done is +to find the day of the month on which the first Sunday, after the paschal +moon, falls. The dominical letters for any period may very easily be found +by counting backwards one letter each year for every common + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + f | 2413 | April 15 | 21 | 0 | 1 + e | 2414 | " 4 | 6 | 11 | 2 + d | 2415 | March 24 | 29 | 22 | 3 + cb | 2416 | April 12 | 17 | 3 | 4 + a | 2417 | " 1 | 2 | 14 | 5 + g | 2418 | March 21 | 25 | 25 | 6 + f | 2419 | April 9 | 14 | 6 | 7 + ed | 2420 | March 29 | 5 | 17 | 8 + c | 2421 | April 17 | 18 | 28 | 9 + b | 2422 | " 6 | 10 | 9 | 10 + a | 2423 | March 26 | 2 | 20 | 11 + gf | 2424 | April 14 | 21 | 1 | 12 + e | 2425 | " 3 | 6 | 12 | 13 + d | 2426 | March 23 | 29 | 23 | 14 + c | 2427 | April 11 | 18 | 4 | 15 + ba | 2428 | March 31 | 2 | 15 | 16 + g | 2429 | April 19 | 22 | 26 | 17 + f | 2430 | " 8 | 14 | 7 | 18 + e | 2431 | March 28 | 30 | 18 | 19 + ag | 2508 | April 16 | 22 | 0 | 1 + f | 2509 | " 5 | 7 | 11 | 2 + e | 2510 | March 25 | 30 | 22 | 3 + d | 2511 | April 13 | 19 | 3 | 4 + cb | 2512 | " 2 | 3 | 14 | 5 + a | 2513 | March 22 | 26 | 25 | 6 + g | 2514 | April 10 | 15 | 6 | 7 + f | 2515 | March 30 | 31 | 17 | 8 + ed | 2516 | April 18 | 19 | 28 | 9 + c | 2617 | " 7 | 11 | 9 | 10 + b | 2518 | March 27 | 3 | 20 | 11 + a | 2519 | April 15 | 16 | 1 | 12 + gf | 2520 | " 4 | 7 | 12 | 13 + e | 2521 | March 24 | 30 | 23 | 14 + d | 2522 | April 12 | 19 | 4 | 15 + c | 2523 | " 1 | 4 | 15 | 16 + ba | 2524 | March 21 | 26 | 26 | 17 + g | 2525 | April 9 | 15 | 7 | 18 + f | 2526 | March 29 | 31 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +year, and two for leap-year, the fourth letter being dominical letter for +January and February and the fifth for the rest of the year; thus, if G be +dominical letter for any given year, we would have then, G, F, E, DC; B, +A, G, FE; D, C, B, AG; F, E, D, CB, etc. By counting these letters +backwards, or in the tables, from the bottom of the column upwards, they +will occur in alphabetical order. Again it may be seen by reference + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + b | 2603 | April 17 | 24 | 0 | 1 + ag | 2604 | " 6 | 8 | 11 | 2 + f | 2605 | March 26 | 31 | 22 | 3 + e | 2606 | April 14 | 20 | 3 | 4 + d | 2607 | " 3 | 5 | 14 | 5 + cb | 2608 | March 23 | 27 | 25 | 6 + a | 2609 | April 11 | 16 | 6 | 7 + g | 2610 | March 31 | 1 | 17 | 8 + f | 2611 | April 19 | 21 | 28 | 9 + ed | 2612 | " 8 | 12 | 9 | 10 + c | 2613 | March 28 | 4 | 20 | 11 + b | 2614 | April 16 | 17 | 1 | 12 + a | 2615 | " 5 | 9 | 12 | 13 + gf | 2616 | March 25 | 31 | 23 | 14 + e | 2617 | April 13 | 20 | 4 | 15 + d | 2618 | " 2 | 5 | 15 | 16 + c | 2619 | March 22 | 28 | 26 | 17 + ba | 2620 | April 10 | 16 | 7 | 18 + g | 2621 | March 30 | 1 | 18 | 19 + b | 2907 | April 18 | 24 | 0 | 1 + ag | 2908 | " 7 | 8 | 11 | 2 + f | 2909 | March 27 | 31 | 22 | 3 + e | 2910 | April 15 | 20 | 3 | 4 + d | 2911 | " 4 | 5 | 14 | 5 + cb | 2912 | March 24 | 27 | 25 | 6 + a | 2913 | April 12 | 16 | 6 | 7 + g | 2914 | " 1 | 8 | 17 | 8 + f | 2915 | March 21 | 24 | 28 | 9 + ed | 2916 | April 9 | 12 | 9 | 10 + c | 2917 | March 29 | 4 | 20 | 11 + b | 2918 | April 17 | 24 | 1 | 12 + a | 2919 | " 6 | 9 | 12 | 13 + gf | 2920 | March 26 | 31 | 23 | 14 + e | 2921 | April 14 | 20 | 4 | 15 + d | 2922 | " 3 | 5 | 15 | 16 + c | 2923 | March 23 | 28 | 26 | 17 + ba | 2924 | April 11 | 16 | 7 | 18 + g | 2925 | March 31 | 1 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +to these tables, that Easter occurs less frequently on the 22d of March, +its earliest possible date, and the 25th of April, which has hitherto been +considered its latest possible date, than any of the days intervening. It +cannot happen on the 22d, only when the paschal moon falls on the 21st, +and that day must be Saturday. It fell on the 22d, first, after the +reformation of the calendar by Gregory in 1598; again in 1693, 1761, + + -----------+-------+----------+---------+--------+--------- + _Dominical_|_Year._| _Paschal_|_Easter._|_Epact._|_Golden_ + _Letter._ | | _Full_ | | |_Number._ + | | _Moon._ | | | + -----------+-------+----------+---------+--------+--------- + ba | 3116 | April 19 | 23 | 0 | 1 + g | 3117 | " 8 | 15 | 11 | 2 + f | 3118 | March 28 | 31 | 22 | 3 + e | 3119 | April 16 | 20 | 3 | 4 + dc | 3120 | " 5 | 11 | 14 | 5 + b | 3121 | March 25 | 27 | 25 | 6 + a | 3122 | April 13 | 16 | 6 | 7 + g | 3123 | " 2 | 8 | 17 | 8 + fe | 3124 | March 22 | 23 | 28 | 9 + d | 3125 | April 10 | 12 | 9 | 10 + c | 3126 | March 30 | 4 | 20 | 11 + b | 3127 | April 18 | 24 | 1 | 12 + ag | 3128 | " 7 | 8 | 12 | 13 + f | 3129 | March 27 | 31 | 23 | 14 + e | 3130 | April 15 | 20 | 4 | 15 + d | 3131 | " 4 | 5 | 15 | 16 + cb | 3132 | March 24 | 27 | 26 | 17 + a | 3133 | April 12 | 16 | 7 | 18 + g | 3134 | " 1 | 8 | 18 | 19 + d | 3401 | March 21 | 22 | 0 | 1 + c | 3402 | April 9 | 11 | 11 | 2 + b | 3403 | March 29 | 3 | 22 | 3 + ag | 3404 | April 17 | 22 | 3 | 4 + f | 3405 | " 6 | 7 | 14 | 5 + e | 3406 | March 26 | 30 | 25 | 6 + d | 3407 | April 14 | 19 | 6 | 7 + cb | 3408 | " 3 | 10 | 17 | 8 + a | 3409 | March 23 | 26 | 28 | 9 + g | 3410 | April 11 | 15 | 9 | 10 + f | 3411 | March 31 | 7 | 20 | 11 + ed | 3412 | April 19 | 26 | 1 | 12 + c | 3413 | " 8 | 11 | 12 | 13 + b | 3414 | March 28 | 3 | 23 | 14 + a | 3415 | April 16 | 23 | 4 | 15 + gf | 3416 | " 5 | 7 | 15 | 16 + e | 3417 | March 25 | 30 | 26 | 17 + d | 3418 | April 13 | 19 | 7 | 18 + c | 3419 | " 2 | 4 | 18 | 19 + -----------+-------+----------+---------+--------+--------- + +and in 1818. It has not occurred since, nor will not again till 2285, a +period of 467 years. The reason that it does not occur on the 22d of March +in this long period is, the paschal moon does not fall on the 21st, from +the year 1900 to 2204, a period of 304 years. We refer to the tabular +moon, not to the true or astronomical moon, which may occur on the 21st +more than once in this long period. + + + + +CHAPTER VII. + +CHURCH FEASTS AND FASTS WHOSE DATE DEPEND ON THE DATE OF EASTER. + + +Feasts, or Festivals, are days set apart by the church, either for the +grateful memorial of the most remarkable events connected with the plan of +redemption, or upon which to commemorate the actions and sufferings of +such persons as have been most instrumental in carrying forward the +designs of God for the salvation of mankind. + +The ecclesiastical year is divided into eight seasons, namely: +Advent-tide, Christmas-tide, Epiphany-tide, Lenten-tide, Easter-tide, +Ascension-tide, Whitsun-tide, and Trinity-tide. The first day of each of +these seasons has been, and is now observed by the church in commemoration +of some of the most remarkable events connected with the plan of +redemption. All these will be noticed in the order in which they occur in +the ecclesiastical year, while many other days intervening, which are +observed as feasts or fasts, will be given a passing notice. + +_a_--Advent Sunday, which is the day nearest St. Andrew's Day (Nov. 30), +or the first Sunday after the 26th of November, has been recognized since +the sixth century as the first day of the ecclesiastical year. + +Advent (Latin _Adventus_, the coming,) signifies the coming of our +Saviour, the period of the approach of the nativity. As Advent-tide lasts +from Advent Sunday to Christmas, the length of the season depends upon +the day of the month on which Advent Sunday falls. As it may happen as +early as the 27th of November or as late as the 3d of December, so +Advent-tide will contain no more than twenty-eight days nor less than +twenty-two. It should be borne in mind that, though this festival is +classed among the movable feasts, it does not depend upon the date of +Easter, but upon the day of the month on which Advent Sunday falls. The +four Sundays before Christmas were made preparation days for the festival +of Christmas, and were called the first, second, third, and fourth Sundays +in Advent. + +Ember days and Ember weeks are the four seasons set apart by the Western +church for special prayer and fasting, and the ordination of clergy; known +in the church as _quatuor tempora_, (the four seasons.) The Ember weeks +are the weeks next following St. Lucy's Day (Dec. 13th), the first Sunday +in Lent, Whitsun Day, and Holy Cross Day (Sept. 14th). The Wednesdays, +Fridays and Saturdays of these weeks are the Ember days distinctively. The +name by some is supposed to be derived from a German word signifying +Abstinence; by others it is supposed to signify Ashes. + +_b_--Christmas (from Christ and the Saxon _maess_, signifying the mass and +a feast), is a festival held in commemoration of the nativity of our +Saviour throughout nearly the whole of Christendom. It is occupied, +therefore, with the event (the incarnation) which forms the center and +turning point of the history of the world. Though the day of Christ's +birth cannot be ascertained from the New Testament, nor from any other +source, yet the whole Christian world for more than 1300 years have +concurred in celebrating the nativity on the 25th of December. This is +the first of the four great feasts in the ecclesiastical year; the other +three are Easter, Ascension, and Whitsun Day. The length of Christmas-tide +or season is twelve days, lasting from the 25th of December to Epiphany. + +_c_--Epiphany (Greek _Epiphania_, _Theophania_ or _Christophania_,) is a +festival in commemoration of the manifestation of Jesus Christ to the +world as the Son of God, and referring to the appearance of the star which +announced our Saviour's birth to the Gentiles, and the visit of the Magi, +or wise Men of the East to the infant Jesus. This festival is held on the +6th of January invariably, consequently is not a movable feast, though the +length of Epiphany-tide depends upon the date of Easter. As Easter may +happen as early as the 22d of March or as late as the 26th of April (a +variation of thirty-five days), so Epiphany-tide may consist of no less +than twelve days nor more than forty-seven, as the season always ends the +day before Septuagesima Sunday. (See tables at the close of this chapter.) + +Septuagesima, Sexagesima, Quinquagesima. There being exactly fifty days +between the Sunday next before Lent and Easter Day, inclusive, that Sunday +was termed Quinquagesima, i. e., the fiftieth; and the two immediately +preceding Sundays were called from the next round numbers Sexagesima, the +sixtieth; and Septuagesima, the seventieth. + +The Paschal Season extends from Septuagesima Sunday to Low Sunday, a +period of seventy days. It takes its name from the Paschal festival or +Easter, whose services end with Low Sunday, the octave, or eighth day, of +Easter. It begins with Septuagesima Sunday because the church services +then begin to prepare the minds of the faithful for the services of Lent, +which are themselves the preparation for Easter. May not Septuagesima +Sunday be so called because there are just seventy days in the Paschal +Season? + +Shrove-tide literally means confession-time, and is the name given to the +days immediately preceding Ash Wednesday. These days were so called +because on them, and especially on the last of them (Shrove Tuesday) +people were accustomed to confess their sins as a preparation for Lent. In +most Roman Catholic countries it begins with Quinquagesima Sunday, the +Sunday before Lent. + +Ash Wednesday, the first day of Lent, (Latin _dies cinerum_, the day of +Ashes), was so called because it was customary on that day for penitents +to appear in sackcloth, upon which occasion ashes were sprinkled upon +them. + +_d_--Lent, (Anglo-Saxon _lengten_. Perhaps from _lenegan_, to lengthen, +because at this season the days lengthen) the forty days fast, is the +preparation for Easter, and is observed in commemoration of our Lord's +fast in the wilderness. In most languages the name given to this fast +signifies the number of days--forty; but our word Lent signifies the +Spring Fast, for Lenten-tide in the Anglo-Saxon language was the Season of +Spring, in German, Lenz. + +The six Sundays in the Lenten-tide of forty-six days are not counted in +the fast, as all Sundays in the year are reckoned as feast days, because +our Saviour arose from the dead on the first day of the week. + +Quadragesima Sunday, the first Sunday in Lent, is so called by analogy +with the three Sundays which precede Lent, and which (as has already been +stated) are called respectively Septuagesima, seventieth; Sexagesima, +sixtieth; Quinquagesima, fiftieth; and then Quadragesima, fortieth; in +round numbers forty days before Easter. + +Holy Week, the last week in Lent, called also Passion Week, because within +it is commemorated our Lord's sufferings. The days specially solemnized +are Palm Sunday, Spy Wednesday, Holy, or Maundy Thursday, and Good Friday. + +Palm Sunday (Latin _Dominica Palmarium_, or _Dominica_ in _Palmis_) is the +name usually given the Sunday before Easter; a day celebrated in +commemoration of Christ's triumphal entry into Jerusalem, so called +because the people who had come to the feast, when they heard that Jesus +was coming, took branches of palm trees and went forth to meet him, and +cried, "Hosanna; blessed is the King of Israel that cometh in the name of +the Lord." + +Spy Wednesday, so called in allusion to the betrayal of Christ by Judas, +or the day on which he made the bargain to deliver him into the hands of +his enemies for thirty pieces of silver. + +Maundy Thursday (from _Dies mandati_, mandate Thursday), so called either +from the command given his disciples to love one another, or to +commemorate the sacrament of His supper. + +Good Friday, so called in acknowledgment of the benefit derived from the +death of Christ. + +The closing scenes in the life of Christ, the events of Wednesday, +Thursday and Friday of Holy Week, are events of much more importance than +were ever before crowded into any one week in the history of the world. +The betrayal on Wednesday, the institution of the sacrament on Thursday +night, also the words of our Saviour as recorded in John's gospel, from +the 14th to the 17th chapters inclusive, the agony and the bloody sweat in +the garden, the arrest and trial during Thursday night and Friday morning, +the crucifixion at the third hour, the darkness that was over all the land +from the sixth to the ninth hour, and the last words of the blessed Jesus, +"It is finished," (tasted death for every man); these we say, are events +of more importance to man than were ever before crowded into any one week +in the world's history. + +The prophets who prophesied of these things, inquired and searched +diligently, "searching what, or what manner of time the Spirit of Christ +which was in them did signify, when it testified beforehand the sufferings +of Christ and the glory that should follow." And about an hour before this +prophecy began to be fulfilled our Saviour uttered these words: "Verily, +verily, I say unto you, that ye shall weep and lament, but the world shall +rejoice; and ye shall be sorrowful, but your sorrow shall be turned into +joy." It was probably not more than an hour from the time these words fell +from the Saviour's lips, that he was arrested and led away to undergo a +trial; cruel mocking and scourging, crucifixion and death upon the cross. + +Then cometh Joseph of Arimathea, bringing fine linen, and Nicodemus with +his hundred pounds of myrrh and aloes, and they two took the body of the +Lord Jesus and wrapped it in the linen with the spices, and laid it in +Joseph's own new tomb, which he had hewn out in a rock, wherein never man +before was laid, and rolled a great stone against the door of the +sepulcher and departed. Thus endeth Passion Week. While the body of Jesus +is in the sepulcher the world is rejoicing, and the disciples are weeping +and lamenting, according to the words of the Saviour, "Ye shall weep and +lament, but the world shall rejoice." + + He dies! the friend of sinners dies! + Lo! Salem's daughters weep around; + A solemn darkness veils the skies, + A sudden trembling shakes the ground. + +_e_--Easter (German, _Ostern_, Old Saxon _Oster_, from _osten_, signifying +rising,) is a church festival in commemoration of the resurrection of our +Lord from the dead. But the apparent victory which the enemies of Christ +had gained was of short duration, the rejoicing of the world did not long +continue, the remaining words of our Saviour must needs be fulfilled: "But +your sorrow shall be turned into joy." Now, upon the first day of the +week, very early in the morning, (Easter morning) the two Marys came to +the sepulcher bringing the sweet spices and ointments which they had +prepared for the purpose of anointing the body of the Lord Jesus, but were +greatly astonished when they saw that the great stone, which they had seen +rolled against the door of the sepulcher on Friday afternoon, was rolled +away, and an angel sitting upon it whose countenance was like lightning, +and for fear of whom the keepers did shake and become as dead men. But to +the women he said, "Fear not ye; for I know that ye seek Jesus which was +crucified, He is not here, for He is risen." That you may know for a +certainty that He is risen, come and see the place where you saw Him laid +only a few hours ago. Now go quickly and tell His disciples that He is +risen from the dead, and behold He goeth before you into Galilee, there +shall ye see Him. And they departed quickly from the sepulcher with fear +and great joy, and did run to carry the good news to the disciples. But +how much greater their joy soon after their departure when Jesus himself +met them with the comforting words, "Be not afraid, but go tell my +brethren that they go into Galilee, and there shall they see Me." + +The subject for conversation for the past two days had been Jesus and the +crucifixion, but now Jesus and the resurrection. Some believed, but some +doubted. Others ran to the sepulcher and found it even as the women had +said. While the chief priests and elders hired the soldiers to say that +the disciples came by night and stole him away while we slept. But how +should they know what had become of Him if they were sleeping? The truth +was they were so overcome with fear by the brightness of the angels' +countenance that they became as dead men, not knowing what was transpiring +around them. But it was truly good tidings and great joy to the disciples +of Christ on that Easter morning. + + The rising God forsakes the tomb; + In vain the tomb forbids His rise; + Vain the stone, the watch, the seal, + Christ has burst the gates of hell; + Death in vain forbids His rise; + Christ hath opened Paradise. + +The spirit of Christ in the prophets had testified beforehand the +suffering of Christ and the glory that should follow. That morning and +that day was not only joyful to the disciples of Christ, but _glorious_; +it was "joy unspeakable and _full_ of glory." Although 1863 years have +rolled around since that Easter morning, yet we are as much interested in +what then and there transpired as were the Marys, and Peter, and John, who +were the first at the sepulcher, and who were permitted the same day to +see their risen Lord, whom having not seen, we love; in whom, though now +we see Him not, yet believing, we [as well as they] rejoice "with joy +unspeakable and full of glory." + +Low Sunday. The first Sunday after Easter is so called because it was +customary to repeat on this day some part of the solemnity which was used +on Easter day, whence it took the name of Low Sunday, being celebrated as +a feast, but of a lower degree than Easter day itself. The next Sunday +after Easter has been popularly, so called in England, perhaps by +corruption for close, (_Pascha Clausum_) close of Easter. _Dominica_ in +_Albis_, (the Sunday of white garments) a title anciently given to the +first Sunday after Easter, because on this day those persons who had been +baptized at Easter appear for the last time in the chrysomes, or white +robes which they received at baptism. These were laid up in the church as +evidences of their baptismal profession. + +Rogation Days, (Latin _rogare_, to beseech,) are the Monday, Tuesday and +Wednesday after Rogation Sunday and before Ascension Day, (Holy Thursday.) +About the middle of the fifth century Mamertus, bishop of Vienna, upon the +prospect of a great fire that threatened his diocese, appointed that +extraordinary prayer and supplication should be offered up to God, with +fasting, for averting the impending evils upon the above mentioned days; +from which supplications (called by the Latins _rogationes_) these days +have ever since been called Rogation Days. As retained in our present +calendar, they are simply private fasts. + +_f_--Ascension Day, or Holy Thursday, one of the great religious festivals +of the Roman Catholic and Episcopal churches, is held on the fortieth day +after Easter, and ten days before Whitsun Day, to commemorate the +Ascension of our Lord into heaven. Ascension Day has been observed at +least since the year of our Lord 64, and perhaps earlier. Saint Augustine +believed it to have been instituted either by the apostles themselves, or +the bishops immediately succeeding them. + +Expectation Week is the whole of the interval between Ascension Day and +Whitsun Day, so called because at this time the apostles, according to the +command of our Saviour, continued at Jerusalem, in earnest prayer and +expectation of the Holy Comforter which was to abide with them forever. +The Sunday between Ascension Day and Whitsun Day is called Expectation +Sunday. + +Pentecost, (Greek, _Pentecostos_, fiftieth), a Jewish festival; so called +because it was observed on the fiftieth day after the feast of unleavened +bread, called also the feast of weeks, being celebrated seven weeks from +the feast of the Passover. It also commemorated the giving of the law on +Mount Sinai upon that day. The origin of the Anglo-Saxon name of White +Sunday, which also occurs in Icelandic, is somewhat obscure, for in the +Roman churches the _Dominica_ in _Albis_, (Low Sunday, q. v.) so called +from the white robes then worn by the persons baptized at Easter, has +always been the Sunday immediately following Easter. It hardly seems +probable that there should be another Sunday of White Garments within six +weeks. In German it is known by the name _Pfingsten_, old German +_Wingsten_, old English _Whitsun_, hence, probably, our word Whitsun Day, +not White Sunday. + +_g_--Whitsun Day, or Pentecost, is the last of the four _great_ festivals +in the ecclesiastical year, held in commemoration of the outpouring of the +Holy Spirit on the infant church ten days after the Ascension. Among the +last words of our Saviour to the apostles on the very day that He was +taken up, were "Behold I send the promise of my Father upon you, but tarry +ye in the city of Jerusalem until ye be endowed with power from on high." +After ten days of earnest, believing prayer, and expectation, suddenly, +but not unexpectedly, there came a sound from heaven as a rushing, mighty +wind, and it filled all the house where they were sitting, and there +appeared unto them cloven tongues like as of fire, and it sat upon each of +them; and they were all filled with the Holy Ghost, and began to speak +with other tongues as the Spirit gave them utterance; and the multitude +came together, and were amazed, saying one to the other what meaneth this? +Others mocking said, these men are full of new wine. But Peter lifted up +his voice and said, these are not drunken as ye suppose, seeing it is but +the third hour of the day, (nine o'clock in the morning,) men are not +usually drunk so early in the morning; but this is that which the prophet +Joel eight hundred years ago said should come to pass in these last days; +the promise of the Father, the baptism of the Holy Ghost for which they +had been waiting for the past ten days; something of that _glory_ that +should follow the crucifixion, death, resurrection and ascension of the +Lord Jesus into Heaven, the glory of the Christian church, of the +Christian dispensation, and which is destined to fill the whole earth. + + "Waft, Waft, ye winds his story, + And you, ye waters, roll, + Till like a sea of glory, + It spreads from pole to pole." + +_h_--Trinity Sunday, the octave, or eighth day of the feast of Pentecost, +is a church festival held in commemoration of the doctrine of the Trinity. +The introduction of this day into the calendar is of comparatively recent +date, it being established by Pope Benedict XI, in the year of our Lord +1305. It is probable that the zeal of many Christians against the use of +images in the eighth and ninth centuries may have been the first cause of +the appointment of a distinct day for meditating upon the nature of the +Holy Trinity in unity, or the one true God as distinguished from idols. +The reason for its late introduction is that in the creed of the church, +and in its psalms, hymns, and doxologies, great prominence was given to +this doctrine, and it was thought that there was no need to set apart a +particular day for that which was done every day. This is the last of the +movable feasts in the ecclesiastical year, being held eight weeks after +Easter; so it may happen as early as the 17th of May or as late as the +20th of June. The length of both Epiphany and Trinity-tide depend upon the +date of Easter. As Epiphany-tide is shortened by the early date of +Easter, so Trinity-tide is lengthened proportionately, and as +Epiphany-tide is lengthened by the later date of Easter so Trinity-tide is +shortened proportionately; so Trinity-tide may contain no more than 196 +days nor less than 161. (See tables at the close of this chapter.) + +All Saints Day, or All hallowmass (Anglo-Saxon _all_, and _halig_, holy) a +festival celebrated by the Roman Catholic and Episcopal churches on the +first day of November, in honor of all Saints and martyrs. It was +introduced into the Western church in the beginning of the seventh century +by Boniface. The number of saints being exceedingly multiplied, it was +found too burdensome to dedicate a feast day to each, there being, indeed, +scarcely hours enough in the year to distribute among them all. It was +therefore resolved to commemorate on one day all who had no particular +day. By order of Gregory IV, it was celebrated on the first of November, +834; formerly the first of May was the day appointed. It was introduced +into England about 870, and is still observed in the English and Lutheran +churches, as well as the Church of Rome on the first of November. + +All-Souls' Day, a festival held by Roman Catholics on the 2d of November, +for special prayer in behalf of all the faithful dead. It was first +introduced in 998, by Odilon, Abbot of Clugni, who enjoined it on his own +order. It was soon after adopted by neighboring churches. It is the day on +which, in the Romish church, extraordinary masses are repeated for the +relief of souls said to be in purgatory. Formerly on this day persons +dressed in black perambulated the towns and cities, each provided with a +bell of dismal tone, which was rung in public places by way of exhortation +to the people to remember the souls in purgatory. In some parts of the +west of England it is still the custom for the village children to go +around to all their neighbors souling, as they call it, collecting small +contributions, and singing the following verses, taken down from two of +the children themselves: + + Soul! Soul! for a soul-cake, + Pray good mistress, for a soul-cake, + One for Peter, two for Paul, + Three for Him that made us all. + + Soul! soul! for an apple or two; + If you've got no apples, pears will do, + Up with your kettle, and down with your pan, + Give me a good big one and I'll be gone. + +The soul cake referred to in the verses is a sort of bun which the people +used to make, and to give to one another on the 2d of November. + +In the following tables there is presented at one view the day of the +month on which the principal feasts and fasts fall in the ecclesiastical +year 1817-18 and 1885-86. In the former Easter happens at its earliest +possible date, in the latter at its latest date in this century: + + ------------------------------------------+--------------+-------------- + _YEAR 1817-18._ | _Days in_ | _Sundays in_ + |_Each Season._|_Each Season._ + ------------------------------------------+--------------+-------------- + | | + _a_--Advent Sunday, November 30th; | | + Advent-tide, | 25 | 4 + | | + _1st_ Ember Week, after December 13th; | | + Ember Days, Wednesday, Friday and | | + Saturday. | | + | | + _b_--Christmas, December 25th; | | + Christmas-tide, | 12 | 2 + | | + _c_--Epiphany, January 6th; Epiphany-tide,| 12 | 1 + Septuagesima Sunday, January 18th, | 7 | 1 + Paschal season from Jan. 18th to | | + March 29th, 70 days | | + Sexagesima Sunday, January 25th, | 7 | 1 + Quinquagesima Sunday, February 1st, | 3 | 1 + Shrove-tide, (confession time) Shrove| | + Tues., Feb. 3d. | | + | | + _d_--Ash Wednesday, Feb 4th, Lent begins; | | + Lenten-tide, | 46 | 6 + First Sunday in Lent (Quadragesima) | | + February 8th. | | + | | + _2d_ Ember Week after first Sunday in | | + Lent; Ember Days, Wednesday, Friday| | + and Saturday. | | + Holy Week, the week before Easter; | | + Special Days, Palm Sunday, Spy | | + Wednesday, Maundy Thursday, and | | + Good Friday, March 15th, 18th, | | + 19th and 20th. | | + | | + _e_--Easter Sunday, March 22d; | | + Easter-tide, | 39 | 6 + Low Sunday, March 29th; Paschal | | + Season ends. | | + Rogation Sunday, April 26th; Rogation| | + Days, the Monday, Tuesday and | | + Wednesday after Rogation Sunday. | | + | | + _f_--Ascension Day (Holy Thursday), April | | + 30th; Ascension-tide, | 10 | 1 + Expectation Sunday, First Sunday | | + after Ascension, May 3d. | | + | | + _g_--Whitsun Day, (Pentecost) May 10th; | | + Whitsun-tide, | 7 | 1 + | | + _3d_ Ember Week, after Whitsun Day; Ember | | + Days, Wednesday, Friday and | | + Saturday. | | + | | + _h_--Trinity Sunday, May 17th; | 196 | 28 + Trinity-tide, | | + | | + _4th_ Ember Week, after September 14th; | | + Ember Days, Wednesday, Friday and | | + Saturday. | | + | | + All Saints' Day, November 1st. | | + | | + All Souls' Day, November 2d. | | + +--------------+-------------- + Appendix K. | 364 | 52 + ------------------------------------------+--------------+-------------- + + ------------------------------------------+--------------+-------------- + _YEAR 1885-86._ | _Days in_ | _Sundays in_ + |_Each Season._|_Each Season._ + ------------------------------------------+--------------+-------------- + | | + _a_--Advent Sunday, November 29th, | | + Advent-tide, | 26 | 4 + | | + _1st_ Ember Week, after December 13th; | | + Ember Days, Wednesday, Friday and | | + Saturday. | | + | | + _b_--Christmas, December 25th; | | + Christmas-tide, | 12 | 2 + | | + _c_--Epiphany, January 6th; Epiphany-tide,| 46 | 6 + Septuagesima Sunday, February 21st, | 7 | 1 + Paschal season, from Feb. 21st to May| | + 2d, 70 days. | | + Sexagesima Sunday, February 28th, | 7 | 1 + Quinquagesima Sunday, March 7th, | 3 | 1 + Shrove-tide, (confession time) Shrove| | + Tues., Mar. 9th. | | + | | + _d_--Ash Wednesday, March 10th, Lent | | + begins; Lenten-tide | 46 | 6 + First Sunday in Lent (Quadragesima) | | + March 14th. | | + | | + _2d_ Ember Week after first Sunday in | | + Lent; Ember Days, Wednesday, Friday| | + and Saturday. | | + Holy Week, the week before Easter; | | + Special Days, Palm Sunday, Spy | | + Wednesday, Maundy Thursday and Good| | + Friday, April 18th, 21st, 22d and | | + 23d. | | + | | + _e_--Easter Sunday, April 25th; | | + Easter-tide, | 39 | 6 + Low Sunday, May 2d, Paschal Season | | + ends. | | + Rogation Sunday, May 30th; Rogation | | + Days, the Monday, Tuesday and | | + Wednesday after Rogation Sunday. | | + | | + _f_--Ascension Day (Holy Thursday), June | | + 3d; Ascension-tide, | 10 | 1 + Expectation Sunday, first Sunday | | + after Ascension, June 6th. | | + | | + _g_--Whitsun Day, (Pentecost) June 13th; | | + Whitsun-tide, | 7 | 1 + | | + _3d_ Ember Week, after Whitsun Day; Ember | | + Days, Wednesday, Friday and | | + Saturday. | | + | | + _h_--Trinity Sunday, June 20th; | | + Trinity-tide, | 161 | 23 + | | + _4th_ Ember Week, after September 14th; | | + Ember Days, Wednesday, Friday and | | + Saturday. | | + | | + All Saints' Day, November 1st. | | + | | + All Souls' Day, November 2d | | + +--------------+-------------- + Appendix K. | 364 | 52 + ------------------------------------------+--------------+-------------- + + + + +CHAPTER VIII. + +HEBREW CALENDAR. + + +To the Bible student a knowledge of the Hebrew calendar is indispensable, +if he would know how the date of events recorded in the Bible are made to +correspond with our present English calendar. From the exodus (1491 B. C.) +downward, the Hebrew month was lunar, and commenced invariably with the +new moon. + +Dr. Smith, author of Bible Dictionary, says that the terms for month and +moon have the same close connection in the Hebrew language as in our own, +only the Hebrew Codesh (that is new moon) is, perhaps, more distinctive +than the corresponding term in our language; for it expresses not simply +the idea of a lunation, but the recurrence of a period commencing +definitely with the new moon. Though the identification of the Jewish +month with our own cannot be effected with precision on account of the +variations that must necessarily exist between the lunar and the solar +month, each of the former ranging over portions of two of the latter, +still it can be shown how they may be made to coincide very nearly by a +systematic method of intercalation. + +Now from new moon to new moon again, is about 29-1/2 days; therefore, the +Hebrew year consisted of 354 days, for 29-1/2 x 12 = 354; so that the +epact, (which is the excess of the solar year beyond the lunar) is eleven +days. Hence, had they no method of intercalation, the commencement of +their year would go back eleven days every year, and consequently make a +revolution of the seasons every thirty-three years, for 365 / 11 = 33 +nearly. + +To illustrate, let us suppose that the new moon of Nisan, which is the +first month in the Sacred year, should on any given year fall on the 10th +of April, then the following year it would fall on the 30th of March, +which is eleven days earlier; the second year it would fall on the 19th of +March or twenty-two days earlier; the third year the new moon would fall +on the 8th of March or thirty-three days earlier, but that would not be +the new moon of Nisan, which cannot happen earlier than the 11th, so the +following moon which happens thirty days later on the 7th of April is the +new moon of Nisan. Hence it may be seen that by intercalating a full month +every three years, or which comes nearer to accuracy seven times in +nineteen years, restores the coincidence of the solar and the lunar year, +and consequently the moons to the same day of the month on which they fell +nineteen years before. + +The method of designating the months previous to the exodus, was by their +numerical order, as the ancient Hebrews had no particular name to express +their month. They said the first, second and third month, and so on. No +names of months appear in the Bible until about the time of the +institution of the passover, when the Lord spake unto Moses and Aaron in +the land of Egypt, saying this month, (Abib, which appears to have had its +origin in Egypt,) shall be unto you the beginning of months; it shall be +the first month of the year to you. + +The names of the months appear to belong to two distinct periods. In the +first place we have those peculiar to the Jews previous to the captivity, +viz: Abib, the first month in commemoration of the exodus; Zif, the +second, Ethanim, the seventh, and Bul, the eighth. These names are of +Hebrew origin, and have reference to the characteristics of the seasons, a +circumstance which clearly shows that the months, by intercalation, were +made to return at the same period of the year. Thus, Abib was the month of +the ears of corn, that is the month in which the ears of corn became full, +or ripe on the 16th day, that is the 2d day of the feast of unleavened +bread. Zif, the month of blossoms or the bloom of flowers. Ethanim, the +month of gifts, that is of fruits, and Bul, the month of rain. These were +superceded after the captivity, by Nisan, Iyar, Tisri and Hesvan, or +Marchesvan. + +Marchesvan, coinciding as it does with the rainy season in Palestine, is +considered a pure Hebrew term. The modern Jews consider it a compound +word, from mar, drop, and Chesvan; the former betokening that it was wet, +and the latter being the proper name of the month. Hence the name +indicates the wet month. In the second place we have the names of six +others which appear in the Bible subsequently to the Babylonian captivity, +viz.: Sivan, the third; Elul, the sixth; Kislev, the ninth; Tebet, the +tenth; Sebat, the eleventh, and Adar, the twelfth. There are two other +months whose names do not appear in the Bible, viz.: Tamuz, the fourth, +and Ab, the fifth. The name of the intercalary month is called Ve-Adar, or +2d Adar because placed in the calendar after Adar and before Nisan. + +Dr. Smith says these names are probably borrowed from the Syrians in whose +regular calendar we find names answering to most of them. He also says it +was the opinion of the Talmudists, that these names were introduced by the +Jews who returned from the Babylonish captivity, and also that they are +certainly used exclusively by writers of the post-Babylonian period. + +Inasmuch as the Hebrew months coincided with the seasons, as we have +already shown, it follows as a matter of course, that an additional month +must have been inserted every third year, which would bring the number up +to thirteen. No notice, however, is taken of this month in the Bible, +neither have we reason to think that it was inserted according to any +exact rule, but it was added whenever it was discovered that the barley +harvest did not coincide with the ordinary return of the month Abib. It +has already been shown that in the modern Jewish calendar the intercalary +month is introduced seven times in nineteen years, according to the +Metonic, or lunar cycle which was adopted by the Jews about 360 A. D. + +The Hebrew calendar is dated from the creation, which is supposed to have +taken place 3761 years before Christ. Hence, to find the number of cycles +elapsed since the creation, also the number in the cycle, we have the +following rule: Add 3761 to the date, divide the sum by nineteen; the +quotient is the number of cycles, and the remainder is the number in the +cycle. Should there be no remainder, the proposed year is, of course, the +last or nineteenth of the cycle. Thus, for the year 1883, we have 1883 + +3761 / 19 = 297, remainder 1; therefore, 297 is the number of cycles, and +1 the number in the cycle. Again, for the year 1893, we have 1893 + 3761 / +19 = 297, remainder 11; therefore 297 is the number of cycles, and 11 the +number in the cycle. Again for the year 1901, we have 1901 + 3761 / 19 = +298, remainder 0; therefore 298 is the number of cycles, and 19 the last +of the cycle. Hence it may be seen that the present cycle commenced with +1883, that 11 is the number in the cycle for the present year 1893, also +that the cycle ends with 1901; so that the next cycle commences with 1902. +If the remainder after dividing by nineteen be 3, 6, 8, 11, 14, 17 or 19 +(0), the year is intercalary or embolismic, consisting of 384 days; if +otherwise it is ordinary, containing only 354 days; so that in a cycle of +nineteen years, we have twelve ordinary years of 354 days each, and seven +embolismic years of 384 days each. But, in either case, the year is +sometimes made a day more, and sometimes a day less, in order that certain +festivals may fall on proper days of the week for their due observance. +Hence the ordinary year may consist of 353, 354 or 355 days, and the +embolismic year of 383, 384 or 385 days. + +In the modern Jewish calendar the New Year commences with the new moon of +Tisri, which may happen as early as the 5th of September or as late as the +5th of October. The new moon of Nisan, which is the first month in the +Sacred year, may happen as early as the 11th of March or as late as the +11th of April. It should be borne in mind that the names of the months +Abib, Zif, Ethanim and Bul were superceded after the captivity, by Nisan, +Iyar, Tisri and Hesvan or Marchesvan; also the name of the third month in +the civil year, Chisleu in the Bible, Kislev in the modern Jewish +calendar. In table No. 1 we have the names of the months in numerical +order, also the number of days in each month. Though the months consist of +30 and 29 days alternately, yet, in the embolismic year, Adar, which in +common years has 29 days, is given 30 days, and 2d Adar 29; so that two +months of 30 days come together. Table No. 2 shows the earliest and the +latest possible date of the new moons of each of the months respectively. + +TABLE 1. HEBREW MONTHS. + + _Sacred Year._ _Civil Year._ + Nisan 30 | Tisri 30 + Iyar 29 | Hesvan 29 + Sivan 30 | Kislev 30 + Tamuz 29 | Tebet 29 + Ab 30 | Sebat 30 + Elul 29 | Adar 30 + Tisri 30 | 2d Adar, Embolismic 29 + Hesvan 29 | Nisan 30 + Kislev 30 | Iyar 29 + Tebet 29 | Sivan 30 + Sebat 30 | Tamuz 29 + Adar 30 | Ab 30 + 2d Adar, Embolismic 29 | Elul 29 + + +TABLE II. HEBREW MONTHS. + + Nisan, March 11th or April 11th + Iyar, April 11th " May 10th + Sivan, May 10th " June 9th + Tamuz, June 9th " July 9th + Ab, July 9th " August 7th + Elul, August 7th " September 5th + Tisri, September 5th " October 5th + Hesvan, October 6th " November 4th + Kislev, November 4th " December 3d + Tebet, December 3d " January 2d + Sebat, January 3d " February 10th + Adar, February 10th " March 12th + +The charts on the three following pages are used to illustrate the +correspondence of the Hebrew months with our own. Each chart represents +the ecliptic, which is the apparent path of the Sun or real path of the +Earth, also the names of the months as they occur in their seasons. The +figures represent the days of the month on which the new moons of the +Hebrew calendar fall. These charts represent the month and the day of the +month on which both the Sacred and the Civil year begins and ends for +three successive years. Hence it may be seen that by intercalating a month +every three years the new moons are restored, very nearly, to the place +they occupied three years before. + + +CHART I. + +[Illustration: This chart represents the day of the month on which all the +new moons fall in the year 1891-92. The sacred year commenced with the new +moon of Nisan on the 9th of April, and the civil year with the new moon of +Tisri on the 3d of October, 1891, and ended respectively with the 28th of +March and the 21st of September, 1892.] + + +CHART II. + +[Illustration: This chart represents the day of the month on which all the +new moons fall in the year 1892-93. It may be here seen that the year +begins and ends about eleven days earlier than the year preceding, also +that all the new moons fall eleven days earlier than they did in the +preceding year.] + + +CHART III. + +[Illustration: This chart represents the year 1893-94. Though the year +begins about eleven days earlier than the preceding, viz.: the 17th of +March, yet it being the year in which a 2d Adar is intercalated, instead +of falling back eleven days, the beginning of the following year is +carried forward 20 days, making a year of 384 days; so that the year +1894-95 will commence with April 5. In 1891 we commenced with April 9. It +will be 19 years before we commence on the 9th of April again.] + + + + +APPENDIX. + + +A.--PAGE 12. + +Authors differ in regard to the length of the solar year. One gives 365 +days, 5 hours, 47 minutes and 51.5 seconds; another, 365 days, 5 hours, 48 +minutes and 46 seconds; and still another, 365 days, 5 hours, 48 minutes +and 49.62 seconds. In this work the last has been accepted as the true +length of the solar year, and all calculations have been made accordingly. + + +B.--PAGE 19. + +There is an apparent discrepancy among authors in regard to the +intercalary day. While one asserts that it was between the 24th and 25th +of February, another equally reliable, says that the 25th was the sexto +calendas and the 24th was the bis-sexto calendas of the Julian calendar. +Now it should be borne in mind that the Julian calendar is the basis of +our own, and is identical with it in the number of months in the year, and +in the number of days in the month. Also when the method of numbering the +days from the beginning of the month was adopted, the intercalation was +made to correspond with the intercalary day in the Julian calendar. + +As in the Julian calendar there were twice the sixth day, so in the +reformed calendar there were twice the 24th day, which was equivalent to +29 days in February. When the calendar was again corrected, making the +29th the intercalary day, then the 24th corresponded with the bis-sexto +calendas of the Julian calendar. This reconciles the apparent +discrepancy. While one author refers to the calendar in which the Julian +rule of intercalation is adopted, another refers to the calendar when so +corrected as to make the 29th of February the intercalary day. See +following table: + + -----------------------------------++----------------------------------- + JULIAN METHOD || MODERN METHOD + OF INTERCALATION. || OF INTERCALATION. + -----------------------------------++----------------------------------- + 1 |_Cal._ | Calendae || 1 |_Cal._ | Calendae + 2 | 4 | Quarto Nonas || 2 | 4 | Quarto Nonas + 3 | 3 | Tertio Nonas || 3 | 3 | Tertio Nonas + 4 | 2 | Pridie Nonas || 4 | 2 | Pridie Nonas + 5 |_Nomes_| Nonae || 5 |_Nomes_| Nonae + 6 | 8 | Octavo Idus || 6 | 8 | Octavo Idus + 7 | 7 | Septimo Idus || 7 | 7 | Septimo Ides + 8 | 6 | Sexto Idus || 8 | 6 | Sexto Idus + 9 | 5 | Quinto Idus || 9 | 5 | Quinto Idus + 10 | 4 | Quarto Idus || 10 | 4 | Quarto Idus + 11 | 3 | Tertio Idus || 11 | 3 | Tertio Idus + 12 | 2 | Pridie Idus || 12 | 2 | Pridie Idus + 13 | _Ides_| Idus || 13 | _Ides_| Idus + 14 | 16 | Sextodecimo Calendas || 14 | 16 | Sextodecimo Calendas + 15 | 15 | Quintodecimo Calendas || 15 | 15 | Quintodecimo Calendas + 16 | 14 | Quartodecimo Calendas || 16 | 14 | Quartodecimo Calendas + 17 | 13 | Tertiodecimo Calendas || 17 | 13 | Tertiodecimo Calendas + 18 | 12 | Duodecimo Calendas || 18 | 12 | Duodecimo Calendas + 19 | 11 | Undecimo Calendas || 19 | 11 | Undecimo Calendas + 20 | 10 | Decimo Calendas || 20 | 10 | Decimo Calendas + 21 | 9 | Nono Calendas || 21 | 9 | Nono Calendas + 22 | 8 | Octavo Calendas || 22 | 8 | Octavo Calendas + 23 | 7 | Septimo Calendas || 23 | 7 | Septimo Calendas + 24 | 6 | Bis-Sexto Calendas || 24 | 6 | Bis-sexto Calendas + 24 | 6 | Sexto Calendas || 25 | 6 | Sexto Calendas + 25 | 5 | Quinto Calendas || 26 | 5 | Quinto Calendas + 26 | 4 | Quarto Calendas || 27 | 4 | Quarto Calendas + 27 | 3 | Tertio Calendas || 28 | 3 | Tertio Calendas + 28 | 2 | Pridie Calendas || 29 | 2 | Pridie Calendas + ---+-------+-----------------------++----+-------+---------------------- + + +C.--PAGE 20. + +The city where the great council was convened in 325 is not in France, as +some have supposed, that being a more modern city of the same orthography, +but pronounced Nees. The city which is so frequently referred to in this +work is in Bythinia, one of the provinces of Asia Minor, situated about 54 +miles southeast of Constantinople, of the same orthography as the former, +but pronounced Ni'ce, and was so named by Lysimachus, a Greek general, +about 300 years before Christ, in honor of his wife Nicea. + + +D.--PAGE 23. + +Between the 23d and 24th of February, 46 years before Christ, there was +intercalated a month of 23 days according to an established method, but +still the civil year was in advance of the solar year by 67 days; so that +when the Earth in her annual revolutions should arrive to that point of +the ecliptic marked the 22d of October, it would be the 1st day of January +in the Roman year. + +Caesar and his astronomers, knowing this fact and fixing on the 1st day of +January, 45 years before Christ and 709 from the foundation of Rome, for +the reformed calendar to take effect, were under the necessity of +intercalating two months, together consisting of 67 days. Now, as the +civil year would end on the 22d of October, true or solar time, it would +be reckoned in the old calendar the 1st day of January; so they let the +old calendar come to a stand while the Earth performs 67 diurnal +revolutions, and thereby restored the concurrence of the solar and the +civil year. + +As an illustration, let us suppose that in a certain shop where hangs a +regulator are two clocks to be regulated. Both are set with the regulator +at 8 a. m. to see how they will run for ten consecutive hours. It was +found that when it was 6 p. m., by the first clock, it was 5:50 by the +regulator, the clock having gained one minute every hour. + +To rectify this discrepancy we must intercalate 10 minutes by stopping the +clock until it is 6 by the regulator. By this means the coincidence is +restored, and the time lost in the preceding hours is now reckoned in this +last hour, making it to consist of 70 minutes. By this it may be seen how +Caesar reformed the Roman calendar. The Roman year was too short, by reason +of which the calendar was thrown into confusion, being 90 days in advance +of the true time, so that December, January and February took the place in +the seasons of September, October and November, and September, October and +November the place of June, July and August. To make the correction he +must stop the old Roman clock (the calendar) while the Earth performs 90 +diurnal revolutions to restore the concurrence of the solar and the civil +year, making the year 46 B. C. to consist of 445 days. + +It was also found that when it was 6 p. m., by the regulator, it was only +5:50 by the second clock, it having lost one minute every hour. To rectify +this discrepancy we must suppress 10 minutes, calling it 6 p. m., turning +the hands of the clock to coincide with the regulator, making the last +hour to consist of only 50 minutes, too much time having been reckoned in +the preceding hours. It may be seen by this illustration, how Gregory +corrected the Julian calendar, the Julian year was too long, consequently +behind true or solar time, so that when the correction was made in 1582, +the ten days gained had to be suppressed to restore the coincidence, +making the year to consist of only 355 days. + +As the solar year consists of 365 days and a fraction, Caesar intended to +retain the concurrence of the solar and the civil year by intercalating a +day every four years; but this made the year a little too long, by reason +of which it became necessary, in 1582, to rectify the error, and by +adopting the Gregorian rule, three intercalations are suppressed every 400 +years; so that by a series of intercalations and suppressions, our +calendar may be preserved in its present state of perfection. + + +E.--PAGE 23. + +As the day and the civil year always commence at the same instance, so +they must end at the same instance; and as the solar year always ends with +a fraction, not only of a day, but of an hour, a minute and even a second; +so there is no rule of intercalation by which the solar and the civil year +can be made to coincide exactly. But the discrepancy is only a few hours +in a hundred years, and that is so corrected by the Gregorian rule of +intercalation that it would amount to a little more than a day in 4,000 +years; and by the improved method less than a day in 100,000 years. + + +F.--PAGE 26. + +It has been stated that by adopting the Julian rule of intercalation, time +was gained; it has also been stated that by the same rule time was lost. +Now both are true. Time is gained in that there is too much time in a +given year, in other words, the year is too long; but what is gained in a +given year is lost to the following year. + +As an illustration let us take the case of the supposed solar year of 365 +days, and the civil year of 366. The civil year would gain one day every +year, or be too long by one day; but the one day gained is lost to the +following years, and if continued 31 years, when the Earth is in that part +of its orbit marked the 1st day of January 32, the civil year would reckon +the 1st day of December 31; so that in the thirty-one years would reckon +thirty-one days too much, and before the civil year is completed, the +Earth will have passed on in its orbit to a point marked the 1st day of +February. + +Now to reform such a calendar, we would have to suppress or drop the +thirty-one days, by calling the 1st day of December the 1st day of +January, and thus the month of December would disappear from the calendar +in the year 31, making a year of only eleven months, consisting of 334 +days. + +If this method be continued 92 years, there would be gained 92 days, to +the loss of 92 days in the year 92. If the calendar be now reformed by +suppressing 92 days, calling the 1st day of October, 92, the 1st day of +January, 93, then October, November and December would disappear from the +calendar in the year 92; and if continued 365 years there would be crowded +into 364 years, 364 days too much; gained to the 364 years to the total +loss of the year 365, passing from 364 to 366; 365 disappearing from the +calendar. + + +G.--PAGE 50. + +An era is a fixed point of time from which a series of years is reckoned. +Among the nations of the Earth there are no less than twenty-five +different eras; but the most of them are not of enough importance to be +mentioned here. Attention is particularly called to the Roman era which +commenced with the building of the city of Rome 753 years before Christ. + +Also the Mahometan era, or the era of the Hegira, employed in Turkey, +Persia and Arabia, which is dated from the flight of Mahomet from Mecca to +Medina, which was Thursday night, the 15th of July, A. D., 622, and it +commenced on Friday, the day following. + +But there is a point from which all computation originally commenced, +namely, the creation of man. Such an era is called the Mundane era. Now +there are different Mundane eras--the common Mundane era 4,004 B. C., the +Grecian Mundane era 5,598 B. C., and the Jewish Mundane era 3,761 B. C. +All these commence computation from the same point, but differ in regard +to the time which has elapsed since their computation commenced. God's +people used the Mundane era, until the Great Creator appeared among us, as +one of us, in the person of our Lord Jesus Christ, to accomplish the great +work of redemption; then His name was introduced as the turning point of +the ages, the starting point of computation. + +This was done by Dionysius Exiguus in the year of our Lord about 540, +known at that time as the Dionysian, as well as the Christian era, and was +first used in historical works by the venerable Bede early in the eighth +century. "It was a great thought of the little monk (whether so called +from his humility or littleness of stature is unknown), to view Christ as +the turning point of the ages, and to introduce this view into +chronology." + +All honor to him who introduced it, and to the nations which have +approved, for thus honoring the Great Redeemer. Dionysius probably did not +know, neither is it now known for a certainty the year of Christ's birth, +but it is evident, however, from the best authorities, that the era +commenced at least five years too late, and probably more. + + +H.--PAGE 57. + +It is recorded that, in the time of Numa, the vernal equinox fell on the +25th of March, and that Julius Caesar restored it to the 25th, when he +reformed the ancient Roman calendar in the year 46 B. C. It is also +recorded that in less than 400 years from that time, at the meeting of the +Council of Nice in 325, it had fallen back to the 21st--four days in less +than 400 years. + +Now there is an error somewhere, for it is found by actual computation +that the discrepancy between the solar and the Julian year is about three +days in 400 years. It certainly is true that the vernal equinox fell on +the 21st in 325, and was restored to that place by Gregory in 1582; since +which time it has been made to fall on the 21st by the Gregorian rule of +intercalation. Again it is stated by the same author that the +discrepancies in time from Caesar to Gregory is thirteen days, from the +Council of Nice to Gregory ten days; now 10 + 4 = 14. While our author +states it is thirteen days, he also states it is fourteen days; a +discrepancy of one day. The mistake evidently is in making the 25th +instead of the 24th, the date of the vernal equinox in the time of Caesar, +consequently a difference of four days instead of three from Caesar to the +Council of Nice. + + +I.--PAGE 59. + +The concurrence of the solar and the civil year was restored by Gregory in +1582, or 1600 is the same in computation; but the discrepancy between +civil and solar time is 11 minutes and 10.38 seconds every year, which in +100 years will amount to 18 hours, and 37.3 minutes; reckoned in round +numbers 18 hours, and is represented on the chart, hours behind time 18. + +The intercalary day or 24 hours being suppressed in 1700, causes the civil +year to be 6 hours in advance of the solar, and is represented on the +chart 6 hours in advance. + +Now this discrepancy of 18 hours for the next 100 years, will cause the +civil year in 1800 to be 12 hours behind; again suppressing the +intercalation it will be 12 hours in advance. In 1900 it will be 6 hours +behind, but the correction makes 18 hours in advance. The 18 hours gained +the next 100 years restores the coincidence in the year 2000 and so on, +the solar and the civil year being made to coincide very nearly every 400 +years. + +From close examination it will become evident that the solar and the civil +year coincide twice every 400 years, though no account is made of it in +computation. From 6 hours in advance in 1700, the civil year falls back to +12 hours behind the solar in 1800, consequently they must coincide in +1733. + +Again from 12 hours in advance in 1800, it falls back to 6 hours behind +the solar in 1900, consequently they must coincide again in 1867. + +Discrepancy between Julian and solar time in--1 year is (365d. 6h.) +- (365d. 5h. 48m. 49.62s.) = (11m. 10.38s.) + + 100 years is (11m. 10.38s.) x 100 = (18h. 37.3.) + 400 " (18h. 37.3m.) x 4 = (3d. 2h. 29.2m.) + 4,000 " (3d. 2h. 29.2m.) x 10 = (31d. 0h. 52m.) + 100,000 " (31d. 0h. 52m.) x 25 = (773d. 21h. 40m.) + +Discrepancy between Gregorian and solar time in-- + + 1 year is .373m. + 100 years is .373m. x 100 = 37.3m. + 400 years 37.3m. x 4 = 2h. 29.2m. + 4,000 " (2h. 29.2m.) x 10 = 1d. 0h. 52m. + 100,000 " (1d. 0h. 52m.) x 25 = 25d. 21h. 40m. + +Discrepancy between corrected Gregorian and solar time in-- + + 4,000 years is (1d. 0h. 52m.) - 1 day = 52m. + 100,000 " " (52m. x 25) = 21h. 40m. + + +J.--PAGE 89. + +Lilius, author of the "Extended Table of Epacts," says, when the full moon +falls on the 10th of March, the following moon, which happens 29 days +later, is the paschal moon, making the 18th of April its latest possible +date. For, says he, because of the double epact that occurs on the 4th and +5th of April that lunation has only 29 days. It may have been very +convenient for Lilius, in his peculiar method of determining the date of +the paschal moon, to give to that lunation only 29 days; but nevertheless, +when he did so, it was at the expense of accuracy, for he makes a +difference of 12 days in the date of the paschal moon of that year, and +the year preceding, and only 10 days difference between that year and the +succeeding year; whereas the difference is uniformly 11 days from year to +year through the whole cycle of 19 years. + +By referring to the table on the 93d page, it will be seen that, in fixing +the date of the paschal moon, six times in a cycle of 19 years the full +moon falls before the 21st of March, and in every instance except this one +the following moon is reckoned by Lilius 30 days later. By this uniform +method of determining the date of the paschal moon, we make the 19th of +April instead of the 18th, its latest possible date; so it should be borne +in mind that whenever the 19th of April is the date of the paschal moon, +as indicated in the tables commencing with the 93d page, that Lilius, and +probably most, if not all other authors, have the 18th. + +Now it is admitted that notwithstanding the cumbersome apparatus employed +by Lilius in his calculations, the conditions of the problem are not +always satisfied, nor is it possible that they can be always satisfied by +any similar method of proceeding. We admit that none of these calculations +are perfectly exact, but the sum of the solar and lunar inequalities is +compensated in the whole period, or corrections made at the end of certain +periods, not by interrupting the order of a uniform method during the +cycle of 19 years. + +Now the table of epacts was introduced by Lilius himself, making the +excess of the solar year beyond the lunar, in round numbers 11 days. Then +why interrupt this order every 19 years, for a period of 114 years; that +is from 1596 to 1710, by making the epact 12 days for one year, and the +following year only 10? After which, from 1710 to 1900, a period of 190 +years, according to Lilius' own calculations, the epact is uniformly 11 +days, coinciding exactly with the calculations made in this work. + +Then again after the year 1900, he gives to that particular lunation, in +every lunar cycle for a period of 304 years, only 29 days; and having done +so, he is under the necessity of giving only 29 days to another lunation +in the same cycle, and also to all the cycles in the period to avoid the +absurdity of making the paschal moon fall twice on the same day in the +course of a lunar cycle. + +By reference to the 101st page, opposite the year 1905, it will be seen +that the date of the paschal moon is the 19th of April. Lilius, by giving +to that lunation only 29 days, makes its date the 18th; and then again in +the year 1916, lest he should make the paschal moon fall twice on the 18th +of April in the course of a lunar cycle, (a thing which cannot really +occur) he for the first time in more than 400 years, gives only 29 days to +a second lunation in the same cycle and of course to all the cycles in the +period of 304 years. Now the epacts for a lunar cycle of 19 years are +represented thus: + + 26 + -- + 0, 11, 22, 3, 14, 25, 6, 17, 28, 9, 20 + + 27 + -- + 1, 12, 23, 4, 15, 26, 7, 18 + +The number 26 placed over the 25 shows Lilius' first error in giving to +that lunation only 29 days. He thereby makes a difference of 12 days +between the epact 14 and 26, and only 10 between 26 and 6. He now has two +epacts of the same number 26. In order to get out of the dilemma he makes +that 27, by giving to another lunation only 29 days. + + +K.--PAGE 122-3. + +It will probably be noticed that according to the showing in the tables +the ecclesiastical year contains only 364 days. The reason for this is, +that Advent Sunday, which is the first day of the year, happens one day +earlier every year until it occurs on the 27th of November, its earliest +possible date; then the first Sunday after the 26th of November, which is +Advent Sunday, falls on the 3d of December, its latest possible date, so +that the year begins six days later, making a year of 371 days. Then there +is the loss of a day every year until Advent Sunday again falls on the +27th of November and so on. Hence, did the civil year always consist of +365 days, then the ecclesiastical year would always contain either 364 or +371 days. But as every fourth year contains 366 days, this order is so +interrupted that sometimes the first Sunday falls on the 2d instead of the +3d of December; so that the year begins only five days later, making a +year of only 370 days. Hence the ecclesiastical year may consist of either +364, 370 or 371 days. But five times out of six it will contain only 364 +days. + + +L.--PAGE 83. + +But why did the Pope, in correcting the Julian calendar in 1582, not +correct the whole error of thirteen days? Why did he leave the three days +uncorrected? This question has been asked an hundred times, but a correct +answer has never yet been given. Some say that the Pope did according to +his best ability, and would make us believe that neither he nor his +astronomers knew what the error was. This is not true, for history records +the fact of the error, and just what that error was. He simply did not +want to correct the three days, and for good reasons, which we shall +endeavor to show; reasons which every churchman ought to know. + +When Caesar formed his calendar, 46 B. C., the vernal equinox fell on the +24th of March. At the meeting of the Council of Nice, in 325, it had +fallen back to the 21st, the error being three days in about 400 years. +Now it should be borne in mind that the Julian calendar was the only one +in use at that time, and for the next 1257 years, when in 1582, it was +corrected by Pope Gregory XIII. Easter, and all the movable feasts, had +been unsettled during the 1257 years intervening, from the Council of Nice +to Gregory, on account of the errors of the Julian calendar. The Easter +question had been the cause of a good deal of discussion between the +Eastern and Western churches during the second and third centuries, as +they could not agree on the day of the week on which that event should be +celebrated. + +The Western churches observed the nearest Sunday to the full moon of +Nisan. The Asiatics, on the other hand, adopted the 14th of Nisan upon +which to commemorate the crucifixion, and observed the festival of Easter +on the third day following, upon whatever day of the week that might fall. +Finally, the Council of Nice was convened, and the matter came before that +council, and a reconciliation was accomplished. It was then and there +agreed by the two parties that Easter should be celebrated on the first +Sunday after the full moon that falls upon or next following the day of +the vernal equinox, and that the 21st of March should be accounted the day +of the vernal equinox. + +It has already been shown that the error in the Julian calendar is three +days in 400 years; so that in 400 years from the Council of Nice the +vernal equinox had fallen back to the 18th of March; in 800 years it had +fallen back to the 15th; in 1257 years, that is in 1582, it fell on the +11th. Still the 21st of March, by the only calendar in use at that time, +was accounted the date of the vernal equinox, by which date Easter was +determined, so that, in 1582, when it was the 21st by the calendar, the +correct date was the 31st. Hence, the error had been increasing at the +rate of three days every 400 years until in 1582 it amounted to ten days. + +Again it should be borne in mind that the Pope was a churchman and wished +to abide by the decision of that council in celebrating the festival of +Easter, so he drops the ten days and restores the vernal equinox to the +21st of March, its date at the meeting of the Council of Nice in 325, the +date by which Easter day was determined. He not only made the correction, +but he so reformed the calendar that the solar and the civil year are now +made to coincide very nearly. Had he dropped the thirteen days, the vernal +equinox would have been restored to the 24th of March, its date in the +time of Caesar, and the 24th would still be its date. But the Council of +Nice decided that the 21st should be the date by which Easter day should +be determined. Hence the reason for dropping the ten days instead of the +thirteen is evident; and it is also evident that the Pope acted +understandingly when he made the correction in 1582. + + + + +ERRATA. + + +On 51st page, ninth line from the bottom of the page, instead of 1453 / 43 += 63+, should be 1453 / 4 = 363+. + +On 76th page, twelfth line from the top of the page, 356 should be 365. + + + + +THE COLUMBUS CELEBRATION. + +THE WELLSBORO MAN WHO BROUGHT ABOUT THE CHANGE IN THE DATE. + +_State Superintendent D. J. Waller, in the School Journal._ + +Who brought about the change in the date? It was down in the books as +October 12th. The Committee of the National Educational Association issued +circulars to the country to observe that day. Congress solemnly resolved +that that day should be celebrated throughout the land. The Commissioners +of the World's Fair fixed upon October 12, as dedication-day, and sent out +invitations to the exercises. Suddenly there was a change. Heralded by no +newspaper discussion, preceded by no exhaustive treatise, without any +authoritative decree, a change was made to October 21. + +The following facts are indisputable. An aged retired minister in the +Methodist Episcopal Church, living in Wellsboro, Tioga County, Pa., author +of a little book entitled "Our Calendar," Rev. George Nichols Packer, saw +the error. He possessed the confidence of Judge Henry W. Williams, of the +Supreme Court of Pennsylvania. After laying the facts before him, he +secured through him the approval by the several Justices composing that +body, of an effort to change to the proper date, October 21st. Equipped +with this approval, he secured the endorsement of his project by Governor +Pattison and some of the heads of the Executive departments at Harrisburg. +He then went to Washington, gained an audience with the President, laid +the subject before the member of Congress from his district, and went +before the Congressional Committee. + +The evidence in support of the proposition was so presented that it could +not be successfully disputed. Congressman W. A. Stone skillfully enlisted +influential collegiates in an effort to correct the error already widely +spread. The correction by the National Legislature was in time to have its +influence upon President Harrison, who named October 21 in his +proclamation, as the day to be observed, and Boston and Chicago fell into +line. + +All honor to Rev. George Nichols Packer, of Wellsboro, Tioga County, +Pennsylvania. + + + + +Transcriber's Notes: + +Passages in italics are indicated by _italics_. + +Punctuation has been corrected without note. + +Corrections noted in the Errata section have been applied to the text. + +The following misprints have been corrected: + "aad" corrected to "and" (page 8) + "leap-year" corrected to "leap-years" (page 45) + missing "the" added (page 45) + "1993" corrected to "1793" (page 63) + "co-incide" standardized to "coincide" (page 71) + "Caesar" standardized to "Caesar" (page 71) + "conseqently" corrected to "consequently" (page 74) + "1736" corrected to "1737" (page 96) + "countenace" corrected to "countenance" (page 114) + +Other than the corrections listed above, inconsistencies in spelling and +hyphenation have been retained from the original. + +On page 37, "3 400" is presented with a space as in the original text. + + + + + + +End of the Project Gutenberg EBook of Our Calendar, by George Nichols Packer + +*** END OF THIS PROJECT GUTENBERG EBOOK OUR CALENDAR *** + +***** This file should be named 36197.txt or 36197.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/3/6/1/9/36197/ + +Produced by Bryan Ness and the Online Distributed +Proofreading Team at http://www.pgdp.net (This file was +produced from images generously made available by The +Internet Archive.) + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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