,,our ,,calendar4 ,the ,julian ,calendar and ,its ,errors4 ,,how ,,corrected ,,by ,,the ,,gregorian4 ,rules ,for ,finding the ,dominical ,letter1 ,,and ,,the ,,day ,,of ,,the ,,week ,,of ,,any ,,event ,,from ,,the ,,days ,,of ,,julius ,,caesar #df ,b4 ,c4 ,,to ,,the ,,year ,,of ,,our ,,lord ,,four ,,thousand--,a ,,new ,,and ,,easy ,,method ,,of ,,fixing ,,the ,,date ,,of ,,easter4 ,,hebrew ,,calendar2 ,,showing ,,the ,,correspondence ,,in ,,the ,,date ,,of ,,events ,,recorded ,,in ,,the ,,bible ,,with ,,our ,,present ,,gregorian ,,calendar4 ,,illustrated ,,by ,,valuable ,,tables ,,and ,,charts4 ,,by ,,rev4 ,,george ,,nichols ,,packer1 ,,corning1 ,n4 ,y4 ,entered according to ,act of ,congress1 in #ahij1 #ahib and #ahic1 ,,by ,,rev4 ,,george ,,nichols ,,packer1 ,in the ,office of the ,librarian of ,congress1 ,washington1 ,d4 ,c4 ,,all ,,rights ,,reserved4 ,,williamsport1 ,,pa43 ,,fred ,r4 ,,miller ,,blank ,,book ,,co4 #ahic4 ,,to ,,hon4 ,,henry ,w4 ,,williams1 ,,justice ,,of ,,the ,,supreme ,,court ,,of ,,pennsylvania ,,whom ,i ,,have ,,found ,a ,,true ,,friend ,,in ,,poverty ,,and ,,in ,,sickness1 ,,and ,,from ,,whom ,i ,,have ,,received ,,words ,,of ,,encouragement ,,and ,,comfort ,,during ,,many ,,years ,,of ,,adversity1 ,,and ,,at ,,whose ,,suggestion ,,this ,,little ,,volume ,,has ,,been ,,written1 ,,and ,,by ,,whose ,,assistance ,,it ,,is ,,now ,,published1 ,,this ,,humble ,,volume ,,is ,,dedicated ,,as ,a ,,tribute ,,of ,,respect ,,by ,,the ,,author4 ,,preface4 ,many years ago1 while engaged in teaching1 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 centuries2 further than this he gave the subject no special attention4 ,a few years ago1 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 month1 but in different years1 he was led to investigate the subject more thoroughly1 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 transpire1 from the commencement of the ,christian era to the year of our ,lord #d1jjj1 and to explain the principles on which these rules rest4 ,when the investigations were entered upon he had no thought of writing a book2 but having been laid aside from active labor by ill health1 he found relief from the despondency in which sickness and poverty plunged him by pursuing the study of the calendar1 its history1 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 ,sun4 ,he became so much interested in the study of this subject that he frequently spoke of it to friends and acquaintances whom he met4 ,on one occasion1 while speaking to ,hon4 ,h4 ,w4 ,williams about some of the curious results of the process by which the coincidence of the solar and the civil year is preserved1 it was suggested to him that he should put the story of the calendar1 its correction by ,gregory1 and the theory and results of intercalation1 in writing4 ,it was urged that this would give increased interest to the study1 help the writer to forget his pains1 and probably enable him to realize a little money from the sale of his work to meet pressing wants4 ,acting upon this suggestion1 an effort has been made to put into this little volume some of the most interesting facts relating to the origin1 condition1 and practical operation of the calendar now in use2 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 era4 ,the writer does not claim absolute originality for all that appears in the following pages2 on the contrary1 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 ,gregory4 ,these materials1 together with his own calculations1 he has arranged in accordance with a plan of his own devising1 so that the outline and the execution of the work may be truly said to be original4 ,of its value the world must judge4 ,it has been prepared in weakness of body and in suffering1 which have been to some extent relieved by the mental occupation thus afforded1 but which may have nevertheless left their impress on the work4 ,but let it be read before pronouncing judgment upon it4 ,cicero could infer the littleness of the ,hebrew ,god from the smallness of the territory he had given his people4 ,to whom ,kitto replies3 ,the interest and importance of a country arise1 not from its territorial extent1 but from the men who form its living soul2 from its institutions bearing the impress of mind and spirit1 and from the events which grow out of the character and condition of its inhabitants4 ,so the value of a book does not consist in the size and number of its pages1 but from the knowledge that may be gained by its perusal4 ,,the ,,author4 ,,preface ,,to ,,the ,,revised ,,edition4 ,soon after the publication of the former edition of this work1 it was suggested that a chapter be added on ,easter2 rules for fixing its date1 and also church festivals that depended upon the date of ,easter4 ,it was suggested that this would add very much to the value of the work1 if so presented as to be brought within the comprehension of ordinary minds4 ,knowing that the determination of ,easter was an affair of considerable nicety and complication1 and had had the attention of our best minds1 and they had failed so to present it1 that even among scholarly men1 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 task4 ,nevertheless it was undertaken1 and the work has been revised and enlarged by a ,chapter on the ,peculiarities of the ,roman ,calendar1 another on fixing the date of events prior to the ,christian era1 and a third part on ,easter1 church festivals1 and the ,hebrew ,calendar4 ,in the opinion of the author1 the rules for determining the date of ,easter are so simplified by his new method that any person of ordinary intelligence may understand them4 ,how well he has succeeded the public will decide4 ,g4 ,n4 ,p4 ,,contents4 ,,part ,,first4 ,,definitions--,,history4 ,pages4 ,,chapter ,i4--,definitions #aa ,,chapter ,,ii4--,history of the divisions of time1 and the old ,roman ,calendar #ab ,,chapter ,,iii--,history of the reformation of the ,calendar by ,julius ,caesar #ah ,,chapter ,,iv4--,history of the reformation of the ,julian ,calendar by ,pope ,gregory ,,xiii #bj ,,chapter ,v4--,peculiarities of the ,roman ,calendar #bf ,,part ,,second4 ,,mathematical4 ,,chapter ,i4--,errors of the ,julian ,calendar #cf ,,chapter ,,ii4--,errors of the ,gregorian ,calendar #ch ,,chapter ,,iii4--,dominical ,letter #ci ,,chapter ,,iv4--,rule for finding the ,dominical ,letter #dd ,,chapter ,v4--,rule for finding the day of the week of any given date1 for both ,old and ,new ,styles #ej ,,chapter ,,vi4--,a simple method of finding the day of the week of events1 which occur quadrennially2 the inaugural of the ,presidents1 the day of the week on which they have occurred and on which they will occur for the next one hundred years #fa ,some peculiarities concerning events which fall on the #bith of ,february #fd ,,chapter ,,vii4--,rule for finding the day of the week of events prior to the ,christian era #fh ,,part ,,third4 ,,cycles--,,julian ,,period--,,easter4 ,,chapter ,i4--,the ,solar ,cycle #gc ,,chapter ,,ii4--,the ,lunar ,cycle #ge ,,chapter ,,iii4--,the ,lunar ,cycle and ,golden ,number #gg ,,chapter ,,iv4--,cycle of ,indiction1 and the ,julian ,period #gi ,,chapter ,v4--,easter #hb ,,chapter ,,vi4--,a new and easy method of fixing the date of ,easter #hh ,,chapter ,,vii4--,church feasts and fasts whose date depend on the date of ,easter #ajh ,,chapter ,,viii4--,hebrew ,calendar #abd ,,appendix #acd ,,errata #adi ,,our ,,calendar4 ,,part ,,first4 ,,definitions4 ,,history4 ,,chapter ,i4 ,,definitions4 a--,a ,calendar is a method of distributing time into certain periods adapted to the purposes of civil life1 as hours1 days1 weeks1 months1 years1 etc4 b--,the only natural divisions of time are the solar day1 the solar year1 and the lunar month4 c--,an hour is one of the subdivisions of the day into twenty-four equal parts4 d--,the true solar day is the interval of time which elapses between two consecutive returns of the same terrestrial meridian to the ,sun1 the mean length of which is twenty-four hours4 e--,the week is a period of seven days1 having no reference whatever to the celestial motions1 a circumstance to which it owes its unalterable uniformity4 f--,the lunar month is the time which elapses between two consecutive new or full moons1 and was used in the ,roman calendar until the time of ,julius ,caesar1 and consists of #bi;d1 #ab;h1 #ddm1 #b4hgs4 g--,the calendar month is usually employed to denote an arbitrary number of days approaching a twelfth part of a year1 and has now its place in the calendar of nearly all nations4 h--,the year is either astronomical or civil4 ,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 again1 and consists of #cfe days1 #e hours1 #dh minutes and #di4fb seconds of mean solar time4 ,appendix ,a4 i--,the civil year is that which is employed in chronology1 and varies among different nations1 both in respect of the seasons at which it commences and of its subdivisions4 ,,chapter ,,ii4 ,,history ,,of ,,the ,,divisions ,,of ,,time ,,and ,,the ,,old ,,roman ,,calendar4 ,day--,the subdivision of the day into twenty-four parts or hours has prevailed since the remotest ages1 though different nations have not agreed either with respect to the epoch of its commencement or the manner of distributing the hours4 ,europeans in general1 like the ancient ,egyptians1 place the commencement of the civil day at midnight2 and reckon twelve morning hours from midnight to midday and twelve evening hours from midday to midnight4 ,astronomers1 after the example of ,ptolemy1 regarded the day as commencing with the ,sun's culmination1 or noon1 and find it most convenient for the purpose of computation to reckon through the whole twenty-four hours4 ,hipparchus reckoned the twenty-four hours from midnight to midnight4 ,the ,roman day1 from sunrise to sunset1 and the night1 from sunset to sunrise1 were each divided at all seasons of the year into twelve hours1 the hour being uniformly one-twelfth of the day or the night1 of course1 varied in length with the length of the day or night at different seasons of the year4 ,week--,although the week did not enter into the calendar of the ,greeks1 and was not introduced at ,rome till after the reign of ,theodosius1 ,a4 ,d4 #bib1 it has been employed from time immemorial in almost all ,eastern countries2 and as it forms neither an aliquot part of a year nor of the lunar months1 those who reject the ,mosaic recital will be at a loss to assign to it an origin having much semblance of probability4 ,in the ,egyptian astronomy the order of the planets1 beginning with the most remote1 is ,saturn1 ,jupiter1 ,mars1 the ,sun1 ,venus1 ,mercury1 the ,moon4 ,now1 the day being divided into twenty-four hours1 each hour was consecrated to a particular planet1 namely3 ,one to ,saturn1 the following to ,jupiter1 third to ,mars1 and so on according to the above order2 and the day received the name of the planet which presided over its first hour4 ,if1 then1 the first hour of a day was consecrated to ,saturn1 that planet would also have the #hth1 the #eth and the #bb;d hours2 the #bc;d would fall to ,jupiter1 the #bdth to ,mars1 and the #beth or the first hour of the second day would belong to the ,sun4 ,in like manner the first hour of the third day would fall to the ,moon1 the first hour of the fourth to ,mars1 of the fifth to ,mercury1 of the sixth to ,jupiter and the seventh to ,venus4 ,the cycle being completed1 the first hour of the eighth day would again return to ,saturn and all the others succeed in the same order4 ,see table on the #agth page4 ,it will be seen by the table1 and it is also recorded by ,dio ,cassius1 of the second ,century1 that the ,egyptian week commenced with ,saturday4 ,on their flight from ,egypt the ,jews1 from hatred to their ancient oppressors1 made ,saturday the last day of the week4 ,it is stated that the ancient ,saxons borrowed the week from some ,eastern nation1 and substituted the names of their own divinities for those of the gods of ,greece4 ,the names of the days are here given in ,latin1 ,saxon and ,english4 ,it will be seen that the ,english names of the days are derived from the ,saxon4 ,,latin4 ,,saxon4 ,,english4 ,dies ,solis4 ,sun's ,day4 ,,sunday4 ,dies ,lunae4 ,moon's ,day4 ,,monday4 ,dies ,martis4 ,tiw's ,day4 ,,tuesday4 ,dies ,mercurii4 ,woden's ,day4 ,,wednesday4 ,dies ,jovis4 ,thor's ,day4 ,,thursday4 ,dies ,veneris4 ,friga's ,day4 ,,friday4 ,dies ,saturni4 ,seterne's ,day4 ,,saturday4 ,month--,the ancient ,roman year contained but ten months and is indicated by the names of the last four4 ,september from ,septem1 seven2 ,october from ,octo1 eight2 ,november from ,novem1 nine1 and ,december from ,decem1 ten2 ,july and ,august were also denominated ,quintilis and ,sextilis1 from ,quintus five1 and ,sex1 six4 ,quintilis was changed to ,july in honor of ,julius ,caesar1 who was born on the #abth of that month #ih ,b4 ,c4 ,sextilis was changed to ,august by the ,roman ,senate to flatter ,augustus on his victories about #h ,b4 ,c4 ,in the reign of ,numa ,pompilius1 about #gjj ,b4 ,c41 two months were added to the year1 ,january at the beginning1 and ,february at the end of the year4 ,this arrangement continued till #dej ,b4 ,c41 when the ,decemvirs 7ten magistrates7 changed the order1 placing ,february after ,january1 making ,march the third instead of the first month of the ,roman year4 ,year--,if the civil year correspond with the solar the seasons of the year will always come at the same period4 ,but if the civil year is supposed to be too long 7as is the case in the ,julian year7 the seasons will go back proportionately2 but if too short they will advance in the same proportion4 ,now1 as the ancient ,egyptians reckoned thirty days to the month invariably1 and to complete the year1 added five days1 called supplementary days1 their year consisted of #cfe days4 ,they made use of no intercalation1 and by losing one-fourth of a day every year1 the commencement of the year went back one day in every period of four years1 and consequently made a revolution of the seasons in #adfj years4 ,hence the ,egyptian year was called a vague or erratic year because the first day of the year in the course of #adfj years wandered1 as it were1 over all the seasons4 ,therefore #adfj ,julian years of #cfe-a_/d days each are equal to #adfa ,egyptian years of #cfe days each4 ,the ancient ,roman year consisted of twelve lunar months1 of twenty-nine and thirty days alternately1 which equals #ced days2 but a day was added to make the number odd1 which was considered more fortunate1 so that the year consisted of #cee days4 ,this differed from the solar year by ten whole days and a fraction2 but to restore the coincidence1 ,numa ordered an additional or intercalary month to be inserted every second year between the #bc;d and #bdth of ,february1 consisting of twenty-two and twenty-three days alternately1 so that four years contained #adfe days1 and the mean length of the year was consequently #cff-a_/d days1 so that the year was then too long by one day4 ,as the error amounted to twenty-four days in as many years1 it was ordered that every third period of eight years1 instead of containing four intercalary months1 two of twenty-two and two of twenty-three days1 amounting in all to ninety days1 should contain only three of those months of twenty-two days each1 amounting to sixty-six days1 thereby suppressing twenty-four days in as many years1 reducing the mean length of the year to #cfe-a_/d days4 ,had the intercalations been regularly made the concurrence of the solar and the civil year would have been preserved very nearly4 ,but its regulation was left to the pontiffs1 who1 to prolong the term of a magistracy or hasten an annual election1 would give to the intercalary month a greater or less number of days1 and consequently the calendar was thrown into confusion1 so that in the time of ,julius ,caesar there was a discrepancy between the solar and the civil year of about three months2 the winter months being carried back into autumn and the autumnal into summer4 ,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 week3 ---------------------------------------- ----------------- ,saturn1 ,jupiter1 ,mars1 ,sun1 ,venus1 ,mercury1 ,moon1 ,saturday4,thursday4,tuesday4,sunday4,fr iday4,wednesday4,monday4 ---------------------------------------- ----------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd ---------------------------------------- ----------------- ,,chapter ,,iii4 ,,history ,,of ,,the ,,reformation ,,of ,,the ,,calendar ,,by ,,julius ,,caesar4 ,in order to put an end to the disorders arising from the negligence or ignorance of the pontiffs1 ,julius ,caesar1 #df ,b4 ,c41 abolished the use of the lunar year and the intercalary month1 and regulated the civil year entirely by the ,sun4 ,with the advice and assistance of the astronomers1 especially ,sosigenes of ,alexandria1 he fixed the mean length of the year at #cfe-a_/d days1 and decided that there should be three consecutive years of #cfe days1 and a fourth of #cff4 ,in order to restore the vernal equinox to the #bdth of ,march1 the place it occupied in the time of ,numa1 two months1 together consisting of #fg days1 were inserted between the last day of ,november and the first day of ,december of that year4 ,an intercalary month of #bc days had already been added to ,february of the same year according to the old method1 so that the first ,julian year commenced with the first day of ,january1 #de years before ,christ1 and #gji from the foundation of ,rome1 making the year ,a4 ,u4 ,c4 #gjh to consist of the prodigious number of #dde days1 7i4 e4 #cee #bc #fg #dde74 ,hence it was called by some the year of confusion2 ,macrobius said it should be named the last year of confusion4 ,there was also adopted at the same time a more commodious arrangement in the distribution of the days throughout the several months4 ,it was decided to give to ,january1 ,march1 ,may1 ,july1 ,september and ,november each thirty-one days2 and the other months thirty1 excepting ,february1 which in common years should have but twenty-nine days1 but every fourth year thirty2 so that the average length of the ,julian year was #cfe-a_/d days4 ,augustus ,caesar interrupted this order by taking one day from ,february1 reducing it to twenty-eight and giving it to ,august1 that the month bearing his name should have as many days as ,july1 which was named in honor of his great-uncle1 ,julius4 ,in order that three months of thirty-one days might not come together1 ,september and ,november were reduced to thirty days1 and thirty-one given to ,october and ,december4 ,in the ,julian calendar a day was added to ,february every fourth year1 it being the shortest month1 which was called the additional or intercalary day1 and was inserted in the calendar between the #bc;d and #bdth of that month4 ,in the ancient ,roman calendar the first day of every month was invariably called the calends4 ,the #bdth of ,february then was the #fth of the calends of ,march--,sexto calendas2 the preceding1 which was the additional or intercalary day1 was called bis-sexto calendas 7from bis1 twice1 and sextus1 six71 twice the sixth day4 ,hence the term bis-sextile as applied to every fourth year1 commonly called leap-year4 ,appendix ,b4 ,,chapter ,,iv4 ,,history ,,of ,,the ,,reformation ,,of ,,the ,,julian ,,calendar ,,by ,,pope ,,gregory ,,xiii4 ,true enough1 the year in which ,julius ,caesar reformed the ancient ,roman calendar was the last year of confusion1 and the method adopted by him a commodious one1 and answered a very good purpose for a short time2 but as the years rolled on and century after century had passed away1 astronomers began to discover the discrepancy between the solar and the civil year2 that the vernal equinox did not occupy the place it occupied in the time of ,caesar1 namely1 the #bdth of ,march1 but was gradually retrograding towards the beginning of the year1 so that at the meeting of the ,council of ,nice in #cbe it fell on the #bast4 ,appendix ,c4 ,the venerable ,bede1 in the #hth century1 observed that these phenomena took place three or four days earlier than at the meeting of that council4 ,roger ,bacon1 in the #acth century1 wrote a treatise on this subject and sent it to the ,pope1 setting forth the errors of the ,julian calendar4 ,the discrepancy at that time amounted to seven or eight days4 ,thus the errors of the calendar continued to increase until #aehb1 when the vernal equinox fell on the #aath instead of the #bast of ,march4 ,gregory1 perceiving that the measure 7of reforming the calendar7 was likely to confer great eclat on his pontificate1 undertook the long desired reformation2 and having found the governments of the principal ,catholic states ready to adopt his views1 he issued a brief in the month of ,march1 #aehb1 in which he abolished the use of the ancient calendar1 and substituted that which has since been received in almost all ,christian countries under the name of the ,gregorian calendar or ,new ,style4 ,the edict of the ,pope took effect in ,october of that year1 causing the #eth to be called the #aeth of that month1 thus suppressing ten days and making the year #aehb to consist of only #cee days4 ,so we see that the ten days that had been gained by incorrect computation during the past #abeg years1 were deducted from #aehb1 restoring the concurrence of the solar and the civil year1 and consequently the vernal equinox to the place it occupied in #cbe1 namely1 the #bast of ,march4 ,the ,pope was promptly obeyed in ,spain1 ,portugal1 and ,italy4 ,the change took place the same year in ,france1 by calling the #ajth the #bjth of ,december4 ,many other ,catholic countries made the change the same year1 and the ,catholic states of ,germany the year following2 but most of the ,protestant countries adhered to the ,old ,style until after the year #agjj4 ,among the last was ,great ,britain2 she1 after having suffered a great deal of inconvenience for nearly two hundred years by using a different date from the most of ,europe1 at length1 by an act of ,parliament1 fixed on ,september1 #ageb1 as the time for making the much desired change1 which was done by calling the #c;d of that month the #adth 7as the error now amounted to eleven days71 adopting at the same time the ,gregorian rule of intercalation4 ,russia is the only ,christian country that still adheres to the ,old ,style1 and by using a different date from the rest of ,europe is now twelve days behind the true time4 ,the discrepancy between solar and civil time does not effect the day1 for1 as has already been shown1 the mean length of the day is twenty-four hours1 and is marked by one revolution of the earth upon its axis4 ,nor does it effect the week1 for the week is uniformly seven of those days4 ,but it effects the year1 the month and the day of the month4 ,russia1 by adhering to the ,old ,style1 has reckoned as many days and as many weeks1 and events have transpired on the same day of the week as they have with us who have adopted the ,new ,style2 as ,christian nations we are observing the same day as the ,sabbath4 ,when it was ,tuesday1 the #bjth day of ,december1 #ahhh1 in ,russia1 it was ,tuesday1 the #ast day of ,january1 #ahhi1 in those countries which have adopted the ,new ,style4 ,columbus sailed from ,palos1 in ,spain1 on ,friday1 ,august #c;d1 #adib1 ,old ,style1 which was ,friday1 ,august #abth1 ,new ,style4 ,washington was born on ,friday1 ,february #aath1 #agcb1 ,old ,style1 which was ,friday1 ,february #bb;d1 ,new ,style4 ,now1 the difference in styles during the #aeth century is nine days2 during the #afth and #agth centuries1 ten days2 the #ahth century1 eleven days1 and the #aith1 twelve days4 ,in regard to the sailing of ,columbus1 the change is made by suppressing nine days1 calling the #c;d the #abth of ,august4 ,in regard to the birth of ,washington1 the change is effected by suppressing eleven days1 calling the #aath of ,february the #bb;d4 ,as regards ,russia1 she could have made the change last year by calling the #bjth of ,december1 #ahhh1 the #ast day of ,january1 #ahhi1 thereby suppressing twelve days1 and making the year #ahhh to consist of only #ced days1 and the month of ,december twenty days4 ,the methods of computation1 both ,old and ,new ,styles1 will be explained in another chapter4 ,to persons unacquainted with astronomy1 the difference between ,old and ,new ,styles would probably be better understood by the diagram on the #beth page4 ,the figures represent the ecliptic1 which is the apparent path of the ,sun1 or the real path of the ,earth as seen from the ,sun1 in her annual or yearly revolution around the ,sun in the order of the months1 as marked on the ecliptic4 ,attention is called to four points on the ecliptic1 namely1 the vernal equinox1 the autumnal equinox1 the winter solstice1 and the summer solstice4 ,these occur1 in the order given above1 on the #bast of ,march1 the #bast of ,september1 the #bast of ,december and the #bast of ,june4 ,it has already been stated that if the civil year correspond with the solar1 the seasons of the year will always come at the same period4 ,julius ,caesar found the ancient ,roman year in advance of the solar2 ,gregory found the ,julian behind the solar year2 so one reforms the calendar by intercalation1 the other by suppression4 ,appendix ,d4 ,caesar restored the coincidence of the solar and the civil year1 but failed to retain it by allowing what probably appeared to him at the time a trifling error in his calendar4 ,the error1 which was #aa minutes and #aj4ch seconds every year1 was hardly perceptable for a short period1 but still amounted to three days every #djj years4 ,hence the necessity in #aehb of reforming the reformed calendar of ,julius ,caesar to restore the coincidence4 ,appendix ,e4 ,from the meeting of the ,council of ,nice1 in #cbe1 to #aehb1 a period of #abeg years1 there was found to be an error in the ,julian calendar of ten days4 ,now1 in #abeg years the ,earth performs #abeg annual and #dei1aji daily revolutions1 after which the vernal equinox was found to occur on the #bast of ,march1 true or solar time2 thus concurring with the vernal equinox of #cbe4 ,but the erroneous ,julian calendar would make the ,earth perform #dei1aai daily revolutions to complete the #abeg years1 a discrepancy of ten days1 making the vernal equinox to fall on the #aath instead of the #bast4 ,it will be seen by the diagram that the ten days were deducted from ,october1 in #aehb1 making it a short month1 consisting of only twenty-one days4 ,the discrepancy between the ,julian and ,gregorian calendar amounts to thirty days in #djjj years2 three months in #ab1age years4 ,hence1 in #ab1age years the equinoxes would take the place of the solstices1 and the solstices the place of the equinoxes4 ,in #bd1cej years1 the vernal equinox would take the place of the autumnal equinox1 and the winter solstice the place of the summer solstice4 ,and in #dh1gjj years1 according to the ,julian rule of intercalation1 there would be gained nearly #cfe-a_/d days1 or one entire revolution of the ,earth4 ,so1 to restore the concurrence of the ,julian and ,gregorian years1 there would have to be suppressed #cfe-a_/d days1 calling the #ast day of ,january1 #dh1fii1 the #ast day of ,january1 #dh1gjj4 ,thus would disappear from the ,julian calendar twelve months1 or one whole year1 it having been divided among the thousands of the preceding years4 ,illustration3 ,the ,julian calendar1 reformed by ,gregory ,,xiii1 ,oct4 #eth1 #aehb1 by suppressing ten days1 calling the #eth of ,oct4 the #aeth1 making it a short month of #ba days1 and the year to consist of #cee days4 ,the ,roman calendar1 reformed by ,julius ,caesar1 #df ,b4 ,c41 by intercalating #ij days1 making that year to consist of #dde days1 that is1 #cee #bc #fg #dde days1 and the last year of confusion4 ,to make this subject better understood1 let us suppose the solar year to consist in round numbers of #cfe days1 and the civil year #cff4 ,it is evident that at the end of the year of #cfe days1 there would still be wanting one day to complete the civil year of #cff days1 so one day must be added to that year1 and to every succeeding year1 to complete the years of #cff days each1 which would be the loss of one year of #cfe days in #cfe years4 ,hence1 #cfd years of #cff days each are equal to #cfe years of #cfe days each1 wanting one day4 ,again1 let us suppose the civil year to consist of #cfd days4 ,it is evident that at the end of the supposed solar year of #cfe days1 there would be an advance or gain of one day in that year and every succeeding year1 so that in #cfe years there would be a gain of #cfe days or one whole year4 ,hence1 #cff years of #cfd days each are equal to #cfe years of #cfe days each1 wanting one day4 ,appendix ,f4 ,,chapter ,v4 ,,peculiarities ,,of ,,the ,,roman ,,calendar4 ,the ,romans1 instead of distinguishing the days of the month by the ordinal numbers1 first1 second1 third1 etc41 counted backwards from three fixed points1 namely1 the ,calends1 the ,nones1 and the ,ides4 ,calends 7,latin ,calandae1 from ,calare1 to call17 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 festivals1 or days that were to be kept sacred during the month4 ,nones 7,latin nonae1 from nonus1 the ninth17 the ninth day before the ,ides4 ,ides 7,latin idus1 supposed to be derived from an obsolete verb iduare1 to divide17 was near the middle of the month1 either the #acth or the #aeth day4 ,the first day of each month was invariably called the ,calends4 ,the ,nones were the fifth1 and the ,ides the thirteenth1 except in ,march1 ,may1 ,july1 and ,october1 in which the ,nones occurred on the seventh day and the ,ides on the fifteenth4 ,from these three points the days of the month were numbered--not forward1 but backward--as so many days before the ,nones1 the ,ides1 or the ,calends1 the point of departure being counted in the reckoning1 so that the last day of every month was the second of the ,calends of the following month4 ,it will be seen by the ,roman and ,english calendar found on the following pages1 that there are six days of ,nones in ,march1 ,may1 ,july and ,october1 and four of all the other months2 also that all the months have eight days of ,ides4 ,the number of days of ,calends depend upon the number of days in the month1 and the day of the month on which the ,ides fall4 ,if the month has thirty-one days and the ,ides fall on the thirteenth1 there are nineteen days of ,calends2 but if the ,ides fall on the fifteenth1 there are only seventeen days of ,calends4 ,as the ,ides fall on the thirteenth of all the months of thirty days1 they have eighteen days of ,calends4 ,february1 the month of twenty-eight days1 has only sixteen1 except in leap-year1 when the sixth of the ,calends is reckoned twice4 ,it may also be seen from the calendar that the ,romans1 after the first day of the month1 began to reckon so many days before the ,nones1 as #dth1 #c;d1 #b;d1 then ,nones2 after the ,nones1 so many days before the ,ides1 as #hth1 #gth1 #fth1 etc41 and after the ,ides1 so many before the ,calends of the next month1 the highest numbers being reckoned first4 ,in reducing the ,roman calendar to our own1 it should be remembered that in reckoning backward from a fixed point1 that the point of departure is counted2 also1 that the last day of the month is not the point from which the ,calends are reckoned1 but the first day of the following month4 ,we have then this rule for finding the ,english expression for any ,latin date3 ,,rule4 ,if the given date be ,calends1 add two to the number of days in the month1 from which subtract the given date2 if the date be ,nones1 or ,ides1 add one to that of the day on which the ,nones or ,ides fall1 from which subtract the given date1 and you will have the day of the month in our calendar4 ,to find the ,latin expression for any ,english date1 the preceding method is to be reversed1 upon the principle that if #e - #c #b1 then #e - #b #c4 ,but in reducing a ,roman date to a date of ,february in leap-year1 for the first twenty-four days1 proceed according to the preceding rule as if the month had only twenty-eight days1 and to obtain the proper expression for the remaining five days1 regard the month as having twenty-nine days1 taking the ,roman date from #ca instead of #cj4 ,thus #ca - #f #be1 while #cj -#f #bd2 the former corresponding with sexto calendas1 the latter with bis-sexto calendas of the ,julian calendar4 ,by referring to the table on the #ceth page1 one may easily learn how to find the ,english expression for any ,latin date1 or the ,latin expression for any ,english date4 ,it has already been stated that in ,january the ,nones fall on the #eth1 and the ,ides on the #acth1 ,january then having thirty one days1 the number from which to subtract the ,roman date to obtain the corresponding day of the month is1 for ,nones1 #e #a #f2 for ,ides1 #ac #a #ad2 for ,calends1 #ca #b #cc4 ,hence the first column in the table under ,january are the numbers #f1 #ad and #cc4 ,february is the same as ,january for ,nones and ,ides4 ,for ,calends in leap-year1 for the first #bd days1 it is #bh #b #cj2 for the remaining #e days it is #bi #b #ca4 ,hence for the first column under ,february are the numbers #f1 #ad1 #cj and #ca4 ,march is the same as ,january1 except that the ,nones fall on the #gth and the ,ides on the #aeth1 consequently we have for ,nones1 #g #a #h1 and for ,ides1 #ae #a #af2 hence1 for the first column under ,march we have the numbers #h1 #af1 and #cc4 ,in the table the three months are taken to illustrate how easily the change may be made from ,roman to ,english1 or from ,english to ,roman date4 ,a complete calendar for #ahib1 both in ,roman and ,english1 which will be very convenient for reference1 may be found on the four following pages4 ,the first seven letters of the alphabet1 used to represent the days of the week1 are placed in the calendar beside the days of the week4 ,the letter that represents ,sunday is called the dominical or ,sunday letter4 ,the letter that represents the first ,sunday in any given year represents all the ,sundays in that year1 unless it be leap-year1 when two ,sunday letters are used4 ,the first represents all the ,sundays in ,january and ,february1 while the letter that precedes it represents all the ,sundays for the rest of the year4 ,the reason of this is1 the day intercalated1 or thrust in1 between the #bhth day of ,february and the #ast day of ,march so interrupts the order of the letters that ,d1 which always represents the #ast day of ,march1 now represents the #bith day of ,february1 so that in #ahib it represents ,monday1 the #bith day of ,february1 also ,tuesday the #ast day of ,march4 ,as it represented all the ,mondays in ,january and ,february1 it will now represent all the ,tuesdays for the rest of the year1 while ,c1 the letter preceding1 represented all the ,sundays1 will now represent all the ,mondays1 and ,b all the ,sundays4 ,for ,january and ,february we have then ,c1 ,sunday2 ,d1 ,monday2 ,e1 ,tuesday2 ,f1 ,wednesday2 ,g1 ,thursday2 ,a1 ,friday1 and ,b1 ,saturday4 ,for the rest of the year we have ,b1 ,sunday2 ,c1 ,monday2 ,d1 ,tuesday2 ,e1 ,wednesday2 ,f1 ,thursday2 ,g1 ,friday1 and ,a1 ,saturday4 ,see ,part ,second1 chapters ,,iv and ,v4 ---------------------------------------- -------------- ,,jan41 #ahib4 ,,feb41 #ahib4 ,,march1 #ahib4 ---------------------------------------- -------------- #a;,cal4 a,fri4 #a;,cal4 d,mon4 #a;,cal4 d,tues4 #b #d b,sat4 #b #d e,tues4 #b #f e,wed4 #c #c c,sun4 #c #c f,wed4 #c #e f,thur4 #d #b d,mon4 #d #b g,thur4 #d #d g,fri4 #e,non4 e,tues4 #e,non4 a,fri4 #e #c a,sat4 #f #h f,wed4 #f #h b,sat4 #f #b b,sun4 #g #g g,thur4 #g #g c,sun4 #g,non4 c,mon4 #h #f a,fri4 #h #f d,mon4 #h #h d,tues4 #i #e b,sat4 #i #e e,tues4 #i #g e,wed4 #aj #d c,sun4 #aj #d f,wed4 #aj #f f,thur4 #aa #c d,mon4 #aa #c g,thur4#aa #e g,fri4 #ab #b e,tues4#ab #b a,fri4 #ab #d a,sat4 #ac;,ides4f,wed4 #ac;,ides4b,sat4 #ac #c b,sun4 #ad #ai g,thur4#ad #af c,sun4 #ad #b c,mon4 #ae #ah a,fri4 #ae #ae d,mon4 #ae;,ides4d,tues4 #af #ag b,sat4 #af #ad e,tues4#af #ag e,wed4 #ag #af c,sun4 #ag #ac f,wed4 #ag #af f,thur4 #ah #ae d,mon4 #ah #ab g,thur4#ah #ae g,fri4 #ai #ad e,tues4#ai #aa a,fri4 #ai #ad a,sat4 #bj #ac f,wed4 #bj #aj b,sat4 #bj #ac b,sun4 #ba #ab g,thur4#ba #i c,sun4 #ba #ab c,mon4 #bb #aa a,fri4 #bb #h d,mon4 #bb #aa d,tues4 #bc #aj b,sat4 #bc #g e,tues4#bc #aj e,wed4 #bd #i c,sun4 #bd #f f,wed4 #bd #i f,thur4 #be #h d,mon4 #be #f g,thur4#be #h g,fri4 #bf #g e,tues4#bf #e a,fri4 #bf #g a,sat4 #bg #f f,wed4 #bg #d b,sat4 #bg #f b,sun4 #bh #e g,thur4#bh #c c,sun4 #bh #e c,mon4 #bi #d a,fri4 #bi #b d,mon4 #bi #d d,tues4 #cj #c b,sat4 #cj #c e,wed4 #ca #b c,sun4 #ca #b f,thur4 ---------------------------------------- ----- ---------------------------------------- -------------- ,,april1 #ahib4 ,,may1 #ahib4 ,,june1 #ahib4 ---------------------------------------- ----- #a;,cal4 g,fri4 #a;,cal4 b,sun4 #a;,cal4 e,wed4 #b #d a,sat4 #b #f c,mon4 #b #d f,thur4 #c #c b,sun4 #c #e d,tues4 #c #c g,fri4 #d #b c,mon4 #d #d e,wed4 #d #b a,sat4 #e,non4 d,tues4 #e #c f,thur4 #e,non4 b,sun4 #f #h e,wed4 #f #b g,fri4 #f #h c,mon4 #g #g f,thur4 #g,non4 a,sat4 #g #g d,tues4 #h #f g,fri4 #h #h b,sun4 #h #f e,wed4 #i #e a,sat4 #i #g c,mon4 #i #e f,thur4 #aj #d b,sun4 #aj #f d,tues4#aj #d g,fri4 #aa #c c,mon4 #aa #e e,wed4 #aa #c a,sat4 #ab #b d,tues4#ab #d f,thur4#ab #b b,sun4 #ac;,ides4e,wed4 #ac #c g,fri4 #ac;,ides4c,mon4 #ad #ah f,thur4#ad #b a,sat4 #ad #ah d,tues4 #ae #ag g,fri4 #ae;,ides4b,sun4 #ae #ag e,wed4 #af #af a,sat4 #af #ag c,mon4 #af #af f,thur4 #ag #ae b,sun4 #ag #af d,tues4#ag #ae g,fri4 #ah #ad c,mon4 #ah #ae e,wed4 #ah #ad a,sat4 #ai #ac d,tues4#ai #ad f,thur4#ai #ac b,sun4 #bj #ab e,wed4 #bj #ac g,fri4 #bj #ab c,mon4 #ba #aa f,thur4#ba #ab a,sat4 #ba #aa d,tues4 #bb #aj g,fri4 #bb #aa b,sun4 #bb #aj e,wed4 #bc #i a,sat4 #bc #aj c,mon4 #bc #i f,thur4 #bd #h b,sun4 #bd #i d,tues4#bd #h g,fri4 #be #g c,mon4 #be #h e,wed4 #be #g a,sat4 #bf #f d,tues4#bf #g f,thur4#bf #f b,sun4 #bg #e e,wed4 #bg #f g,fri4 #bg #e c,mon4 #bh #d f,thur4#bh #e a,sat4 #bh #d d,tues4 #bi #c g,fri4 #bi #d b,sun4 #bi #c e,wed4 #cj #b a,sat4 #cj #c c,mon4 #cj #b f,thur4 #ca #b d,tues4 ---------------------------------------- ----- ---------------------------------------- ------------- ,,july1 #ahib4 ,,aug41 #ahib4 ,,sept41 #ahib4 ---------------------------------------- ----- #a;,cal4 g,fri4 #a;,cal4 c,mon4 #a;,cal4 f,thur4 #b #f a,sat4 #b #d d,tues4 #b #d g,fri4 #c #e b,sun4 #c #c e,wed4 #c #c a,sat4 #d #d c,mon4 #d #b f,thur4 #d #b b,sun4 #e #c d,tues4 #e,non4 g,fri4 #e,non4 c,mon4 #f #b e,wed4 #f #h a,sat4 #f #h d,tues4 #g,non4 f,thur4 #g #g b,sun4 #g #g e,wed4 #h #h g,fri4 #h #f c,mon4 #h #f f,thur4 #i #g a,sat4 #i #e d,tues4 #i #e g,fri4 #aj #f b,sun4 #aj #d e,wed4 #aj #d a,sat4 #aa #e c,mon4 #aa #c f,thur4#aa #c b,sun4 #ab #d d,tues4#ab #b g,fri4 #ab #b c,mon4 #ac #c e,wed4 #ac;,ides4a,sat4 #ac;,ides4d,tues4 #ad #b f,thur4#ad #ai b,sun4 #ad #ah e,wed4 #ae;,ides4g,fri4 #ae #ah c,mon4 #ae #ag f,thur4 #af #ag a,sat4 #af #ag d,tues4#af #af g,fri4 #ag #af b,sun4 #ag #af e,wed4 #ag #ae a,sat4 #ah #ae c,mon4 #ah #ae f,thur4#ah #ad b,sun4 #ai #ad d,tues4#ai #ad g,fri4 #ai #ac c,mon4 #bj #ac e,wed4 #bj #ac a,sat4 #bj #ab d,tues4 #ba #ab f,thur4#ba #ab b,sun4 #ba #aa e,wed4 #bb #aa g,fri4 #bb #aa c,mon4 #bb #aj f,thur4 #bc #aj a,sat4 #bc #aj d,tues4#bc #i g,fri4 #bd #i b,sun4 #bd #i e,wed4 #bd #h a,sat4 #be #h c,mon4 #be #h f,thur4#be #g b,sun4 #bf #g d,tues4#bf #g g,fri4 #bf #f c,mon4 #bg #f e,wed4 #bg #f a,sat4 #bg #e d,tues4 #bh #e f,thur4#bh #e b,sun4 #bh #d e,wed4 #bi #d g,fri4 #bi #d c,mon4 #bi #c f,thur4 #cj #c a,sat4 #cj #c d,tues4#cj #b g,fri4 #ca #b b,sun4 #ca #b e,wed4 ---------------------------------------- ----- ---------------------------------------- -------------- ,,oct41 #ahib4 ,,nov41 #ahib4 ,,dec41 #ahib4 ---------------------------------------- ----- #a;,cal4 a,sat4 #a;,cal4 d,tues4 #a;,cal4 f,thur4 #b #f b,sun4 #b #d e,wed4 #b #d g,fri4 #c #e c,mon4 #c #c f,thur4 #c #c a,sat4 #d #d d,tues4 #d #b g,fri4 #d #b b,sun4 #e #c e,wed4 #e,non4 a,sat4 #e,non4 c,mon4 #f #b f,thur4 #f #h b,sun4 #f #h d,tues4 #g,non4 g,fri4 #g #g c,mon4 #g #g e,wed4 #h #h a,sat4 #h #f d,tues4 #h #f f,thur4 #i #g b,sun4 #i #e e,wed4 #i #e g,fri4 #aj #f c,mon4 #aj #d f,thur4#aj #d a,sat4 #aa #e d,tues4#aa #c g,fri4 #aa #c b,sun4 #ab #d e,wed4 #ab #b a,sat4 #ab #b c,mon4 #ac #c f,thur4#ac;,ides4b,sun4 #ac;,ides4d,tues4 #ad #b g,fri4 #ad #ah c,mon4 #ad #ai e,wed4 #ae;,ides4a,sat4 #ae #ag d,tues4#ae #ah f,thur4 #af #ag b,sun4 #af #af e,wed4 #af #ag g,fri4 #ag #af c,mon4 #ag #ae f,thur4#ag #af a,sat4 #ah #ae d,tues4#ah #ad g,fri4 #ah #ae b,sun4 #ai #ad e,wed4 #ai #ac a,sat4 #ai #ad c,mon4 #bj #ac f,thur4#bj #ab b,sun4 #bj #ac d,tues4 #ba #ab g,fri4 #ba #aa c,mon4 #ba #ab e,wed4 #bb #aa a,sat4 #bb #aj d,tues4#bb #aa f,thur4 #bc #aj b,sun4 #bc #i e,wed4 #bc #aj g,fri4 #bd #i c,mon4 #bd #h f,thur4#bd #i a,sat4 #be #h d,tues4#be #g g,fri4 #be #h b,sun4 #bf #g e,wed4 #bf #f a,sat4 #bf #g c,mon4 #bg #f f,thur4#bg #e b,sun4 #bg #f d,tues4 #bh #e g,fri4 #bh #d c,mon4 #bh #e e,wed4 #bi #d a,sat4 #bi #c d,tues4#bi #d f,thur4 #cj #c b,sun4 #cj #b e,wed4 #cj #c g,fri4 #ca #b c,mon4 #ca #b a,sat4 ---------------------------------------- ----- ---------------------------------------- ------ ,,january4 ,,february4 ,,march4 ---------------------------------------- ------ ,cal4 #a ,cal4 #a ,cal4 #a #f - #d #b #f - #d #b #h - #f #b #f - #c #c #f - #c #c #h - #e #c #f - #b #d #f - #b #d #h - #d #d ,nones #e ,nones #e #h - #c #e #ad - #h #f #ad - #h #f #h - #b #f #ad - #g #g #ad - #g #g ,nones #g #ad - #f #h #ad - #f #h #af - #h #h #ad - #e #i #ad - #e #i #af - #g #i #ad - #d #aj #ad - #d #aj #af - #f #aj #ad - #c #aa #ad - #c #aa #af - #e #aa #ad - #b #ab #ad - #b #ab #af - #d #ab ,ides #ac ,ides #ac #af - #c #ac #cc - #ai #ad #cj - #af #ad #af - #b #ad #cc - #ah #ae #cj - #ae #ae ,ides #ae #cc - #ag #af #cj - #ad #af #cc - #ag #af #cc - #af #ag #cj - #ac #ag #cc - #af #ag #cc - #ae #ah #cj - #ab #ah #cc - #ae #ah #cc - #ad #ai #cj - #aa #ai #cc - #ad #ai #cc - #ac #bj #cj - #aj #bj #cc - #ac #bj #cc - #ab #ba #cj - #i #ba #cc - #ab #ba #cc - #aa #bb #cj - #h #bb #cc - #aa #bb #cc - #aj #bc #cj - #g #bc #cc - #aj #bc #cc - #i #bd #cj - #f #bd #cc - #i #bd #cc - #h #be #ca - #f #be #cc - #h #be #cc - #g #bf #ca - #e #bf #cc - #g #bf #cc - #f #bg #ca - #d #bg #cc - #f #bg #cc - #e #bh #ca - #c #bh #cc - #e #bh #cc - #d #bi #ca - #b #bi #cc - #d #bi #cc - #c #cj #cc - #c #cj #cc - #b #ca #cc - #b #ca ---------------------------------------- ------ ,,part ,,second4 ,,mathematical4 ,,chapter ,i4 ,,errors ,,of ,,the ,,julian ,,calendar4 ,it will be necessary in the first place to understand the difference between the ,julian and ,gregorian rule of intercalation4 ,if the number of any year be exactly divisible by four it is leap year2 if the remainder be #a1 it is the first year after leap-year2 if #b1 the second2 if #c1 the third2 thus3 #ahhh _/ #d #dgb1 no remainder4 #ahhi _/ #d #dgb1 remainder1 #a4 #ahij _/ #d #dgb1 remainder1 #b4 #ahia _/ #d #dgb1 remainder1 #c4 #ahib _/ #d #dgc1 no remainder4 ,and so on1 every fourth year being leap-year of #cff days4 ,this is the ,julian rule of intercalation1 which is corrected by the ,gregorian by making every centurial year1 or the year that completes the century1 a common year1 if not exactly divisible by #djj2 so that only every fourth centurial year is leap-year2 thus1 #a1gjj1 #a1hjj1 and #a1ijj are common years1 but #b1jjj1 the fourth centurial year1 is leap year1 and so on4 ,by the ,julian rule three-fourths of a day is gained every century1 which in #djj years amounts to three days4 ,this is corrected by the ,gregorian1 by making three consecutive centurial years common years1 thus suppressing three days in #djj years4 ,,rule4 ,multiply the difference between the ,julian and the solar year by #ajj1 and we have the error in #ajj years4 ,multiply this product by #d and we have the error in #djj years4 ,now1 #djj is the tenth of #d1jjj2 therefore1 multiply the last product by #aj1 and we have the error in #d1jjj years4 ,now1 as the discrepancy between the ,julian and ,gregorian year is three days in #djj years1 making #c-djj of a day every year1 so by dividing #cfe-a_/d1 the number of days in a year1 by #c-djj1 we have the time it would take to make a revolution of the seasons4 ,,solution4 7#cfe d1 #f h47 - 7#cfe d1 #e h1 #dh m1 #di4fb s47 7#aa m1 #aj4ch s47 ,now1 7#aa m1 #aj4ch s47 x #ajj #ah h1 #cg4c m1 the gain in #ajj years4 ,this is1 reckoned in round numbers1 #ah hours1 or three-fourths of a day4 ,now1 7#c_/d x #d7 7#a x #c7 #c3 the ,julian rule gaining three days1 the ,gregorian suppressing three days in #djj years4 7#c x #aj7 #cj1 the number of days gained by the ,julian rule in #d1jjj years4 #cfe-a_/d _/ #c #djj #dh1gjj1 so that in this long period of time1 this falling back #c_/d of a day every century would amount to #cfe-a_/d days2 therefore1 #dh1fii ,julian years are equal to #dh1gjj ,gregorian years4 ,,chapter ,,ii4 ,,errors ,,of ,,the ,,gregorian ,,calendar4 ,by reference to the preceding chapter it will be seen that there is an error of #cg4c minutes in every #ajj years not corrected by the ,gregorian calendar2 this amounts to only 4#cgc of a minute a year1 or one day in #c1hfa years1 and one day and fifty-two minutes in #d1jjj years4 ,,rule4 ,to find how long it would take to gain one day3 ,divide the number of minutes in a day by the decimal 4#cgc1 that being the fraction of a minute gained every year4 ,to find how much time would be gained in #d1jjj years1 multiply the decimal 4#cgc by #d1jjj1 and you will have the answer in minutes1 which must be reduced to hours4 ,,solution4 7#bd x #fj7 _/ 4#cgc #c1hfa1 nearly2 hence the error would amount to only one day in #c1hfa years4 74#cgc x #d1jjj7 _/ #fj 7#bd h1 #eb m17 7#a d1 #j h1 #eb m71 the error in #d1jjj years4 ,this trifling error in the ,gregorian calendar may be corrected by suppressing the intercalations in the year #d1jjj1 and its multiples1 #h1jjj1 #ab1jjj1 #af1jjj1 etc41 so that it will not amount to a day in #ajj1jjj years4 ,,rule4 ,divide #ajj1jjj by #d1jjj and you will have the number of intercalations suppressed in #ajj1jjj years4 ,multiply #a d1 #eb m1 7that being the error in #d1jjj years7 by this quotient1 and you will have the discrepancy between the ,gregorian and solar year for #ajj1jjj years4 ,by this improved method we suppress #be days1 so that the error will only amount to #be times #eb minutes4 ,,solution4 #ajj1jjj _/ #d1jjj x 7#a d1 #eb m17 7#be;d1 #ba h1 #dj m47 ,now1 7#be;d1 #ba h1 #dj m17 - #be d 7#ba h1 #dj m17 the error in #ajj1jjj4 ,,chapter ,,iii4 ,,dominical ,,letter4 ,dominical 7from the ,latin ,dominus1 ,lord17 indicating the ,lord's day or ,sunday4 ,dominical letter1 one of the first seven letters of the alphabet used to denote the ,sabbath or ,lord's day4 ,for the sake of greater generality1 the days of the week are denoted by the first seven letters of the alphabet1 ,a1 ,b1 ,c1 ,d1 ,e1 ,f1 ,g1 which are placed in the calendar beside the days of the year1 so that ,a stands opposite the first day of ,january1 ,b opposite the second1 ,c opposite the third1 and so on to ,g1 which stands opposite the seventh2 after which ,a returns to the eighth1 and so on through the #cfe days of the year4 ,now1 if one of the days of the week1 ,sunday for example1 is represented by ,f1 ,monday will be represented by ,g1 ,tuesday by ,a1 ,wednesday by ,b1 ,thursday by ,c1 ,friday by ,d1 and ,saturday by ,e2 and every ,sunday throughout the year will have the same character1 ,f1 every ,monday ,g1 every ,tuesday ,a1 and so with regard to the rest4 ,the letter which denotes ,sunday is called the ,dominical or ,sunday letter for that year2 and when the dominical letter of the year is known1 the letters which respectively correspond to the other days of the week become known also4 ,did the year consist of #cfd days1 or #eb weeks invariably1 the first day of the year and the first day of the month1 and in fact any day of any year1 or any month1 would always commence on the same day of the week4 ,but every common year consists of #cfe days1 or #eb weeks and #a day1 so that the following year will begin one day later in the week than the year preceding4 ,thus the year #ahcg commenced on ,sunday1 the following year1 #ahch1 on ,monday1 #ahci on ,tuesday1 and so on4 ,as the year consists of #eb weeks and #a day1 it is evident that the day which begins and ends the year must occur #ec times2 thus the year #ahcg begins on ,sunday and ends on ,sunday2 so the following year1 #ahch1 must begin on ,monday4 ,as ,a represented all the ,sundays in #ahcg and as ,a always stands for the first day of ,january1 so in #ahch it will represent all the ,mondays1 and the dominical letter goes back from ,a to ,g2 so that ,g represents all the ,sundays in #ahch1 ,a all the ,mondays1 ,b all the ,tuesdays1 and so on1 the dominical letter going back one place in every year of #cfe days4 ,while the following year commences one day later in the week than the year preceding1 the dominical letter goes back one place from the preceding year2 thus while the year #ahfe commenced on ,sunday1 #ahff on ,monday1 #ahfg on ,tuesday1 the dominical letters are ,a1 ,g and ,f1 respectively4 ,therefore1 if every year consisted of #cfe days1 the dominical cycle would be completed in seven years1 so that after seven years the first day of the year would again occur on the same day of the week4 ,but this order is interrupted every four years by giving ,february #bi days1 thereby making the year to consist of #cff days1 which is #eb weeks and two days1 so that the following year would commence two days later in the week than the year preceding1 thus the year #ahhh being leap-year1 had two dominical letters1 ,a and ,g2 ,a for ,january and ,february1 and ,g for the rest of the year4 ,the year commenced on ,sunday and ended on ,monday1 making #ec ,sundays and #ec ,mondays1 and the following year1 #ahhi1 to commence on ,tuesday4 ,it now becomes evident that if the years all consisted of #cfd days1 or #eb weeks1 they would all commence on the same day of the week2 if they all consisted of #cfe days1 or #eb weeks and one day1 they would all commence one day later in the week than the year preceding2 if they all consisted of #cff days1 or #eb weeks and two days1 they would commence two days later in the week2 if #cfg days or #eb weeks and three days1 then three days later1 and so on1 one day later for every additional day4 ,it is also evident that every additional day causes the dominical letter to go back one place4 ,now in leap-year the #bith day of ,february is the additional or intercalary day4 ,so one letter for ,january and ,february1 and another for the rest of the year4 ,if the number of years in the intercalary period were two1 and seven being the number of days in the week1 their product would be #b x #g #ad2 fourteen1 then1 would be the number of years in the cycle4 ,again1 if the number of years in the intercalary period were three1 and the number of days in the week being seven1 their product would be #c x #g #ba2 twenty-one would then be the number of years in the cycle4 ,but the number of years in the intercalary period is four1 and the number of days in the week is seven1 therefore their product is #d x #g #bh2 twenty-eight is then the number of years in the cycle4 ,this period is called the dominical or solar cycle1 and restores the first day of the year to the same day of the week4 ,at the end of the cycle the dominical letters return again in the same order1 on the same days of the month4 ,thus1 for the year #ahja1 the dominical letter is ,d2 #ahjb1 ,c2 #ahjc1 ,b2 #ahjd1 ,a and ,g2 and so on1 going back five places every four years for twenty-eight years1 when the cycle1 being ended1 ,d is again dominical letter for #ahbi1 ,c for #ahcj1 and so on every #bh years forever1 according to the ,julian rule of intercalation4 ,but this order is interrupted in the ,gregorian calendar at the end of the century by the secular suppression of the leap-year4 ,it is not interrupted1 however1 at the end of every century1 for the leap-year is not suppressed in every fourth centurial year2 consequently the cycle will then be continued for two hundred years4 ,it should be here stated that this order continued without interruption from the commencement of the era until the reformation of the calendar in #aehb1 during which time the ,julian calendar1 or ,old ,style was used4 ,it has already been shown that if the number of years in the intercalary period be multiplied by seven1 the number of days in the week1 their product will be the number of years in the cycle4 ,now1 in the ,gregorian calendar1 the intercalary period is #djj years2 this number being multiplied by seven1 their product would be #b1hjj years1 as the interval in which the coincidence is restored between the days of the year and the days of the week4 ,this long period1 however1 may be reduced to #djj years2 for since the dominical letter goes back five places every four years1 in #djj years it will go back #ejj places in the ,julian and #dig in the ,gregorian calendar1 three intercalations being suppressed in the ,gregorian every #djj years4 ,now #dig is exactly divisible by seven1 the number of days in the week1 therefore1 after #djj years the cycle will be completed1 and the dominical letters will return again in the same order1 on the same days of the month4 ,in answer to the question1 ,why two dominical letters for leap-year8 we reply1 because of the additional or intercalary day after the #bhth of ,february4 ,it has already been shown that every additional day causes the dominical letter to go back one place4 ,as there are #cff days in leap-year1 the letter must go back two places1 one being used for ,january and ,february1 and the other for the rest of the year4 ,did we continue one letter through the year and then go back two places1 it would cause confusion in computation1 unless the intercalation be made at the end of the year4 ,whenever the intercalation is made there must necessarily be a change in the dominical letter4 ,had it been so arranged that the additional day was placed after the #cjth of ,june or ,september1 then the first letter would be used until the intercalation is made in ,june or ,september1 and the second to the end of the year4 ,or suppose that the end of the year had been fixed as the time and place for the intercalation1 7which would have been much more convenient for computation17 then there would have been no use whatever for the second dominical letter1 but at the end of the year we would go back two places2 thus1 in the year #ahhh1 instead of ,a being dominical letter for two months merely1 it would be continued through the year1 and then passing back to ,f1 no use whatever being made of ,g1 and so on at the end of every leap-year4 ,hence it is evident that this arrangement would have been much more convenient1 but we have this order of the months1 and the number of days in the months as ,augustus ,caesar left them eight years before ,christ4 ,the dominical letter probably was not known until the ,council of ,nice1 in the year of our ,lord #cbe1 where1 in all probability1 it had its origin4 ,,chapter ,,iv4 ,,rule ,,for ,,finding ,,the ,,dominical ,,letter4 ,divide the number of the given year by #d1 neglecting the remainders1 and add the quotient to the given number4 ,divide this amount by #g1 and if the remainder be less than three1 take it from #c2 but if it be #c or more than #c1 take it from #aj and the remainder will be the number of the letter calling ,a1 #a2 ,b1 #b2 ,c1 #c1 etc4 ,by this rule the dominical letter is found from the commencement of the era to ,october #eth1 #aehb4 ,o4 ,s4 ,from ,october #aeth1 #aehb1 till the year #agjj1 take the remainder as found by the rule from #f1 if it be less than #f1 but if the remainder be #f1 take it from #ac1 and so on according to instructions given in the table on #dith page4 ,it should be understood here1 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 #bith of ,february1 while the letter which follows it will be the one for ,january and ,february4 ,,examples4 ,to find the dominical letter for #acfe1 we have #acfe _/ #d #cda 2 #acfe #cda #agjf2 #agjf _/ #g #bdc1 remainder #e4 ,then #aj - #e #e2 therefore ,e being the fifth letter is the dominical letter for #acfe4 ,to find the dominical letter for #afbj1 we have #afbj _/ #d #dje2 #afbj #dje #bjbe2 #bjbe _/ #g #bhi1 remainder #b4 ,then #f - #b #d2 therefore1 ,d and ,e are the dominical letters for #afbj2 ,e for ,january and ,february1 and ,d for the rest of the year4 ,the process of finding the dominical letter is very simple and easily understood1 if we observe the following order3 #ast4 ,divide by #d4 #b;d4 ,add to the given number4 #c;d4 ,divide by #g4 #dth4 ,take the remainder from #c or #aj1 from the commencement of the era to ,october #eth1 #aehb4 ,from ,october #aeth1 #aehb to #agjj1 from #f or #ac4 ,from #agjj to #ahjj1 from #g1 and so on4 ,see table on #dith page4 ,we divide by #d because the intercalary period is four years2 and as every fourth year contains the divisor #d once more than any of the three preceding years1 so there is one more added to the fourth year than there is to any of the three preceding years2 and as every year consists of #eb weeks and one day1 this additional year gives an additional day to the remainder after dividing by #g4 ,for example1 the year #a of the era consists of #eb w4 #a d4 #b years consist of #ajd w4 #b d4 #c years consist of #aef w4 #c d4 7#d _/ #d7 #d #e years consist of #bfj w4 #e d4 ,hence the numbers thus formed will be #a1 #b1 #c1 #e1 #f1 #g1 #h1 #aj1 #aa1 #ab1 #ac1 #ae1 and so on4 ,we divide by #g1 because there are seven days in the week1 and the remainders show how many days more than an even number of weeks there are in the given year4 ,take1 for example1 the first twelve years of the era after being increased by one-fourth1 and we have #a _/ #g #j remainder #a ,then #c - #a #b ,b #b _/ #g #j #b #c - #b #a ,a #c _/ #g #j #c #aj - #c #g ,g #e _/ #g #j #e #aj - #e #e ,f ,e #f _/ #g #j #f #aj - #f #d ,d #g _/ #g #a #j #c - #j #c ,c #h _/ #g #a #a #c - #a #b ,b #aj _/ #g #a #c #aj - #c #g ,a ,g #aa _/ #g #a #d #aj - #d #f ,f #ab _/ #g #a #e #aj - #e #e ,e #ac _/ #g #a #f #aj - #f #d ,d #ae _/ #g #b #a #c - #a #b ,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 year1 that we have to deal with in finding the dominical letter4 ,did the year consist of #cfd days1 or #eb weeks1 invariably1 there would be no change in the dominical letter from year to year1 but the letter that represents ,sunday in any given year would represent ,sunday in every year4 ,did the year consist of only #cfc days1 thus wanting one day of an even number of weeks1 then these remainders1 instead of being taken from a given remainder1 would be added to that number1 thus removing the dominical letter forward one place1 and the beginning of the year1 instead of being one day later1 would be one day earlier in the week than in the preceding year4 ,thus1 if the year #a of the era be taken from #c1 we would have #c - #a #b2 therefore1 ,b being the second letter1 is dominical letter for the year #a4 ,but if the year consist of only #cfc days1 then the #a instead of being taken from #c would be added to #c2 then we would have #c #a #d2 therefore1 ,d being the fourth letter would be dominical letter for the year #a4 ,the former going back from ,c to ,b1 the latter forward from ,c to ,d2 or which amounts to the same thing1 make the year to consist of #ea weeks and #f days2 then #aj - #f #d1 making ,d the dominical letter as before4 ,as seven is the number of days in the week1 and the object of these subtractions is to remove the dominical letter back one place every common year1 and two in leap-year1 why not take these remainders from #g8 ,we answer1 all depends upon the day of the week on which the era commenced4 ,had ,g1 the seventh letter been dominical letter for the year preceding the era1 then these remainders would be taken from #g2 and #g would be used until change of style in #aehb4 ,but we know from computation that ,c1 the third letter1 is dominical letter for the year preceding the era2 so we commence with three1 and take the smaller remainders1 #a and #b from #c2 that brings us to ,a4 ,we take the larger remainders1 from #c to #f1 from #c #g #aj4 ,we add the #g because there are seven days in the week4 ,we use the number #aj until we get back to ,c1 the third letter1 the place from whence we started4 ,for example1 we have #c - #a #b ,b #c - #b #a ,a #aj - #c #g ,g #aj - #d #f ,f #aj - #e #e ,e #aj - #f #d ,d #c - #j #c ,c ,the cycle of seven days being completed1 we commence with the number three again1 and so on until #aehb1 when on account of the errors of the ,julian calendar1 ten days were suppressed to restore the coincidence of the solar and civil year4 ,now every day suppressed removes the dominical letter forward one place2 so counting from ,c to ,c again is seven1 ,d is eight1 ,e is nine1 and ,f is ten4 ,as ,f is the sixth letter1 we take the remainders from #a to #e1 from #f2 if the remainder be #f1 take it from #f #g #ac4 ,then #f or #ac is used till #agjj1 when1 another day being suppressed1 the number is increased to #g4 ,and again in #ahjj1 for the same reason1 a change is made to #a or #h2 in #aijj to #b or #i1 and so on4 ,it will be seen by the table on the #dith page that the smaller numbers run from #a to #g2 the larger ones from #h to #ac4 ,from the commencement of the ,christian era to ,october #eth1 #aehb1 take the remainders1 after dividing by #g1 from #c or #aj2 from ,october #aeth1 #aehb to #agjj from #f or #ac #agjj to #ahjj #g #ahjj to #aijj #a or #h #aijj to #bajj #b or #i #bajj to #bbjj #c or #aj #bbjj to #bcjj #d or #aa #bcjj to #bejj #e or #ab #bejj to #bfjj #f or #ac #bfjj to #bgjj #g #bgjj to #bijj #a or #h #bijj to #cjjj #b or #i #cjjj to #cajj #c or #aj #cajj to #ccjj #d or #aa #ccjj to #cdjj #e or #ab #cdjj to #cejj #f or #ac #cejj to #cgjj #g #cgjj to #chjj #a or #h #chjj to #cijj #b or #i #cijj to #djjj #c or #aj #djjj to #dajj #d or #aa #dajj to #dbjj #e or #ab #dbjj to #dcjj #f or #ac #dcjj to #dejj #g #dejj to #dfjj #a or #h #dfjj to #dgjj #b or #i #dgjj to #dijj #c or #aj #dijj to #ejjj #d or #aa #ejjj to #eajj #e or #ab ,,chapter ,v4 ,,rule ,,for ,,finding ,,the ,,day ,,of ,,the ,,week ,,of ,,any ,,given ,,date1 ,,for ,,both ,,old ,,and ,,new ,,styles4 ,by arranging the dominical letters in the order in which the different months commence1 the day of the week on which any month of any year1 or day of the month has fallen or will fall1 from the commencement of the ,christian era to the year of our ,lord #djjj1 may be calculated4 7,appendix ,g47 ,they have been arranged thus in the following couplet1 in which ,at stands for ,january1 ,dover for ,february1 ,dwells for ,march1 etc4 ,at ,dover ,dwells ,george ,brown1 ,esquire1 ,good ,carlos ,finch1 and ,david ,fryer4 ,now if ,a be dominical or ,sunday letter for a given year1 then ,january and ,october being represented by the same letter1 begin on ,sunday2 ,february1 ,march and ,november1 for the same reason1 begin on ,wednesday2 ,april and ,july on ,saturday2 ,may on ,monday1 ,june on ,thursday1 ,august on ,tuesday1 ,september and ,december on ,friday4 ,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 alphabet4 ,now let ,january #ast be represented by ,a1 ,sun4 ,feb4 #ast 7#d w4 #c d4 from the preceding date7 by ,d1 ,wed4 ,mar4 #ast #d w4 #j d4 by ,d1 ,wed4 ,apr4 #ast #d w4 #c d4 by ,g1 ,sat4 ,may #ast #d w4 #b d4 by ,b1 ,mon4 ,june #ast #d w4 #c d4 by ,e1 ,thur4 ,july #ast #d w4 #b d4 by ,g1 ,sat4 ,aug4 #ast #d w4 #c d4 by ,c1 ,tues4 ,sept4 #ast #d w4 #c d4 by ,f1 ,fri4 ,oct4 #ast #d w4 #b d4 by ,a1 ,sun4 ,nov4 #ast #d w4 #c d4 by ,d1 ,wed4 ,dec4 #ast #d w4 #b d4 by ,f1 ,fri4 ,now each of these letters placed opposite the months respectively represents the day of the week on which the month commences1 and they are the first letters of each word in the preceding couplet4 ,to find the day of the week on which a given day of any year will occur1 we have the following ,,rule4 ,find the dominical letter for the year4 ,read from this to the letter which begins the given month1 always reading from ,a toward ,g1 calling the dominical letter ,sunday1 the next ,monday1 etc4 ,this will show on what day of the week the month commenced2 then reckoning the number of days from this will give the day required4 ,,examples4 ,history records the fall of ,constantinople on ,may #bith1 #adec4 ,on what day of the week did it occur8 ,we have then #adec _/ #d #cfc 2 #adec #cfc #ahaf2 #ahaf _/ #g #bei1 remainder #c4 ,then #aj - #c #g2 therefore1 ,g being the seventh letter is dominical letter for #adec4 ,now reading from ,g to ,b1 the letter for ,may1 we have ,g ,sunday1 ,a ,monday1 and ,b ,tuesday2 hence ,may commenced on ,tuesday and the #bith was ,tuesday4 ,the change from ,old to ,new ,style was made by ,pope ,gregory ,,xiii1 ,october #eth1 #aehb4 ,on what day of the week did it occur8 ,we have then #aehb _/ #d #cie2 #aehb #cie #aigg2 #aigg _/ #g #bhb1 remainder #c4 ,then #aj - #c #g2 therefore1 ,g being the seventh letter1 is dominical letter for #aehb4 ,now reading from ,g to ,a1 the letter for ,october1 we have ,g ,sunday1 ,a ,monday1 etc4 ,hence ,october commenced on ,monday1 and the #eth was ,friday4 ,on what day of the week did the #aeth of the same month fall in #aehb8 ,we have then #aehb _/ #d #cie2 #aehb #cie #aigg2 #aigg _/ #g #bhb1 remainder #c4 ,then #f - #c #c2 therefore1 ,c being the third letter1 is the dominical letter for #aehb4 ,now reading from ,c to ,a1 the letter for ,october1 we have ,c ,sunday1 ,d ,monday1 ,e ,tuesday1 etc4 ,hence ,october commenced on ,friday1 and the #aeth was ,friday4 ,how is this1 says one8 ,you have just shown by computation that ,october1 #aehb1 commenced on ,monday1 you now say that it occurred on ,friday4 ,you also stated that the #eth was ,friday2 you now say that the #aeth was ,friday4 ,this is absurd2 ten is not a multiple of seven4 ,there is nothing absurd about it4 ,the former computation was ,old ,style1 the latter ,new ,style1 the ,old being ten days behind the new4 ,as regards an interval of ten days between the two ,fridays1 there was none2 ,friday1 the #eth1 and ,friday1 the #aeth1 was one and the same day2 there was no interval1 nothing ever occurred1 there was no time for anything to occur2 the edict of the ,pope decided it2 he said the #eth should be called the #aeth1 and it was so4 ,hence to ,october the #eth1 #aehb1 the computation should be ,old ,style2 from the #aeth to the end of the year ,new ,style4 ,on what day of the week did the years #a1 #b and #c1 of the era commence8 ,none of these numbers can be divided by #d2 neither are they divisible by #g2 but they may be treated as remainders after dividing by #g4 ,now each of these numbers of years consists of an even number of weeks with remainders of #a1 #b and #c days respectively4 ,hence we have then for the year #a1 #c - #a #b2 therefore1 ,b being the second letter1 is the dominical letter for the year #a4 ,now reading from ,b to ,a1 the letter for ,january1 we have ,b ,sunday1 ,c ,monday1 ,d ,tuesday1 etc4 ,hence ,january commenced on ,saturday4 ,then we have for the year #b1 #c - #b #a2 therefore ,a being the first letter1 is dominical letter for the year #b2 hence it is evident that ,january commenced on ,sunday4 ,again we have for the year #c1 #aj - #c #g2 therefore1 ,g being the seventh letter1 is dominical letter for the year #c4 ,now reading from ,g to ,a1 the letter for ,january1 we have ,g ,sunday1 ,a ,monday2 hence ,january commenced on ,monday4 ,on what day of the week did the year #d commence8 ,now we have a number that is divisible by #d1 it being the first leap-year in the era1 so we have #d _/ #d #a2 #d #a #e2 #e _/ #g #j1 remainder #e4 ,then #aj - #e #e2 therefore1 ,e being the #eth letter1 is dominical letter for that part of the year which follows the #bith of ,february1 while ,f1 the letter that follows it1 is dominical letter for ,january and ,february4 ,now reading from ,f to ,a1 the letter for ,january1 we have ,f ,sunday1 ,g ,monday1 ,a ,tuesday2 hence ,january commenced on ,tuesday4 ,now we have disposed of the first four years of the era2 the dominical letters being ,b1 ,a1 ,g1 and ,f1 ,e4 ,hence it is evident1 while one year consists of an even number of weeks and one day1 two years of an even number of weeks and two days1 three years of an even number of weeks and three days1 that every fourth year1 by intercalation1 is made to consist of #cff days2 so that four years consist of an even number of weeks and five days2 for we have 7#d _/ #d7 #d #e1 the dominical letter going back from ,g in the year #c1 to ,f1 for ,january and ,february in the year #d1 and from ,f to ,e for the rest of the year1 causing the following year to commence two days later in the week than the year preceding4 ,the year #a had #ec ,saturdays2 the year #b1 #ec ,sundays2 the year #c1 #ec ,mondays1 and the year #d1 #ec ,tuesdays and #ec ,wednesdays1 causing the year #e to commence on ,thursday1 two days later in the week than the preceding year4 ,now what is true concerning the first four years of the era1 is true concerning all the future years1 and the reason for the divisions1 additions and subtractions in finding the dominical letter is evident4 ,the ,declaration of ,independence was signed ,july #d1 #aggf4 ,on what day of the week did it occur8 ,we have then #aggf _/ #d #ddd2 #aggf #ddd #bbbj2 #bbbj _/ #g #cag1 remainder #a4 ,then #g - #a #f1 therefore ,f and ,g are the dominical letters for #aggf1 ,g for ,january and ,february1 and ,f for the rest of the year4 ,now reading from ,f to ,g1 the letter for ,july1 we have ,f ,sunday1 ,g ,monday2 hence ,july commenced on ,monday1 and the fourth was ,thursday4 ,on what day of the week did ,lee surrender to ,grant1 which occurred on ,april #ith1 #ahfe8 ,we have then #ahfe _/ #d #dff2 #ahfe #dff #bcca2 #bcca _/ #g #ccc1 remainder #j4 ,then #a - #j #a2 therefore1 ,a being the first letter1 is dominical letter for #ahfe4 ,now reading from ,a to ,g1 the letter for ,april1 we have ,a ,sunday1 ,b ,monday1 ,c ,tuesday1 etc4 ,hence ,april commenced on ,saturday1 and the #ith was ,sunday4 ,benjamin ,harrison was inaugurated ,president of the ,united ,states on ,monday1 ,march #d1 #ahhi4 ,on what day of the week will the #dth of ,march fall in #aihi8 ,we have then #aihi _/ #d #dig2 #aihi #dig #bdhf2 #bdhf _/ #g #cee1 remainder #a4 ,then #b - #a #a2 therefore1 ,a being the first letter1 is dominical letter for #aihi4 ,now1 reading from ,a to ,d1 the letter for ,march1 we have ,a ,sunday1 ,b ,monday1 ,c ,tuesday1 and ,d ,wednesday2 hence ,march will commence on ,wednesday1 and the #dth will fall on ,saturday4 ,columbus landed on the island of ,san ,salvador on ,friday1 ,october #ab1 #adib4 ,on what day of the month and on what day of the week will the four hundredth anniversary fall in #ahib8 ,the day of the month on which ,columbus landed is1 of course1 the day to be observed in commemoration of that event4 ,the ,julian calendar1 which was then in use throughout ,europe1 and the very best that had ever been given to the world1 made the year too long by more than eleven minutes4 ,those eleven minutes a year had accumulated1 from the council of ,nice1 in #cbe1 to the discovery of ,america1 in #adib1 to nine days1 so that the civil year was nine days behind the true or solar time2 that is1 when the ,earth1 in her annual revolution1 had arrived at that point of the ecliptic coinciding with the #bast of ,october1 the civil year1 according to the ,julian calendar1 was the #abth4 ,now1 to restore the coincidence1 the nine days must be dropped1 or suppressed1 calling what was erroneously called the #abth of ,october1 the #bast4 ,since the ,julian calendar was corrected by ,gregory1 in #aehb1 we have so intercalated as to retain1 very nearly1 the coincidence of the solar and the civil year4 ,it has already been shown in ,chapter ,,iii1 7q4 v47 that in the ,gregorian calendar1 the cycle which restores the coincidence of the day of the month and the day of the week1 is completed in #djj years2 so that after #djj years1 events will again transpire in the same order1 on the same day of the week4 ,now1 as ,columbus landed on ,friday1 ,october #bast1 #adib1 so ,friday1 ,october #bast1 #ahib1 is the day of the month and also the day of the week to be observed in commemoration of that event4 ,we have then #ahib _/ #d #dgc2 #ahib #dgc #bcfe2 #bcfe _/ #g #ccg1 remainder #f4 ,then #h - #f #b2 therefore1 ,b and ,c are dominical letters for #ahib1 ,c for ,january and ,february1 and ,b for the rest of the year4 ,now1 reading from ,b to ,a1 the letter for ,october1 we have ,b ,sunday1 ,c ,monday1 etc4 ,hence ,october will commence on ,saturday and the #bast will be ,friday4 ,although there was an error of thirteen days in the ,julian calendar when it was reformed by ,gregory1 in #aehb1 there was a correction made of only ten days4 ,there was still an error of three days from the time of ,julius ,caesar to the ,council of ,nice1 which remained uncorrected4 ,gregory restored the vernal equinox to the #bast of ,march1 its date at the meeting of that council1 not to the place it occupied in the time of ,caesar1 namely1 the #bdth of ,march4 ,had he done so it would now fall on the #bdth1 by adopting the ,gregorian rule of intercalation4 ,appendix ,h4 ,if desirable calculations may be made in both ,old and ,new ,styles from the year of our ,lord #cjj4 ,there is no perceptible discrepancy in the calendars1 however1 until the close of the #dth century1 when it amounts to nearly one day1 reckoned in round numbers one day4 ,now in order to make the calculation1 proceed according to rule already given for finding the dominical letter1 and for ,new ,style take the remainders after dividing by seven from the numbers in the following table3 ,from #djj to #ejj ,from #d or #aa #ejj #fjj #e #ab #fjj #gjj #f #ac #gjj #ijj #g #ijj #ajjj #a #h #ajjj #aajj #b #i #aajj #acjj #c #aj #acjj #adjj #d #aa #adjj #aejj #e #ab #aejj #agjj #f #ac ,it will be found by calculation that from the year #djj to #ejj the discrepancy is #a day #ejj #fjj #b #fjj #gjj #c #gjj #ijj #d #ijj #ajjj #e #ajjj #aajj #f #aajj #acjj #g #acjj #adjj #h #adjj #aejj #i #aejj #agjj #aj ,hence the necessity1 in reforming the calendar in #aehb1 of suppressing ten days4 7,see table on #eith page47 ,on what day of the week did ,january commence in #dej8 ,we have then #dej _/ #d #aab2 #dej #aab #efb2 #efb _/ #g #hj1 remainder #b4 ,then #c - #b #a2 therefore1 ,a being the first letter1 is dominical letter for #dej1 ,old ,style1 and ,january commenced on ,sunday4 ,for ,new ,style we have #d - #b #b2 therefore1 ,b being the second letter1 is dominical letter for the year #dej4 ,now reading from ,b to ,a1 the letter for ,january1 we have ,b ,sunday1 ,c ,monday1 ,d ,tuesday1 etc4 ,hence1 ,january commenced on ,saturday4 ,old ,style makes ,sunday the first day2 ,new ,style makes ,saturday the first and ,sunday the second4 ,on what day of the week did ,january commence in the year #abej8 ,we have then #abej _/ #d #cab2 #abej #cab #aefb2 #aefb _/ #g #bbc1 remainder #a4 ,then #c - #a #b2 therefore1 ,b being the second letter1 is dominical letter for the year #abej1 ,old ,style4 ,now1 reading from ,b to ,a1 the letter for ,january1 we have ,b ,sunday1 ,c ,monday1 etc4 ,hence ,january commenced on ,saturday4 ,b is also dominical letter1 ,new ,style2 for we take the remainder after dividing by #g1 from the same number4 ,as both ,old and ,new ,styles have the same dominical letter1 so both make ,january to commence on the same day of the week2 but ,old ,style1 during this century1 is seven days behind the true time1 so that when it is the first day of ,january by the ,old1 it is the eighth by the ,new4 ,vernal equinox in the time of ,numa1 about #gjj ,b4 ,c4 ,it is here seen by the errors of the ,julian ,calendar the ,vernal ,equinox is made to occur three days earlier every #djj years1 so that in #aehb it fell on the #aath instead of the #bast of ,march4 #ah #ag #af #ae #ad #ac #ab #aa ,by suppressing #aj d ,hou ,hou ,by the ,gregorian rule of intercalation the coincidence of years4 ,march #bd1 #df ,b4 ,c4 #bc #a ,a4 ,d4 ,restored #bb #ajj by #ba #cjj ,julius #bj #djj ,caesar1 #ai ,vernal #ejj equinox #df ,b4 ,c41 at the #fjj ,council to the of #hjj ,nice1 place it #cbe #ijj ,a4 ,d4 occupied #ajjj in the #abjj time of #acjj ,numa4 #adjj ays1 ,coincidence #j ,restored in #afjj rs behind time1 #ah #f in advance4 #agjj #ab #ab #ahjj #f #ah #aijj ,coincidence #j ,restored4 #bjjj rs behind time1 #ah #f in advance4 #bajj #ab #ab #bbjj #f #ah #bcjj ,coincidence #j ,restored4 #bdjj the solar and civil year is restored very nearly every #djj ,appendix ,i4 ,,chapter ,,vi4 ,a ,,simple ,,method ,,for ,,finding ,,the ,,day ,,of ,,the ,,week ,,of ,,events ,,which ,,occur ,,quadrennially4 ,the inaugural of the ,presidents4 ,the day of the week on which they have occurred1 and on which they will occur for the next one hundred years3 ,april #cjth1 #aghi1 ,thursday1 ,george ,washington4 ,march #dth1 #agic1 ,monday1 #agig1 ,saturday1 ,john ,adams #ahja1 ,wednesday1 ,thomas ,jefferson4 #ahje1 ,monday1 #ahji1 ,saturday1 ,james ,madison4 #ahac1 ,thursday1 #ahag1 ,tuesday1 ,james ,monroe4 #ahba1 ,sunday1 #ahbe1 ,friday1 ,john ,q4 ,adams4 #ahbi1 ,wednesday1 ,andrew ,jackson4 #ahcc1 ,monday1 #ahcg1 ,saturday1 ,martin ,van ,buren4 #ahda1 ,thursday1 ,wm4 ,h4 ,harrison4 #ahde1 ,tuesday1 ,james ,k4 ,polk4 #ahdi1 ,sunday1 ,zachary ,taylor4 #ahec1 ,friday1 ,franklin ,pierce4 #aheg1 ,wednesday1 ,james ,buchanan4 #ahfa1 ,monday1 ,abraham ,lincoln4 #ahfe1 ,saturday1 #ahfi1 ,thursday1 ,ulysses ,s4 ,grant4 #ahgc1 ,tuesday1 #ahgg1 ,sunday1 ,rutherford ,b4 ,hays4 #ahha1 ,friday1 ,james ,a4 ,garfield4 #ahhe1 ,wednesday1 ,grover ,cleveland4 #ahhi1 ,monday1 ,benjamin ,harrison4 #ahic1 ,saturday1 ,grover ,cleveland4 #ahig1 ,thursday1 #aija1 ,monday1 #aije1 ,saturday1 #aiji1 ,thursday1 #aiac1 ,tuesday1 #aiag1 ,sunday1 #aiba1 ,friday1 #aibe1 ,wednesday1 #aibi1 ,monday1 #aicc1 ,saturday1 #aicg1 ,thursday1 #aida1 ,tuesday1 #aide1 ,sunday1 #aidi1 ,friday1 #aiec1 ,wednesday1 #aieg1 ,monday1 #aifa1 ,saturday1 #aife1 ,thursday1 #aifi1 ,tuesday1 #aigc1 ,sunday1 #aigg1 ,friday1 #aiha1 ,wednesday1 #aihe1 ,monday1 #aihi1 ,saturday1 #aiic1 ,thursday4 ,any one understanding what has been said in a preceding chapter concerning the dominical letter1 can very easily make out such a table without going through the process of making calculations for every year4 ,as every succeeding year1 or any day of the year1 commences one day later in the week than the year preceding1 and two days later in leap-year1 which makes five days every four years1 and as the ,presidential term is four years1 so every inaugural occurs five days later in the week than it did in the preceding term4 ,now1 as counting forward five days is equivalent to counting back two1 it will be much more convenient to count back two days every term4 ,there is one exception1 however1 to this rule2 the year which completes the century is reckoned as a common year 7that is1 three centuries out of four71 consequently we count forward only four days or back three4 ,commencing1 then1 with the second inaugural of ,washington1 which occurred on ,monday1 ,march #d1 #agic1 and counting back two days to ,saturday in #agig1 three days to ,wednesday in #ahja and two days to #ahje1 and so on two days every term till #aija1 when1 for reasons already given1 we count back three days again for one term only1 after which it will be two days for the next two hundred years2 hence anyone can make his calculations as he writes1 and as fast as he can write4 ,see table on #fast page4 ,,some ,,peculiarities ,,concerning ,,events ,,which ,,fall ,,on ,,the ,,twenty-,,ninth ,,day ,,of ,,february4 ,the civil year and the day must be regarded as commencing at the same instant4 ,we cannot well reckon a fraction of a day1 giving to ,february #bh days and #f hours1 making the following month to commence six hours later every year2 if so1 then ,march1 for example1 in #ahhh would commence at #ab m4 night4 #ahhi #f a4 m4 #ahij #ab m4 #ahia #f p4 m4 #ahib #ab m4 night1 again1 and so on4 ,instead of doing so1 we wait until the fraction accumulates to a whole day2 then give to ,february #bi days1 and the year #cff4 ,therefore1 events which fall on the #bith of ,february cannot be celebrated annually1 but only quadrennially2 and at the close of those centuries in which the intercalations are suppressed only octennially4 ,for example3 ,from the year #afif to #agjd1 #agif to #ahjd1 and #ahif to #aijd1 there is no #bith day of ,february2 consequently no day of the month in the civil year on which an event falling on the #bith of ,february could be celebrated4 ,therefore1 a person born on the #bith of ,february1 #ahif1 could celebrate no birthday till #aijd1 a period of eight years4 ,in every common year ,february has #bh days1 each day of the week being contained in the number of days in the month four times2 but in leap-year1 when ,february has #bi days1 the day which begins and ends the month is contained five times4 ,let us suppose that in a certain year1 when ,february has #bi days1 the month comes in on ,friday2 it also must necessarily end on ,friday4 ,after four years it will commence on ,wednesday1 and end on ,wednesday1 and so on1 going back two days in the week every four years1 until after #bh years we come back to ,friday again4 ,this1 as has already been explained1 is the dominical or solar cycle4 ,for example3 ,february in ,the year #d has five ,fridays4 #h ,wednesdays4 #ab ,mondays4 #af ,saturdays4 #bj ,thursdays4 #bd ,tuesdays4 #bh ,sundays4 #cb ,fridays4 ,so that after #bh years we come back to ,friday again2 and so on every #bh years1 until change of style in #aehb1 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 centuries4 ,for example--#agjj1 #ahjj and #aijj1 after which the cycle of #bh years will be continued until #bajj1 and so on4 ,the cycle being interrupted by the ,gregorian rule of intercalation1 causes all events which occur between #bh and #ab years of the close of the centuries to fall on the same day of the week again in #dj years2 and those events that fall within #ab years of the close of these centuries1 to fall on the same day of the week again in #ab years2 after which the cycle of #bh years will be continued during the century4 ,see following table3 #ahjd ,february has five ,wednesdays4 #ahjh ,mondays4 #ahab ,saturdays4 #ahaf ,thursdays4 #ahbj ,tuesdays4 #ahbd ,sundays4 #ahbh ,fridays4 #ahcb ,wednesdays4 #ahcf ,mondays4 #ahdj ,saturdays4 #ahdd ,thursdays4 #ahdh ,tuesdays4 #aheb ,sundays4 #ahef ,fridays4 #ahfj ,wednesdays4 #ahfd ,mondays4 #ahfh ,saturdays4 #ahgb ,thursdays4 #ahgf ,tuesdays4 #ahhj ,sundays4 #ahhd ,fridays4 #ahhh ,wednesdays4 #ahib ,mondays4 #ahif ,saturdays4 #aijj #aijd ,mondays4 #aijh ,saturdays4 #aiab ,thursdays4 #aiaf ,tuesdays4 #aibj ,sundays4 #aibd ,fridays4 #aibh ,wednesdays4 ,it will be seen from this table that in #ahjd ,february had five ,wednesdays2 and then again in #ahcb1 #ahfj and #ahhh2 then suppressing the intercalation in the year #aijj suppresses the #bith of ,february2 so opposite #aijj in the table is blank1 and the #bith of ,february does not occur again till #aijd1 and the five ,wednesdays do not occur again till #aibh--that is1 #dj years from #ahhh1 when it last occurred4 ,again taking the five ,mondays which occurred first in this century1 in #ahjh1 and then again in #ahcf1 #ahfd and in #ahib1 you will see1 for reasons already given1 that it will occur again in #ab years1 that is1 in #aijd2 and so on with all the days of the week1 when it will be seen what is peculiar concerning the #bith of ,february4 ,but attention is particularly called to the five ,thursdays1 which occur first in this century #ahaf1 and then again in #ahdd and #ahgb1 the last date being within #bh years of the close of the century4 ,suppressing the intercalation suppresses the #bith of ,february2 consequently the five ,thursdays do not occur again till #aiab1 that is #dj years from the preceding date1 after which the cycle will be continued for two hundred years4 ,hence it may be seen that the dominical or solar cycle of #bh years is so interrupted at the close of these centuries by the suppression of the leap-year1 that certain events do not occur again on the same day of the week under #dj years1 while others are repeated again on the same day of the week in #ab years2 also the number of years in the cycle1 that is #bh #ab #dj4 ,and again the change of style in #aehb1 causes all events which occur between #bh and #h years of that change1 to fall again on the same day of the week in #cf years1 and all that occur within #h years of that change to be repeated again on the same day of the week in #h years1 after which the cycle of #bh years is continued for #ajj years2 also that the number of years in the cycle1 that is1 #bh #h #cf4 ,,chapter ,,vii4 ,,rules ,,for ,,finding ,,the ,,day ,,of ,,the ,,week ,,of ,,events ,,that ,,transpired ,,prior ,,to ,,the ,,christian ,,era4 ,first1 it should be understood that the year #d is the first leap year in our era1 reckoning from the year #a ,b4 ,c41 which must necessarily be leap year2 so that the odd numbers #a1 #e1 #i1 #ac1 etc41 are leap years4 ,hence every year that is divisible by four and one remainder1 is leap year2 if no remainder1 it is the first year after leap-year2 if #c1 the second2 if #b1 the third1 thus3 #de _/ #d #aa1 remainder1 #a1 #dd _/ #d #aa1 no remainder1 #dc _/ #d #aj1 remainder1 #c1 #db _/ #d #aj1 remainder1 #b1 #da _/ #d #aj1 remainder1 #a1 and so on1 every year being divided by four and #a remainder is leap-year of #cff days4 ,it should be borne in mind that the same calendar was in use without any correction from the days of ,julius ,caesar #df ,b4 ,c4 to ,pope ,gregory ,,xiii in #aehb2 consequently the method of finding the dominical letter is1 in some respects1 similar to the one already given on the #ddth page4 ,but in some respects the one is the reverse of the other1 for we reckon backward and forward from a fixed point--the era2 that is the numbers increase each way from the era4 ,also the dominical letters occur in the natural order of the letters in reckoning backward1 but exactly the reverse in reckoning forward4 ,see table on the #gc;d page1 where the dominical letter is placed opposite each year from #de ,b4 ,c4 to #de ,a4 ,d4 ,now we use the same number #c1 because ,c1 the third letter is dominical letter for the year #a ,b4 ,c41 the point from which we reckon4 ,but instead of taking the remainder1 after dividing by #g1 from #c or #aj1 to find the number of the letter1 as in ,part ,second1 ,chapter ,,iv1 7q4 v47 we add the remainder to #c2 hence we have the following3 ,,rule4 ,divide the number of the given year by #d1 neglecting the remainders1 and add the quotient to the given number1 divide this amount by #g1 and add the remainder to #c1 and that amount will give the number of the letter1 calling ,a1 #a2 ,b1 #b2 ,c1 #c1 etc42 except the first year after leap-year1 7which is the year exactly divisible by #d71 the number of the letter is one less than is indicated by the rule4 ,this rule gives the dominical letter for ,january and ,february only1 in leap-year1 while the letter that precedes it1 is the letter for the rest of the year4 ,if the amount be greater than seven1 we should reckon from ,a to ,a or ,b again4 ,it has already been stated in ,part ,first1 ,chapter ,,iii1 7q4 v471 that a change was made by ,augustus ,caesar about #h ,b4 ,c41 in the number of days in the month2 and1 as this change effects the day of the week on which certain events fall1 it becomes necessary that they should be presented as they were arranged by ,julius ,caesar1 and as corrected by ,augustus4 ,julius ,caesar gave to ,february #bi days in common years1 and in leap-year #cj4 ,this arrangement was the very best that could possibly be made1 but1 as has already been shown1 it was interrupted to gratify the vanity of ,augustus4 ,the left hand column in the table on the #gb;d page represents the number of days in each month from the days of ,julius ,caesar to ,augustus1 a period of #cg years4 ,the right hand column represents the number of days in the months as they now are1 and have been since the change was made by ,augustus1 #h ,b4 ,c4 ,consequently the rule for finding the day of the week on which events have fallen for the #cg years prior to the last mentioned date1 is not perfectly exact1 and needs a little explanation here4 ,the rule itself is given1 and fully explained in ,part ,second1 ,chapter ,v1 7q4 v47 but cannot be applied to the #cg years without some correction4 ,in all the months marked with a star1 events fall one day later in the week than that which is indicated by the rule4 ,this should be borne in mind1 and make the event one day later in the week than that which is found by the rule4 ,for example1 ,julius ,caesar was assassinated on the #aeth of ,march1 #dd ,b4 ,c4 ,by giving to ,february #bh days the first day of ,march would fall on ,wednesday1 and1 of course1 the #aeth would be ,wednesday4 ,but ,caesar gave to ,february #bi days1 so that the first day of ,march fell on ,thursday1 and the #aeth was ,thursday4 ,hence1 every event from ,march to ,september will fall one day later in the week than the rule indicates4 ,but the rule is applicable to ,september1 for it will make no difference whether there are #bi days in ,february or #ca in ,august1 there are the same number of days from ,february to ,september4 ,but the #ca days in ,september will cause all events to fall one day later in the week during the month of ,october1 but they coincide again during the month of ,november4 ,the order is interrupted again in ,december by giving #ca days to ,november4 ,see following table3 ,as ,arranged by ,julius ,as ,corrected by ,augustus1 ,caesar4 #h ,b4 ,c4 ,january1 #ca ,january1 #ca ,february1 #bi ,february1 #bh ,march1 #ca99 ,march1 #ca ,april1 #cj99 ,april1 #cj ,may1 #ca99 ,may1 #ca ,june1 #cj99 ,june1 #cj ,july1 #ca99 ,july1 #ca ,august1 #cj99 ,august1 #ca ,september1 #ca ,september1 #cj ,october1 #cj99 ,october1 #ca ,november1 #ca ,november1 #cj ,december1 #cj99 ,december1 #ca ---------------------------------------- ---------------- ,dominical,year4,dominical,year4,dominic al,year4,dominical,year4 ,letter4 ,letter4 ,letter4 ,letter4 ---------------------------------------- ---------------- ,b4 ,c4 ,b4 ,c4 ,a4 ,d4 ,a4 ,d4 cb #de b #bb b #a c #bc a #dd ag #ba a #b ba #bd g #dc f #bj g #c g #be f #db e #ai fe #d f #bf ed #da d #ah d #e e #bg c #dj cb #ag c #f dc #bh b #ci a #af b #g b #bi a #ch g #ae ag #h a #cj gf #cg f #ad f #i g #ca e #cf ed #ac e #aj fe #cb d #ce c #ab d #aa d #cc c #cd b #aa cb #ab c #cd ba #cc a #aj a #ac b #ce g #cb gf #i g #ad ag #cf f #ca e #h f #ae f #cg e #cj d #g ed #af e #ch dc #bi c #f c #ag d #ci b #bh ba #e b #ah cb #dj a #bg g #d a #ai a #da g #bf f #c gf #bj g #db fe #be e #b e #ba f #dc d #bd dc #a d #bb ed #dd c #bc c #de ---------------------------------------- ---------------- ,,part ,,third4 ,,cycles--,,julian ,,period--,,easter4 ,,hebrew ,,calendar4 ,,chapter ,i4 ,,the ,,solar ,,cycle4 ,cycle1 7,latin ,cyclus1 ring or circle74 ,the revolution of a certain period of time which finishes and re-commences perpetually4 ,cycles were invented for the purpose of chronology1 and for marking the intervals in which two or more periods of unequal length are each completed a certain number of times1 so that both begin exactly in the same circumstance as at first4 ,cycles used in chronology are three3 ,the solar cycle1 the lunar cycle1 and the cycle of indiction4 ,the solar cycle is a period of time after which the same days of the year recur on the same days of the week4 ,if every year contained #cfe days1 then every year would commence one day later in the week than the year preceding1 and the cycle would be completed in seven years4 ,for if the first day of ,january1 in any given year1 fall on ,sunday1 then the following year on ,monday1 the third on ,tuesday1 and so on to ,sunday again in seven years4 ,but this order is interrupted in the ,julian calendar every four years by giving to ,february #bi days1 and consequently the year #cff4 ,now the number of years in the intercalary period being four and the days of the week being seven1 their product is #d x #g #bh2 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 week4 ,this period is called the solar cycle or the cycle of the sun1 the origin of which is unknown2 but is supposed to have been invented about the time of the ,council of ,nice1 in the year of our ,lord #cbe2 but the first year of the cycle is placed by chronologists nine years before the commencement of the ,christian era4 ,hence the year of the cycle corresponding to any given year in the ,julian calendar is found by the following rule3 ,add nine to the date and divide the sum by twenty-eight2 the quotient is the number of cycles elapsed1 and the remainder is the year of the cycle4 ,should there be no remainder1 the proposed year is the twenty-eighth1 or last of the cycle4 ,thus1 for the year #ahib1 we have 7#ahib #i7 _/ #bh #fg1 remainder #be4 ,therefore1 #fg is the number of cycles1 and #be the number in the cycle4 ,,chapter ,,ii4 ,,the ,,lunar ,,cycle4 ,the ,lunar cycle1 or the cycle of the moon1 is a period of nineteen years1 after which the new and full moons fall on the same days of the year as they did nineteen years before4 ,this cycle was invented by ,meton1 a celebrated astronomer of ,athens1 and may be regarded as the masterpiece of ancient astronomy4 ,in nineteen solar years there are #bce lunations1 a number which1 on being divided by nineteen1 gives twelve lunations1 with seven of a remainder1 to be distributed among the years of the period4 ,the period of ,meton1 therefore1 consisted of twelve years containing twelve months each1 and seven years containing thirteen mouths each1 and these last formed the third1 fifth1 eighth1 eleventh1 thirteenth1 sixteenth1 and nineteenth years of the cycle4 ,as it had now been discovered that the exact length of the lunation is a little more than twenty-nine and a half days1 it became necessary to abandon the alternate succession of full and deficient months2 and1 in order to preserve a more accurate correspondence between the civil month and the lunation1 ,meton divided the cycle into #abe full months of #cj days1 and #aaj deficient months of #bi days each4 ,the number of days in the period was1 therefore1 #fidj2 for 7#abe x #cj7 7#aaj x #bi7 #fidj4 ,in order to distribute the deficient months through the period in the most equable manner1 the whole period may be regarded as consisting of #bce full months of thirty days1 or #gjej days1 from which #aaj days are to be deducted2 for 7#bce x #cj7 #gjej2 #gjej - #aaj #fidj1 as before4 ,this gives one day to be suppressed in sixty-four1 so that if we suppose the months to contain each thirty days1 and then omit every sixty-fourth day in reckoning from the beginning of the period1 those months in which the omission takes place will1 of course1 be the deficient months4 ,the number of days in the period being known1 it is easy to ascertain its accuracy both in respect of the solar and lunar motions4 ,the exact length of nineteen solar years is 7#cfe;d1 #e;h1 #dhm1 #di4fbs47 x #ai #fici;d1 #ad;h1 #bgm1 #db4ghs42 hence1 the period1 which is exactly #fidj days1 exceeds nineteen annual revolutions of the earth by a little more than nine and a half hours4 ,on the other hand1 the exact time of the synodic revolution of the moon is #bi;d1 #ab;h1 #ddm1 #b4hgs42 #bce lunations1 therefore1 contain #bce x 7#bi;d1 #ab;h1 #ddm1 #b4hgs47 7#fici;d1 #af;h1 #cam1 #ad4des471 so that the period exceeds #bce lunations by nearly seven and a half hours4 ,at the end of four cycles1 or seventy-six years1 the accumulation of the seven and a half hours of difference between the cycle and #bce lunations amounts to thirty hours1 or one whole day and six hours4 ,calippus1 therefore1 in order to make a correction of the ,metonic cycle1 proposed to quadruple the period of ,meton1 and deduct one day at the end of that time by changing one of the full months into a deficient month4 ,the period of ,calippus1 therefore1 consisted of three ,metonic cycles of #fidj days each1 and a period of #fici days2 and its error in respect to the moon1 consequently1 amounted to only six hours1 or to one day in #cjd years4 ,this period exceeds seventy-six true solar years by #ad;h1 #im1 #h4hhs41 but coincides exactly with seventy-six ,julian years2 and in the time of ,calippus the length of the solar year was almost universally supposed to be exactly #cfe-a_/d days4 ,,chapter ,,iii4 ,,the ,,lunar ,,cycle ,,and ,,golden ,,number4 ,in connecting the lunar month with the solar year1 the framers of the ecclesiastical calendar adopted the period of ,meton1 or lunar cycle1 which they supposed to be exact4 ,a different arrangement has1 however1 been followed with respect to the distribution of the months4 ,the lunations are supposed to consist of twenty-nine and thirty days alternately1 or the lunar year of #ced days2 and in order to make up nineteen solar years1 six embolismic or intercalary months1 of thirty days each1 are introduced in the course of the cycle1 and one of twenty-nine days is added at the end4 ,this gives 7#ai x #ced7 7#f x #cj7 #bi #fice days1 to be distributed among #bce lunar months4 ,but every leap-year one day must be added to the lunar month in which the #bith of ,february is included4 ,now if leap-year happened on the first1 second or third year of the period1 there will be five leap-years in the period1 but only four when the first leap-year falls on the fourth4 ,in the former case the number of days in the period becomes #fidj1 and in the latter #fici4 ,the mean length of the cycle is1 therefore1 #fici-c_/d days1 agreeing exactly with nineteen ,julian years4 ,by means of the lunar cycle the new moons of the calendar were indicated before the reformation in #aehb4 ,as the cycle restores these phenomena to the same days of the civil month1 they will fall on the same days in any two years which occupy the same place in the cycle2 consequently a table of the moon's phases for nineteen years will serve for any year whatever when we know its number in the cycle4 ,the number of the year in the cycle is called the ,golden ,number2 either because it was so termed by the ,greeks1 who1 on account of its utility1 ordered it to be inscribed in letters of gold in their temples1 or more probably because it was usual to distinguish it by red letters in the calendar4 ,the ,golden ,numbers were introduced into the calendar about the year #ecj1 but disposed as they would have been if they had been inserted at the time of the ,council of ,nice4 ,the cycle is supposed to commence with the year in which the new moon falls on the first day of ,january1 which took place the year preceding the commencement of our era4 ,hence to find the ,golden ,number for any year1 we have the following rule3 ,add one to the date1 divide the sum by nineteen2 the quotient is the number of cycles elapsed1 and the remainder is the ,golden ,number4 ,should there be no remainder1 the proposed year is1 of course1 the last or nineteenth of the cycle4 ,thus1 for the year #ahib1 we have 7#ahib #a7 _/ #ai #ii1 remainder #ab2 therefore1 #ii is the number of cycles1 and #ab the number in the cycle1 or the ,golden number4 ,it ought to be remarked that the new moons determined in this manner1 may differ from the astronomical new moons sometimes as much as two days4 ,the reason is1 that the sum of the solar and lunar inequalities which are compensated in the whole period1 may amount in certain cases to #aj degrees and thereby cause the new moon to arrive on the second day before or after its mean time4 ,the cycle of the sun brings back the days of the month to the same day of the week2 the cycle of the moon restores the new moons to the same day of the month2 therefore1 #bh x #ai #ecb years1 includes all the variations in respect of the new moons and the dominical letter1 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 week4 ,this is called the ,dionysian or ,great ,paschal ,period1 from its having been employed by ,dionysius ,exiguus in determining ,easter ,sunday4 ,,chapter ,,iv4 ,,cycle ,,of ,,indiction1 ,,and ,,the ,,julian ,,period4 ,the cycle of ,indiction or ,roman ,indiction1 is a period of fifteen years2 not astronomical like the two former1 but entirely arbitrary4 ,its origin and the purpose for which it was established are alike uncertain2 but it is conjectured that it was introduced by ,constantine the ,great1 about the year #cab of the common era1 and had reference to certain judicial acts that took place under the ,greek emperors at stated intervals of fifteen years4 ,in chronological reckoning1 it is considered as having commenced on the first day of ,january of the year #cac4 ,by extending it backward1 it will be found that the cycle commenced three years before the beginning of our era4 ,in order1 therefore1 to find the number of any year in the cycle of indiction1 we have this rule3 ,add three to the date1 divide the number by fifteen2 and the remainder is the year of the indiction4 ,should there be no remainder1 the proposed year is the fifteenth or last of the cycle4 ,thus1 for the year #ahib1 we have 7#ahib #c7 _/ #ae #abf1 remainder #e4 ,therefore1 #e is the number in the cycle4 ,the ,julian period1 proposed by the celebrated ,joseph ,scaliger1 as an universal measure of chronology1 is a period of #gihj years1 and is formed by the continual multiplication of the three numbers1 #bh1 #ai and #ae2 that is1 of the cycle of the sun1 the cycle of the moon1 and the cycle of indiction4 ,thus1 7#bh x #ai x #ae7 #gihj4 ,in the course of this long period no two years can be expressed by the same numbers in all the three cycles4 ,the first year of the ,christian era had #aj for its number in the cycle of the sun1 #b in the cycle of the moon1 and #d in the cycle of the indiction4 ,now1 it is found by actual calculation1 that the only number less than #gihj which1 on being divided successively by #bh1 #ai1 and #ae1 leaves the respective remainders #aj1 #b and #d1 is #dgad4 ,hence1 the first year of the ,christian era corresponded with the year #dgad of the ,julian period1 which period coincides with the #gajth before the common mundane era #djjd ,b4 ,c42 for #djjd #gaj #dgad4 ,hence1 also1 the year of our era corresponding to any other year of the period1 or vice versa1 is found by the following rule3 ,when the given year is anterior to the commencement of the era1 subtract the number of the year of the ,julian period from #dgad1 and the remainder is the year before ,christ2 or1 subtract the year before ,christ from #dgad1 and the remainder is the corresponding year in the ,julian period4 ,thus1 ,rome was founded in the year #cifj of the ,julian period4 ,what was the year before ,christ8 ,we have then #dgad - #cifj #ged4 ,julius ,caesar was assassinated #dd years before ,christ1 what was the corresponding year of the ,julian period8 ,we have then1 #dgad - #dd #dfgj4 ,when the given year is after ,christ1 subtract #dgac from the year of the period1 and the remainder is the year of the era2 or add #dgac to the year of the era1 and the sum is the corresponding year in the ,julian period4 ,thus1 the ,council of ,nice was convened in the year #ejch of the ,julian period1 what was the year of our era8 ,we have then1 #ejch - #dgac #cbe4 ,what year of the ,julian period corresponds with the present year1 #ahib8 ,we have then1 #dgac #ahib #ffje4 ,,chapter ,v4 ,,easter4 ,easter 7,germ4 ,ostern1 ,old ,saxon ,oster1 from ,osten1 signifying rising74 ,the ,english name is probably derived from ,ostera or ,eostre1 the ,teutonic goddess of spring1 whose festival occurred about the same time of the year as the celebration of ,easter4 ,the ,hebrew-,greek word ,pascha has passed into the name given to this feast by most ,christian nations4 ,this festival is held in commemoration of our ,lord's resurrection4 ,the ,jews celebrated their passover1 in conformity with the directions given them by ,moses1 on the #adth day of the month ,nisan1 being the lunar month of which the #adth day either falls on or next follows the day of the vernal equinox4 ,in the year of our ,lord's crucifixion this fell on a ,friday2 the resurrection1 therefore1 took place on the first day of the week1 which from thence is denominated the ,lord's ,day4 ,the primitive ,christians1 in celebrating this anniversary1 fell into two different systems4 ,the ,western churches observed the nearest ,sunday to the full moon of ,nisan1 taking no account of the day on which the passover would be celebrated4 ,the ,asiatics1 on the other hand1 following the ,jewish calendar1 adopted the #adth of ,nisan upon which to commemorate the crucifixion1 and observed the festival of ,easter on the third day following1 upon whatever day of the week that might fall1 hence they obtained the name of ,quartodecimans1 7from quarto1 four1 and decem1 ten17 the fourteenth day men4 ,the former appealed to the authority of ,st4 ,peter and ,st4 ,paul1 the latter to that of ,st4 ,john4 ,the dispute which took place upon this point in the second and third centuries of our era is remarkable1 as connected with perhaps the first event which can be brought to bear upon the question of the primacy of the ,roman bishop2 and it is the more interesting as both parties are accustomed to claim it as a testimony in favor of their own views4 ,victor1 bishop of ,rome1 wrote an imperious letter to the ,asiatic bishops1 requiring their conformity to the ,western rule2 which was answered by ,polycrates1 bishop of ,ephesus1 in the name of the rest1 expressing their resolution to maintain the custom handed down to them by their ancestors4 ,the ,roman bishop thereupon broke off communion with them2 but he was rebuked by ,irenaeus1 of ,lyons1 and it was agreed by his mediation that each party should retain its customs4 ,such continued to be the practice till the time of ,constantine1 when the ,council of ,nice determined the matter by the following ,canons3 a--,easter must be celebrated on a ,sunday4 b--,this ,sunday must follow the #adth day of the paschal moon1 so that if the #adth day of the paschal moon fall on a ,sunday1 then ,easter must be celebrated on the ,sunday following4 c--,the paschal moon is that moon of which the #adth day either falls on or next follows the day of the vernal equinox4 d--,the #bast of ,march is to be accounted the day of the vernal equinox4 7,appendix ,l47 ,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 epact1 and not by the true full moon1 which in general1 occurs one or two days earlier4 ,from these conditions it follows1 that if the paschal full moon fall on ,saturday1 the #bast of ,march1 then ,easter will happen on the #bb;d1 its earliest possible date4 ,for if the full moon arrive on the #bjth1 it would not be the paschal full moon1 which cannot happen before the #bast1 consequently the following moon is the paschal full moon1 which happens #cj days after the #bjth of ,march1 which is the #aith of ,april4 ,now1 if in this case the #aith of ,april is ,sunday1 then ,easter must be celebrated the following ,sunday1 or the #bfth of ,april4 ,hence1 ,easter ,sunday cannot happen earlier than the #bb;d of ,march1 or later than the #bfth of ,april4 ,the observance of these rules renders it necessary to reconcile three periods which have no common measure1 namely1 the week1 the lunar month1 and the solar year2 and as this can be done only approximately1 and within certain limits1 the determination of ,easter is an affair of considerable nicety and complication4 ,it has already been shown that the lunar cycle contained #fici days and #ah hours2 also1 that the exact time of #bce lunations is #fici;d1 #af;h1 #cam1 #ad4des4 ,the difference1 which is #a;h1 #bhm1 #de4ees41 amounts to a day in #cjh years1 so that at the end of this time the new moons occur one day earlier than they are indicated by the ,golden ,numbers4 ,during the #abeg years that elapsed between the ,council of ,nice and the reformation1 the error had accumulated to four days1 so that the new moons1 which were marked in the calendar as happening1 for example1 on the #eth of the month1 actually fell on the #ast4 ,it would have been easy to correct this error by placing the ,golden ,numbers four lines higher in the new calendar1 but the suppression of ten days had already rendered it necessary to place them ten lines lower1 and to carry those which belonged1 for example1 to the #eth and #fth of the month1 to the #aeth and #afth4 ,but supposing this correction to have been made1 it would have become necessary1 at the end of #cjh years1 to place them one line higher1 in consequence of the accumulation of the error of the cycle to a whole day4 ,on the other hand1 as the ,golden ,numbers were only adapted to the ,julian calendar1 every omission of the centenary intercalation would require them to be placed one line lower1 opposite the #fth1 for example1 instead of the #eth of the month1 so that1 generally speaking1 the places of the ,golden ,numbers would have to be changed every century4 ,on this account ,lilius thought fit to reject the ,golden ,numbers from the ,calendar1 and supply their places by another set of numbers called ,epacts1 the use of which we shall now proceed to explain4 ,epact1 7,greek epaktos1 added or introduced74 ,the excess of the solar year beyond the lunar1 employed in the calendar to signify the moon's age at the beginning of the year4 ,the common solar year consisted of #cfe days and the lunar year only #ced days1 the difference is eleven2 whence1 if a new moon fall on the first day of ,january in any year1 the moon will be eleven days old on the first day of the following year1 and twenty-two days old on the first of the third year4 ,the numbers eleven and twenty-two are therefore the epacts of those years respectively4 ,another addition of eleven gives thirty-three for the epact of the fourth year2 but in consequence of the insertion of the intercalary month in each third year of the lunar cycle1 this epact is reduced to three2 for #cc - #cj #c4 ,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 year1 and rejecting thirty as often as the sum exceeds or equals that number4 ,in order to show how the epacts are connected with the ,golden ,numbers1 let a cypher represent the new moon on the first day of ,january in any year1 then the epacts and ,golden ,numbers for a whole lunar cycle would be represented thus3 #a #b #c #d #e #f #g #h #i #j #aa #bb #c #ad #be #f #ag #bh #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #i #bj #a #ab #bc #d #ae #bf #g #ah ,but the order is interrupted at the end of the cycle2 for the epact of the following year found in the same manner would be #ah #aa #bi1 whereas it ought to be a cipher to correspond with the moon's age and the ,golden ,number #a4 ,the reason for this is1 that the intercalary month1 inserted at the end of the cycle1 contains only twenty-nine days instead of thirty2 whence1 after #aa has been added to the epact of the year corresponding to the ,golden ,number #ai1 we must reject twenty-nine instead of thirty1 in order to have the epact of the succeeding year2 or1 which comes to the same thing1 we must add twelve to the epact of the last year of the cycle1 and then reject thirty as before4 ,thus1 #ah #ab #cj2 #cj - #cj #j2 the cipher corresponding with the ,golden ,number #a4 ,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 exact2 but as neither of these suppositions is true1 two equations or corrections must be applied1 one depending on the error of the ,julian year1 which is called the solar equation2 the other on the errors of the lunar cycle1 which is called the lunar equation4 ,the solar equation occurs three times in #djj years1 namely1 in every secular year which is not a leap-year2 for in this case the omission of the intercalary day causes the new moons to arrive one day later in all the following months1 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 made1 and the epacts must accordingly be all diminished by unity4 ,thus1 the epacts #aa1 #bb1 #c1 #ad1 etc41 become #aj1 #ba1 #b1 #ac1 etc4 ,on the other hand1 when the time by which the new moons anticipate the lunar cycle amounts to a whole day1 which1 as we have seen1 it does in #cjh years1 the new moons will arrive one day earlier and the epacts must1 consequently1 be increased by unity4 ,thus1 the epacts #aa1 #bb1 #c1 #ad1 etc41 in consequence of the lunar equation1 becomes #ab1 #bc1 #d1 #ae1 etc4 ,in order to preserve the uniformity of the calendar1 the epacts are changed only at the commencement of the century2 the correction of the error of the lunar cycle is therefore made at the end of #cjj years4 ,in the ,gregorian calendar this error is assumed to amount to a day in #cab-a_/b years1 or eight days in #bejj years1 an assumption which requires the line of epacts to be changed seven times successively at the end of each period of #cjj years1 and once at the end of #djj years2 and from the manner in which the epacts were disposed at the reformation1 it was found most correct to suppose one of the periods of #bejj years to terminate with the year #ahjj4 ,the years in which the solar equation occurs1 counting from the reformation1 are #agjj1 #ahjj1 #aijj1 #bajj1 #bbjj1 #bcjj1 #bejj1 etc4 ,those in which the lunar equation occurs are #ahjj1 #bajj1 #bdjj1 #bgjj1 #cjjj1 #ccjj1 #cfjj1 #cijj1 after which #dcjj1 #dfjj1 and so on4 ,when the solar equation occurs1 the epacts are diminished by unity2 when the lunar equation occurs1 the epacts are augmented by unity2 and when both equations occur together1 as in #ahjj1 #bajj1 #bgjj1 etc41 they compensate each other1 and the epacts are not changed4 ,,chapter ,,vi4 ,a ,,new ,,and ,,easy ,,method ,,of ,,fixing ,,the ,,date ,,of ,,easter4 ,in determining the date of ,easter1 we make use of the numbers called epacts2 and1 as these numbers have already been explained in the preceding chapter1 7q4 v47 it will be necessary to give them only a brief notice here4 ,epact1 as has already been defined1 is the excess of the solar year beyond the lunar1 employed in the calendar to signify the moon's age at the beginning of the year2 that is1 if a new moon fall on the first day of ,january in any year1 it will be eleven days old on the first day of the following year1 and twenty-two days old on the first day of the third year1 and so on4 ,now1 in this work1 in fixing the date of ,easter1 we abandon the use of the new moons altogether1 and make calculations wholly from the paschal full moons1 which cannot happen earlier than the #bast of ,march1 nor later than the #aith of ,april4 ,appendix ,j4 ,the epacts are here used to show the day of the month on which the paschal full moons fall2 that is1 if the paschal moon fall on a given day of the month in any year1 it will happen eleven days earlier the following year1 and twenty-two days earlier the third year1 and so on4 ,to illustrate1 suppose the paschal moon fall on the #ahth of ,april in any given year1 on the following year it would fall on the #gth1 in the third year on the #bgth of ,march2 and in the fourth year the moon would full on the #afth of ,march1 but that would not be the paschal moon1 which cannot happen earlier than the #bast2 so the following moon would be the paschal moon1 which happens thirty days later1 or the #aeth of ,april2 then the fifth year it would fall on the #dth of ,april1 and so on4 ,the solar and lunar equations or corrections are not made by change of epacts1 for only one line of epacts is used in this work1 but these corrections are made by a change of the day of the month on which the cycle commences4 ,this change is made at the beginning of a century1 and1 of course1 does not occur but once in a hundred years1 and frequently no change is made for two1 and even three hundred years4 ,the reason for making these changes has been given in the preceding chapter1 7q4 v471 and will again be noticed in the proper place4 ,the line of epacts used are thus represented1 commencing with a cipher as the point of departure3 #j1 #aa1 #bb1 #c1 #ad1 #be1 #f1 #ag1 #bh1 #i1 #bj1 #a1 #ab1 #bc1 #d1 #ae1 #bf1 #g1 #ah4 ,it should be borne in mind that the epacts are obtained by successively adding eleven to the epact of the former year1 and rejecting thirty as often as the sum exceeds or equals that number4 ,but1 as the intercalary month inserted at the end of the cycle contains only #bi days1 add twelve instead of eleven1 to eighteen1 the last of the cycle1 and then reject thirty as before2 thus1 #ah #ab #cj2 then #cj - #cj #j4 ,the cycle being completed1 we again commence with the cipher as the point of departure4 ,after having found the paschal full moons for one lunar cycle1 a period of nineteen years1 then the paschal moons again occur in the same order1 on the same days of the month1 as they did nineteen years before4 ,now1 as has also been shown in the preceding chapter1 this cycle might have been continued indefinitely had the ,julian intercalation been followed without correction1 and the cycle been perfectly exact2 but neither of these being true1 two equations or corrections must be made1 one depending on the error of the ,julian calendar1 which is called the solar-equation2 the other on the error of the lunar cycle1 which is called the lunar equation4 ,every omission of the intercalary day1 which occurs three times in #djj years1 will cause the full moons to fall one day later2 for example1 on the #acth of the month instead of the #abth4 ,on the other hand1 as has also been shown in the preceding chapter1 the error of the lunar cycle is one day in #cjj years2 so that at the end of every #cjj years the full moons will fall one day earlier1 for example1 on the #aath of the month instead of the #abth4 ,now1 when both equations occur together1 they compensate each other2 that is1 while the solar equation would cause the full moon to fall on the #acth1 the lunar equation would make it fall on the #aath2 therefore1 no correction is to be made--there is nothing to correct4 ,had they occurred singly1 the full moon1 at the beginning of the cycle1 would have fallen either on the #acth or the #aath2 but as they occur together1 no change is made2 and the full moons of the calendar will remain as they are for the next one hundred years4 ,hence1 the date of ,easter may very easily be determined1 as indicated in the following tables 7q4 v474 ,it is known by actual calculation that the paschal full moon fell on the #abth of ,april in the year #aeif1 which moon was the first of a cycle after the reformation of the calendar by ,gregory4 ,now1 by taking the epact of the following years of the cycle1 which are #aa1 #bb1 #c1 #ad1 #be1 etc41 from #ab1 the date of the first paschal moon1 and you will have all the moons of the cycle4 ,of course1 the epacts #bb1 #be1 etc41 cannot be taken from #ab1 but being carried back from the #abth of ,april1 they will show on what day in ,march the full moons fall4 ,when the epacts are greater than #ab1 it would be more convenient to take them from #dc1 as the number of days in ,march being #ca1 so #ab #ca #dc4 ,to find the paschal moons of the cycle1 we have then this rule3 ,if the epact is less than #ab1 take it from #ab2 if greater1 take it from #dc1 and the remainder will be the date of the paschal moon2 unless the full moon fall before the #bast of ,march1 in which case the following moon will be the paschal moon1 which happens thirty days later4 ,but when the solar equation occurs in #agaj1 causing the cycle to commence with the #acth of ,april1 then the epacts must be taken from #ac1 or #ac #ca #dd4 ,and again in #aijj1 the correction makes the cycle commence on the #adth of ,april2 so the number from which the epacts are taken is #ad1 or #ad #ca #de1 and so on4 ,whenever there is a change of date of the paschal moon in the beginning of the cycle1 as there is again in #bbjd1 #bcah and #bdac1 etc41 as may be seen in the following tables1 then the epacts must be taken from that date1 or that date plus #ca1 the number of days in ,march4 ,or the date of the paschal moons may very easily be determined by taking eleven successively from the date of every preceding full moon1 and that will give the date of the paschal moons2 only it should be borne in mind that1 whenever the full moon falls before the #bast of ,march1 the following moon is the paschal moon1 which happens thirty days later4 ,as ,easter ,sunday is the first ,sunday after the paschal full moon1 so all that remains to be done in fixing the date of ,easter1 is to find the day of the month on which that ,sunday falls2 and as this can easily be done by the use of the dominical letter1 which letter and its use in fixing dates having been fully explained in ,part ,second1 ,chapters ,,iv and ,v1 7q4 v471 a repetition seems to be unnecessary here4 ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- gf #aeif ,april #ab #ad #j #a e #aeig #a #f #aa #b d #aeih ,march #ba #bb #bb #c c #aeii ,april #i #aa #c #d ba #afjj ,march #bi #b #ad #e g #afja ,april #ag #bb #be #f f #afjb #f #g #f #g e #afjc ,march #bf #cj #ag #h dc #afjd ,april #ad #ah #bh #i b #afje #c #aj #i #aj a #afjf ,march #bc #bf #bj #aa g #afjg ,april #aa #ae #a #ab fe #afjh ,march #ca #f #ab #ac d #afji ,april #ai #bf #bc #ad c #afaj #h #aa #d #ae b #afaa ,march #bh #c #ae #af ag #afab ,april #af #bb #bf #ag f #afac #e #g #g #ah e #afad ,march #be #cj #ah #ai d #afae ,april #ab #ai #j #a cb #afaf #a #c #aa #b a #afag ,march #ba #bf #bb #c g #afah ,april #i #ae #c #d f #afai ,march #bi #ca #ad #e ed #afbj ,april #ag #ai #be #f c #afba #f #aa #f #g b #afbb ,march #bf #bg #ag #h a #afbc ,april #ad #af #bh #i gf #afbd #c #g #i #aj e #afbe ,march #bc #cj #bj #aa d #afbf ,april #aa #ab #a #ab c #afbg ,march #ca #d #ab #ac ba #afbh ,april #ai #bc #bc #ad g #afbi #h #ae #d #ae f #afcj ,march #bh #ca #ae #af e #afca ,april #af #bj #bf #ag dc #afcb #e #aa #g #ah b #afcc ,march #be #bg #ah #ai ---------------------------------------- -------------- ,by close examination of the above tables1 it will be seen that there is just eleven days difference in the date of these paschal moons1 from year to year1 through the whole lunar cycle1 and through all lunar cycles4 ,in determining the date of ,easter1 it will also be seen1 that whenever the full moon falls before the #bast of ,march1 then the following moon1 which happens thirty days later1 is the paschal moon1 as the #bast of ,march is its earliest possible date4 ,also when the cycle is ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- a #afcd ,april #ab #af #j #a g #afce #a #h #aa #b fe #afcf ,march #ba #bc #bb #c d #afcg ,april #i #ab #c #d c #afch ,march #bi #d #ad #e b #afci ,april #ag #bd #be #f ag #afdj #f #h #f #g f #afda ,march #bf #ca #ag #h e #afdb ,april #bd #bj #bh #i d #afdc #c #e #i #aj cb #afdd ,march #bc #bg #bj #aa a #afde ,april #aa #af #a #ab g #afdf ,march #ca #a #ab #ac f #afdg ,april #ai #ba #bc #ad ed #afdh #h #ab #d #ae c #afdi ,march #bh #d #ae #af b #afej ,april #af #ag #bf #ag a #afea #e #i #g #ah gf #afeb ,march #be #ca #ah #ai e #afec ,april #ab #ac #j #a d #afed #a #e #aa #b c #afee ,march #ba #bh #bb #c ba #afef ,april #i #af #c #d g #afeg ,march #bi #a #ad #e f #afeh ,april #ag #ba #be #f e #afei #f #ac #f #g dc #affj ,march #bf #bh #ag #h b #affa ,april #ad #ag #bh #i a #affb #c #i #i #aj g #affc ,march #bc #be #bj #aa fe #affd ,april #aa #ac #a #ab d #affe ,march #ca #e #ab #ac c #afff ,april #ai #be #bc #ad b #affg #h #aj #d #ae ag #affh ,march #bh #a #ae #af f #affi ,april #af #ba #bf #ag e #afgj #e #f #g #ah d #afga ,march #be #bi #ah #ai ---------------------------------------- -------------- completed1 then the paschal moons again occur in the same order1 on the same day of the month as they did nineteen years before4 ,now this cycle is six times repeated in a period of #aad years1 when the intercalary day being suppressed in #agjj1 causes the first paschal moon of the cycle to fall on the #acth of ,april instead of the #abth1 and all the moons of the cycle to fall one day later than they would had the correction not been made4 ,the cycle is now repeated ten times without ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- cb #afgb ,april #ab #ag #j #a a #afgc #a #b #aa #b g #afgd ,march #ba #be #bb #c f #afge ,april #i #ad #c #d ed #afgf ,march #bi #e #ad #e c #afgg ,april #ag #ah #be #f b #afgh #f #aj #f #g a #afgi ,march #bf #b #ag #h gf #afhj ,april #bd #ba #bh #i e #afha #c #f #i #aj d #afhb ,march #bc #bi #bj #aa c #afhc ,april #aa #ah #a #ab ba #afhd ,march #ca #b #ab #ac g #afhe ,april #ai #bb #bc #ad f #afhf #h #ad #d #ae e #afhg ,march #bh #cj #ae #af dc #afhh ,april #af #ah #bf #ag b #afhi #e #aj #g #ah a #afij ,march #be #bf #ah #ai g #afia ,april #ab #ae #j #a fe #afib #a #f #aa #b d #afic ,march #ba #bb #bb #c c #afid ,april #i #aa #c #d b #afie ,march #bi #c #ad #e ag #afif ,april #ag #bb #be #f f #afig #f #g #f #g e #afih ,march #bf #cj #ag #h d #afii ,april #ad #ai #bh #i c #agjj #c #d #i #aj b #agja ,march #bc #bg #bj #aa a #agjb ,april #aa #af #a #ab g #agjc ,march #ca #a #ab #ac fe #agjd ,april #ai #bj #bc #ad d #agje #h #ab #d #ae c #agjf ,march #bh #d #ae #af b #agjg ,april #af #ag #bf #ag ag #agjh #e #h #g #ah f #agji ,march #be #ca #ah #ai ---------------------------------------- -------------- correction1 that is1 till the year #aijj1 a period of #aij years1 when the intercalation being again suppressed1 causes the first paschal moon of the cycle to fall on the #adth of ,april1 and1 of course1 all the other moons of the cycle to fall one day later4 ,the reason the correction is not made the first year of the century is1 the lunar cycle must first be completed1 and that did not occur until #agaj4 ,as #ajj is not a multiple of #ai1 the number of years in the cycle1 and1 as the corrections ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- e #agaj ,april #ac #bj #j #a d #agaa #b #e #aa #b cb #agab ,march #bb #bg #bb #c a #agac ,april #aj #af #c #d g #agad ,march #cj #a #ad #e f #agae ,april #ah #ba #be #f ed #agaf #g #ab #f #g c #agag ,march #bg #bh #ag #h b #agah ,april #ae #ag #bh #i a #agai #d #i #i #aj gf #agbj ,march #bd #ca #bj #aa e #agba ,april #ab #ac #a #ab d #agbb #a #e #ab #ac c #agbc ,march #ba #bh #bc #ad ba #agbd ,april #i #af #d #ae g #agbe ,march #bi #a #ae #af f #agbf ,april #ag #ba #bf #ag e #agbg #f #ac #g #ah dc #agbh ,march #bf #bh #ah #ai b #agbi ,april #ac #ag #j #a a #agcj #b #i #aa #b g #agca ,march #bb #be #bb #c fe #agcb ,april #aj #ac #c #d d #agcc ,march #cj #e #ad #e c #agcd ,april #ah #be #be #f b #agce #g #aj #f #g ag #agcf ,march #bg #a #ag #h f #agcg ,april #ae #ba #bh #i e #agch #d #f #i #aj d #agci ,march #bd #bi #bj #aa cb #agdj ,april #ab #ag #a #ab a #agda #a #b #ab #ac g #agdb ,march #ba #be #bc #ad f #agdc ,april #i #ad #d #ae ed #agdd ,march #bi #e #ae #af c #agde ,april #ag #ah #bf #ag b #agdf #f #aj #g #ah a #agdg ,march #bf #b #ah #ai ---------------------------------------- -------------- cannot be made only at the beginning of the cycle1 so they cannot be made the first year of the century only once in #aijj years4 ,it may be seen from one of the above tables that the correction is made in the year #aijj1 for the reason that that is the first century which is a multiple of #ai4 ,the next centurial year that is exactly divisible by #ai1 is #chjj4 ,therefore1 none of the corrections for the next #aijj years1 will occur on the first year of the century4 ,it may also be seen from ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- gf #agdh ,april #ac #ad #j #a e #agdi #b #f #aa #b d #agej ,march #bb #bi #bb #c c #agea ,april #aj #aa #c #d ba #ageb ,march #cj #b #ad #e g #agec ,april #ah #bb #be #f f #aged #g #ad #f #g e #agee ,march #bg #cj #ag #h dc #agef ,april #ae #ah #bh #i b #ageg #d #aj #i #aj a #ageh ,march #bd #bf #bj #aa g #agei ,april #ab #ae #a #ab fe #agfj #a #f #ab #ac d #agfa ,march #ba #bb #bc #ad c #agfb ,april #i #aa #d #ae b #agfc ,march #bi #c #ae #af ag #agfd ,april #ag #bb #bf #ag f #agfe #f #g #g #ah e #agff ,march #bf #cj #ah #ai d #agfg ,april #ac #ai #j #a cb #agfh #b #c #aa #b a #agfi ,march #bb #bf #bb #c g #aggj ,april #aj #ae #c #d f #agga ,march #cj #ca #ad #e ed #aggb ,april #ah #ai #be #f c #aggc #g #aa #f #g b #aggd ,march #bg #c #ag #h a #agge ,april #ae #af #bh #i gf #aggf #d #g #i #aj e #aggg ,march #bd #cj #bj #aa d #aggh ,april #ab #ai #a #ab c #aggi #a #d #ab #ac ba #aghj ,march #ba #bf #bc #ad g #agha ,april #i #ae #d #ae f #aghb ,march #bi #ca #ae #af e #aghc ,april #ag #bj #bf #ag dc #aghd #f #aa #g #ah b #aghe ,march #bf #bg #ah #ai ---------------------------------------- -------------- the above tables1 that1 though the intercalary day was suppressed in the year #ahjj1 no change is made in the date of the paschal moon4 ,the reason is1 the lunar equation also occurred2 while the former correction would cause the paschal moon to fall one day later1 that is on the #adth day of ,april1 the latter would make it fall one day earlier1 that is on the #abth2 so they compensate each other1 and there is no correction to be made until the year #aijj1 when the solar equation ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- a #aghf ,april #ac #af #j #a g #aghg #b #h #aa #b fe #aghh ,march #bb #bc #bb #c d #aghi ,april #aj #ab #c #d c #agij ,march #cj #d #ad #e b #agia ,april #ah #bd #be #f ag #agib #g #h #f #g f #agic ,march #bg #ca #ag #h e #agid ,april #ae #bj #bh #i d #agie #d #e #i #aj cb #agif ,march #bd #bg #bj #aa a #agig ,april #ab #af #a #ab g #agih #a #h #ab #ac f #agii ,march #ba #bd #bc #ad e #ahjj ,april #i #ac #d #ae d #ahja ,march #bi #e #ae #af c #ahjb ,april #ag #ah #bf #ag b #ahjc #f #aj #g #ah ag #ahjd ,march #bf #a #ah #ai f #ahje ,april #ac #ad #j #a e #ahjf #b #f #aa #b d #ahjg ,march #bb #bi #bb #c cb #ahjh ,april #aj #ag #c #d a #ahji ,march #cj #b #ad #e g #ahaj ,april #ah #bb #be #f f #ahaa #g #ad #f #g ed #ahab ,march #bg #bi #ag #h c #ahac ,april #ae #ah #bh #i b #ahad #d #aj #i #aj a #ahae ,march #bd #bf #bj #aa gf #ahaf ,april #ab #ad #a #ab e #ahag #a #f #ab #ac d #ahah ,march #ba #bb #bc #ad c #ahai ,april #i #aa #d #ae ba #ahbj ,march #bi #b #ae #af g #ahba ,april #ag #bb #bf #ag f #ahbb #f #g #g #ah e #ahbc ,march #bf #cj #ah #ai ---------------------------------------- -------------- again occurs1 and the first paschal moon of the cycle falls on the #adth2 which cycle is repeated sixteen times in a period of #cjd years1 after which1 in #bbjd1 the date of the first paschal moon is the #aeth of ,april4 ,the reason there is no correction to make in this long period is1 first1 the year #bjjj is a common year in the ,gregorian calendar2 second1 in the year #bajj both the solar and the lunar equations again occur1 and occurring together1 they compensate each other2 consequently ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- dc #ahbd ,april #ac #ag #j #a b #ahbe #b #b #aa #b a #ahbf ,march #bb #be #bb #c g #ahbg ,april #aj #ad #c #d fe #ahbh ,march #cj #e #ad #e d #ahbi ,april #ah #ah #be #f c #ahcj #g #aj #f #g b #ahca ,march #bg #b #ag #h ag #ahcb ,april #ae #ba #bh #i f #ahcc #d #f #i #aj e #ahcd ,march #bd #bi #bj #aa d #ahce ,april #ab #ah #a #ab cb #ahcf #a #b #ab #ac a #ahcg ,march #ba #bb #bc #ad g #ahch #i #ad #d #ae f #ahci ,march #bi #cj #ae #af ed #ahdj ,april #ag #ah #bf #ag c #ahda #f #aj #g #ah b #ahdb ,march #bf #bf #ah #ai a #ahdc ,april #ac #ae #j #a gf #ahdd #b #f #aa #b e #ahde ,march #bb #bb #bb #c d #ahdf ,april #aj #aa #c #d c #ahdg ,march #cj #c #ad #e ba #ahdh ,april #ah #bb #be #f g #ahdi #g #g #f #g f #ahej ,march #bg #cj #ag #h e #ahea ,april #ae #ai #bh #i dc #aheb #d #d #i #aj b #ahec ,march #bd #bg #bj #aa a #ahed ,april #ab #af #a #ab g #ahee #a #a #ab #ac fe #ahef ,march #ba #bj #bc #ad d #aheg #i #ab #d #ae c #aheh ,march #bi #d #ae #af b #ahei ,april #ag #ag #bf #ag ag #ahfj #f #h #g #ah f #ahfa ,march #bf #ca #ah #ai ---------------------------------------- -------------- the cycle is continued until #bbjd1 after which1 as has already been stated1 the date of the first paschal moon is the #aeth of ,april4 ,this cycle is repeated six times in a period of #aad years1 when in #bcah1 for reasons already given1 the date of the first paschal moon of the next cycle falls on the #afth1 and is repeated five times in a period of #ie years1 when1 in #bdac1 the lunar equation occurs alone1 and the date of the first paschal moon for the next #ie years1 that is till the year #bejh1 ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- e #ahfb ,april #ac #bj #j #a d #ahfc #b #e #aa #b cb #ahfd ,march #bb #bg #bb #c a #ahfe ,april #aj #af #c #d g #ahff ,march #cj #a #ad #e f #ahfg ,april #ah #ba #be #f ed #ahfh #g #ab #f #g c #ahfi ,march #bg #bh #ag #h b #ahgj ,april #ae #ag #bh #i a #ahga #d #i #i #aj gf #ahgb ,march #bd #ca #bj #aa e #ahgc ,april #ab #ac #a #ab d #ahgd #a #e #ab #ac c #ahge ,march #ba #bh #bc #ad ba #ahgf ,april #i #af #d #ae g #ahgg ,march #bi #a #ae #af f #ahgh ,april #ag #ba #bf #ag e #ahgi #f #ac #g #ah dc #ahhj ,march #bf #bh #ah #ai b #ahha ,april #ac #ag #j #a a #ahhb #b #i #aa #b g #ahhc ,march #bb #be #bb #c fe #ahhd ,april #aj #ac #c #d d #ahhe ,march #cj #e #ad #e c #ahhf ,april #ah #be #be #f b #ahhg #g #aj #f #g ag #ahhh ,march #bg #a #ag #h f #ahhi ,april #ae #ba #bh #i e #ahij #d #f #i #aj d #ahia ,march #bd #bi #bj #aa cb #ahib ,april #ab #ag #a #ab a #ahic #a #b #ab #ac g #ahid ,march #ba #be #bc #ad f #ahie ,april #i #ad #d #ae ed #ahif ,march #bi #e #ae #af c #ahig ,april #ag #ah #bf #ag b #ahih #f #aj #g #ah a #ahii ,march #bf #b #ah #ai ---------------------------------------- -------------- falls back to the #aeth of ,april4 ,after which the #afth1 on account of the solar equation1 is again the date of the first paschal moon of the cycle for another period of #ie years2 that is till the year #bfjc1 when the solar equation causes the first paschal moon to fall on the #agth1 which cycle is repeated sixteen times during another period of #cjd years1 after which1 in #bijg1 the correction makes the date of the first paschal moon of the ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- g #aijj ,april #ad #ae #j #a f #aija #c #g #aa #b e #aijb ,march #bc #cj #bb #c d #aijc ,april #aa #ab #c #d cb #aijd ,march #ca #c #ad #e a #aije ,april #ai #bc #be #f g #aijf #h #ae #f #g f #aijg ,march #bh #ca #ag #h ed #aijh ,april #af #ai #bh #i c #aiji #e #aa #i #aj b #aiaj ,march #be #bg #bj #aa a #aiaa ,april #ac #af #a #ab gf #aiab #b #g #ab #ac e #aiac ,march #bb #bc #bc #ad d #aiad ,april #aj #ab #d #ae c #aiae ,march #cj #d #ae #af ba #aiaf ,april #ah #bc #bf #ag g #aiag #g #h #g #ah f #aiah ,march #bg #ca #ah #ai e #aiai ,april #ad #bj #j #a dc #aibj #c #d #aa #b b #aiba ,march #bc #bg #bb #c a #aibb ,april #aa #af #c #d g #aibc ,march #ca #a #ad #e fe #aibd ,april #ai #bj #be #f d #aibe #h #ab #f #g c #aibf ,march #bh #d #ag #h b #aibg ,april #af #ag #bh #i ag #aibh #e #h #i #aj f #aibi ,march #be #ca #bj #aa e #aicj ,april #ac #bj #a #ab d #aica #b #e #ab #ac cb #aicb ,march #bb #bg #bc #ad a #aicc ,april #aj #af #d #ae g #aicd ,march #cj #a #ae #af f #aice ,april #ah #ba #bf #ag ed #aicf #g #ab #g #ah c #aicg ,march #bg #bh #ah #ai ---------------------------------------- -------------- cycle1 the #ahth of ,april1 which cycle is continued without correction till the year #caaf1 a period of #bji years4 ,by reference to the above tables1 it will be seen that the solar and lunar equations occur together in the year #bgjj and compensate each other2 also1 that the year #bhjj is a common year in the ,gregorian calendar2 consequently there is no correction to make from #bfjc to #bijg2 also the two equations occur together ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- b #aich ,april #ad #ag #j #a a #aici #c #i #aa #b gf #aidj ,march #bc #bd #bb #c e #aida ,april #aa #ac #c #d d #aidb ,march #ca #e #ad #e c #aidc ,april #ai #be #be #f ba #aidd #h #i #f #g g #aide ,march #bh #a #ag #h f #aidf ,april #af #ba #bh #i e #aidg #e #f #i #aj dc #aidh ,march #be #bh #bj #aa b #aidi ,april #ac #ag #a #ab a #aiej #b #i #ab #ac g #aiea ,march #bb #be #bc #ad fe #aieb ,april #aj #ac #d #ae d #aiec ,march #cj #e #ae #af c #aied ,april #ah #be #bf #ag b #aiee #g #aj #g #ah ag #aief ,march #bg #a #ah #ai f #aieg ,april #ad #ba #j #a e #aieh #c #f #aa #b d #aiei ,march #bc #bi #bb #c cb #aifj ,april #aa #ag #c #d a #aifa ,march #ca #b #ad #e g #aifb ,april #ai #bb #be #f f #aifc #h #ad #f #g ed #aifd ,march #bh #bi #ag #h c #aife ,april #af #ah #bh #i b #aiff #e #aj #i #aj a #aifg ,march #be #bf #bj #aa gf #aifh ,april #ac #ad #a #ab e #aifi #b #f #ab #ac d #aigj ,march #bb #bi #bc #ad c #aiga ,april #aj #aa #d #ae ba #aigb ,march #cj #b #ae #af g #aigc ,april #ah #bb #bf #ag f #aigd #g #ad #g #ah e #aige ,march #bg #cj #ah #ai ---------------------------------------- -------------- again in the year #cjjj and compensate each other1 is the reason there is no correction to make from #bijg to #caaf1 after which the first paschal moon falls on the #aith1 and is repeated fifteen times in a period of #bhe years1 that is till the year #cdja1 when the correction makes the #bjth of ,april1 the date of the full moon1 but that cannot be the paschal moon1 which cannot happen later than the #aith2 consequently the ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- dc #aigf ,april #ad #ah #j #a b #aigg #c #aj #aa #b a #aigh ,march #bc #bf #bb #c g #aigi ,april #aa #ae #c #d fe #aihj ,march #ca #f #ad #e d #aiha ,april #ai #bf #be #f c #aihb #h #aa #f #g b #aihc ,march #bh #c #ag #h ag #aihd ,april #af #bb #bh #i f #aihe #e #g #i #aj e #aihf ,march #be #cj #bj #aa d #aihg ,april #ac #ai #a #ab cb #aihh #b #c #ab #ac a #aihi ,march #bb #bf #bc #ad g #aiij ,april #aj #ae #d #ae f #aiia ,march #cj #ca #ae #af ed #aiib ,april #ah #ai #bf #ag c #aiic #g #aa #g #ah b #aiid ,march #bg #c #ah #ai a #aiie ,april #ad #af #j #a gf #aiif #c #g #aa #b e #aiig ,march #bc #cj #bb #c d #aiih ,april #aa #ab #c #d c #aiii ,march #ca #d #ad #e ba #bjjj ,april #ai #bc #be #f g #bjja #h #ae #f #g f #bjjb ,march #bh #ca #ag #h e #bjjc ,april #af #bj #bh #i dc #bjjd #e #aa #i #aj b #bjje ,march #be #bg #bj #aa a #bjjf ,april #ac #af #a #ab g #bjjg #b #h #ab #ac fe #bjjh ,march #bb #bc #bc #ad d #bjji ,april #aj #ab #d #ae c #bjaj ,march #cj #d #ae #af b #bjaa ,april #ah #bd #bf #ag ag #bjab #g #h #g #ah f #bjac ,march #bg #ca #ah #ai ---------------------------------------- -------------- moon that precedes it by thirty days1 and which falls on the #bast of ,march1 is the date of the first paschal moon of the cycle which commences with the year #cdja4 ,the day of the month on which ,easter ,sunday has fallen or will fall1 from the year #aeif to #bjac1 is already determined1 and may be seen by reference to the above tables4 ,from #bjac to #cdja1 the date of ,easter is determined for one lunar cycle only1 at the ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- ag #bbjd ,april #ae #bb #j #a f #bbje #d #g #aa #b e #bbjf ,march #bd #cj #bb #c d #bbjg ,april #ab #ai #c #d cb #bbjh #a #c #ad #e a #bbji ,march #ba #bf #be #f g #bbaj ,april #i #ae #f #g f #bbaa ,march #bi #ca #ag #h ed #bbab ,april #ag #ai #bh #i c #bbac #f #aa #i #aj b #bbad ,march #bf #bg #bj #aa a #bbae ,april #ad #af #a #ab gf #bbaf #c #g #ab #ac e #bbag ,march #bc #cj #bc #ad d #bbah ,april #aa #ab #d #ae c #bbai ,march #ca #d #ae #af ba #bbbj ,april #ai #bc #bf #ag g #bbba #h #ae #g #ah f #bbbb ,march #bh #ca #ah #ai f #bcah ,april #af #ba #j #a e #bcai #e #f #aa #b dc #bcbj ,march #be #bh #bb #c b #bcba ,april #ac #ag #c #d a #bcbb #b #i #ad #e g #bcbc ,march #bb #be #be #f fe #bcbd ,april #aj #ac #f #g d #bcbe ,march #cj #e #ag #h c #bcbf ,april #ah #be #bh #i b #bcbg #g #aj #i #aj ag #bcbh ,march #bg #a #bj #aa f #bcbi ,april #ae #ba #a #ab e #bccj #d #f #ab #ac d #bcca ,march #bd #bi #bc #ad cb #bccb ,april #ab #ag #d #ae a #bccc #a #b #ae #af g #bccd ,march #ba #be #bf #ag f #bcce ,april #i #ad #g #ah ed #bccf ,march #bi #e #ah #ai ---------------------------------------- -------------- beginning of each period2 for the reason that it was deemed unnecessary1 because the paschal moons1 the epacts1 and the ,golden ,numbers are the same for every cycle in the period4 ,therefore1 all that remains to be done is to find the day of the month on which the first ,sunday1 after the paschal moon1 falls4 ,the dominical letters for any period may very easily be found by counting backwards one letter each year for every common ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- f #bdac ,april #ae #ba #j #a e #bdad #d #f #aa #b d #bdae ,march #bd #bi #bb #c cb #bdaf ,april #ab #ag #c #d a #bdag #a #b #ad #e g #bdah ,march #ba #be #be #f f #bdai ,april #i #ad #f #g ed #bdbj ,march #bi #e #ag #h c #bdba ,april #ag #ah #bh #i b #bdbb #f #aj #i #aj a #bdbc ,march #bf #b #bj #aa gf #bdbd ,april #ad #ba #a #ab e #bdbe #c #f #ab #ac d #bdbf ,march #bc #bi #bc #ad c #bdbg ,april #aa #ah #d #ae ba #bdbh ,march #ca #b #ae #af g #bdbi ,april #ai #bb #bf #ag f #bdcj #h #ad #g #ah e #bdca ,march #bh #cj #ah #ai ag #bejh ,april #af #bb #j #a f #beji #e #g #aa #b e #beaj ,march #be #cj #bb #c d #beaa ,april #ac #ai #c #d cb #beab #b #c #ad #e a #beac ,march #bb #bf #be #f g #bead ,april #aj #ae #f #g f #beae ,march #cj #ca #ag #h ed #beaf ,april #ah #ai #bh #i c #bfag #g #aa #i #aj b #beah ,march #bg #c #bj #aa a #beai ,april #ae #af #a #ab gf #bebj #d #g #ab #ac e #beba ,march #bd #cj #bc #ad d #bebb ,april #ab #ai #d #ae c #bebc #a #d #ae #af ba #bebd ,march #ba #bf #bf #ag g #bebe ,april #i #ae #g #ah f #bebf ,march #bi #ca #ah #ai ---------------------------------------- -------------- year1 and two for leap-year1 the fourth letter being dominical letter for ,january and ,february and the fifth for the rest of the year2 thus1 if ,g be dominical letter for any given year1 we would have then1 ,g1 ,f1 ,e1 ,,dc2 ,b1 ,a1 ,g1 ,,fe2 ,d1 ,c1 ,b1 ,,ag2 ,f1 ,e1 ,d1 ,,cb1 etc4 ,by counting these letters backwards1 or in the tables1 from the bottom of the column upwards1 they will occur in alphabetical order4 ,again it may be seen by reference ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- b #bfjc ,april #ag #bd #j #a ag #bfjd #f #h #aa #b f #bfje ,march #bf #ca #bb #c e #bfjf ,april #ad #bj #c #d d #bfjg #c #e #ad #e cb #bfjh ,march #bc #bg #be #f a #bfji ,april #aa #af #f #g g #bfaj ,march #ca #a #ag #h f #bfaa ,april #ai #ba #bh #i ed #bfab #h #ab #i #aj c #bfac ,march #bh #d #bj #aa b #bfad ,april #af #ag #a #ab a #bfae #e #i #ab #ac gf #bfaf ,march #be #ca #bc #ad e #bfag ,april #ac #bj #d #ae d #bfah #b #e #ae #af c #bfai ,march #bb #bh #bf #ag ba #bfbj ,april #aj #af #g #ah g #bfba ,march #cj #a #ah #ai b #bijg ,april #ah #bd #j #a ag #bijh #g #h #aa #b f #biji ,march #bg #ca #bb #c e #biaj ,april #ae #bj #c #d d #biaa #d #e #ad #e cb #biab ,march #bd #bg #be #f a #biac ,april #ab #af #f #g g #biad #a #h #ag #h f #biae ,march #ba #bd #bh #i ed #biaf ,april #i #ab #i #aj c #biag ,march #bi #d #bj #aa b #biah ,april #ag #bd #a #ab a #biai #f #i #ab #ac gf #bibj ,march #bf #ca #bc #ad e #biba ,april #ad #bj #d #ae d #bibb #c #e #ae #af c #bibc ,march #bc #bh #bf #ag ba #bibd ,april #aa #af #g #ah g #bibe ,march #ca #a #ah #ai ---------------------------------------- -------------- to these tables1 that ,easter occurs less frequently on the #bb;d of ,march1 its earliest possible date1 and the #beth of ,april1 which has hitherto been considered its latest possible date1 than any of the days intervening4 ,it cannot happen on the #bb;d1 only when the paschal moon falls on the #bast1 and that day must be ,saturday4 ,it fell on the #bb;d1 first1 after the reformation of the calendar by ,gregory in #aeih2 again in #afic1 #agfa1 ---------------------------------------- -------------- ,dominical,year4 ,paschal,easter4,epact4,golden ,letter4 ,full ,number4 ,moon4 ---------------------------------------- -------------- ba #caaf ,april #ai #bc #j #a g #caag #h #ae #aa #b f #caah ,march #bh #ca #bb #c e #caai ,april #af #bj #c #d dc #cabj #e #aa #ad #e b #caba ,march #be #bg #be #f a #cabb ,april #ac #af #f #g g #cabc #b #h #ag #h fe #cabd ,march #bb #bc #bh #i d #cabe ,april #aj #ab #i #aj c #cabf ,march #cj #d #bj #aa b #cabg ,april #ah #bd #a #ab ag #cabh #g #h #ab #ac f #cabi ,march #bg #ca #bc #ad e #cacj ,april #ae #bj #d #ae d #caca #d #e #ae #af cb #cacb ,march #bd #bg #bf #ag a #cacc ,april #ab #af #g #ah g #cacd #a #h #ah #ai d #cdja ,march #ba #bb #j #a c #cdjb ,april #i #aa #aa #b b #cdjc ,march #bi #c #bb #c ag #cdjd ,april #ag #bb #c #d f #cdje #f #g #ad #e e #cdjf ,march #bf #cj #be #f d #cdjg ,april #ad #ai #f #g cb #cdjh #c #aj #ag #h a #cdji ,march #bc #bf #bh #i g #cdaj ,april #aa #ae #i #aj f #cdaa ,march #ca #g #bj #aa ed #cdab ,april #ai #bf #a #ab c #cdac #h #aa #ab #ac b #cdad ,march #bh #c #bc #ad a #cdae ,april #af #bc #d #ae gf #cdaf #e #g #ae #af e #cdag ,march #be #cj #bf #ag d #cdah ,april #ac #ai #g #ah c #cdai #b #d #ah #ai ---------------------------------------- -------------- and in #ahah4 ,it has not occurred since1 nor will not again till #bbhe1 a period of #dfg years4 ,the reason that it does not occur on the #bb;d of ,march in this long period is1 the paschal moon does not fall on the #bast1 from the year #aijj to #bbjd1 a period of #cjd years4 ,we refer to the tabular moon1 not to the true or astronomical moon1 which may occur on the #bast more than once in this long period4 ,,chapter ,,vii4 ,,church ,,feasts ,,and ,,fasts ,,whose ,,date ,,depend ,,on ,,the ,,date ,,of ,,easter4 ,feasts1 or ,festivals1 are days set apart by the church1 either for the grateful memorial of the most remarkable events connected with the plan of redemption1 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 mankind4 ,the ecclesiastical year is divided into eight seasons1 namely3 ,advent-tide1 ,christmas-tide1 ,epiphany-tide1 ,lenten-tide1 ,easter-tide1 ,ascension-tide1 ,whitsun-tide1 and ,trinity-tide4 ,the first day of each of these seasons has been1 and is now observed by the church in commemoration of some of the most remarkable events connected with the plan of redemption4 ,all these will be noticed in the order in which they occur in the ecclesiastical year1 while many other days intervening1 which are observed as feasts or fasts1 will be given a passing notice4 a--,advent ,sunday1 which is the day nearest ,st4 ,andrew's ,day 7,nov4 #cj71 or the first ,sunday after the #bfth of ,november1 has been recognized since the sixth century as the first day of the ecclesiastical year4 ,advent 7,latin ,adventus1 the coming17 signifies the coming of our ,saviour1 the period of the approach of the nativity4 ,as ,advent-tide lasts from ,advent ,sunday to ,christmas1 the length of the season depends upon the day of the month on which ,advent ,sunday falls4 ,as it may happen as early as the #bgth of ,november or as late as the #c;d of ,december1 so ,advent-tide will contain no more than twenty-eight days nor less than twenty-two4 ,it should be borne in mind that1 though this festival is classed among the movable feasts1 it does not depend upon the date of ,easter1 but upon the day of the month on which ,advent ,sunday falls4 ,the four ,sundays before ,christmas were made preparation days for the festival of ,christmas1 and were called the first1 second1 third1 and fourth ,sundays in ,advent4 ,ember days and ,ember weeks are the four seasons set apart by the ,western church for special prayer and fasting1 and the ordination of clergy2 known in the church as quatuor tempora1 7the four seasons47 ,the ,ember weeks are the weeks next following ,st4 ,lucy's ,day 7,dec4 #acth71 the first ,sunday in ,lent1 ,whitsun ,day1 and ,holy ,cross ,day 7,sept4 #adth74 ,the ,wednesdays1 ,fridays and ,saturdays of these weeks are the ,ember days distinctively4 ,the name by some is supposed to be derived from a ,german word signifying ,abstinence2 by others it is supposed to signify ,ashes4 b--,christmas 7from ,christ and the ,saxon maess1 signifying the mass and a feast71 is a festival held in commemoration of the nativity of our ,saviour throughout nearly the whole of ,christendom4 ,it is occupied1 therefore1 with the event 7the incarnation7 which forms the center and turning point of the history of the world4 ,though the day of ,christ's birth cannot be ascertained from the ,new ,testament1 nor from any other source1 yet the whole ,christian world for more than #acjj years have concurred in celebrating the nativity on the #beth of ,december4 ,this is the first of the four great feasts in the ecclesiastical year2 the other three are ,easter1 ,ascension1 and ,whitsun ,day4 ,the length of ,christmas-tide or season is twelve days1 lasting from the #beth of ,december to ,epiphany4 c--,epiphany 7,greek ,epiphania1 ,theophania or ,christophania17 is a festival in commemoration of the manifestation of ,jesus ,christ to the world as the ,son of ,god1 and referring to the appearance of the star which announced our ,saviour's birth to the ,gentiles1 and the visit of the ,magi1 or wise ,men of the ,east to the infant ,jesus4 ,this festival is held on the #fth of ,january invariably1 consequently is not a movable feast1 though the length of ,epiphany-tide depends upon the date of ,easter4 ,as ,easter may happen as early as the #bb;d of ,march or as late as the #bfth of ,april 7a variation of thirty-five days71 so ,epiphany-tide may consist of no less than twelve days nor more than forty-seven1 as the season always ends the day before ,septuagesima ,sunday4 7,see tables at the close of this chapter47 ,septuagesima1 ,sexagesima1 ,quinquagesima4 ,there being exactly fifty days between the ,sunday next before ,lent and ,easter ,day1 inclusive1 that ,sunday was termed ,quinquagesima1 i4 e41 the fiftieth2 and the two immediately preceding ,sundays were called from the next round numbers ,sexagesima1 the sixtieth2 and ,septuagesima1 the seventieth4 ,the ,paschal ,season extends from ,septuagesima ,sunday to ,low ,sunday1 a period of seventy days4 ,it takes its name from the ,paschal festival or ,easter1 whose services end with ,low ,sunday1 the octave1 or eighth day1 of ,easter4 ,it begins with ,septuagesima ,sunday because the church services then begin to prepare the minds of the faithful for the services of ,lent1 which are themselves the preparation for ,easter4 ,may not ,septuagesima ,sunday be so called because there are just seventy days in the ,paschal ,season8 ,shrove-tide literally means confession-time1 and is the name given to the days immediately preceding ,ash ,wednesday4 ,these days were so called because on them1 and especially on the last of them 7,shrove ,tuesday7 people were accustomed to confess their sins as a preparation for ,lent4 ,in most ,roman ,catholic countries it begins with ,quinquagesima ,sunday1 the ,sunday before ,lent4 ,ash ,wednesday1 the first day of ,lent1 7,latin dies cinerum1 the day of ,ashes71 was so called because it was customary on that day for penitents to appear in sackcloth1 upon which occasion ashes were sprinkled upon them4 d--,lent1 7,anglo-,saxon lengten4 ,perhaps from lenegan1 to lengthen1 because at this season the days lengthen7 the forty days fast1 is the preparation for ,easter1 and is observed in commemoration of our ,lord's fast in the wilderness4 ,in most languages the name given to this fast signifies the number of days--forty2 but our word ,lent signifies the ,spring ,fast1 for ,lenten-tide in the ,anglo-,saxon language was the ,season of ,spring1 in ,german1 ,lenz4 ,the six ,sundays in the ,lenten-tide of forty-six days are not counted in the fast1 as all ,sundays in the year are reckoned as feast days1 because our ,saviour arose from the dead on the first day of the week4 ,quadragesima ,sunday1 the first ,sunday in ,lent1 is so called by analogy with the three ,sundays which precede ,lent1 and which 7as has already been stated7 are called respectively ,septuagesima1 seventieth2 ,sexagesima1 sixtieth2 ,quinquagesima1 fiftieth2 and then ,quadragesima1 fortieth2 in round numbers forty days before ,easter4 ,holy ,week1 the last week in ,lent1 called also ,passion ,week1 because within it is commemorated our ,lord's sufferings4 ,the days specially solemnized are ,palm ,sunday1 ,spy ,wednesday1 ,holy1 or ,maundy ,thursday1 and ,good ,friday4 ,palm ,sunday 7,latin ,dominica ,palmarium1 or ,dominica in ,palmis7 is the name usually given the ,sunday before ,easter2 a day celebrated in commemoration of ,christ's triumphal entry into ,jerusalem1 so called because the people who had come to the feast1 when they heard that ,jesus was coming1 took branches of palm trees and went forth to meet him1 and cried1 ,hosanna2 blessed is the ,king of ,israel that cometh in the name of the ,lord4 ,spy ,wednesday1 so called in allusion to the betrayal of ,christ by ,judas1 or the day on which he made the bargain to deliver him into the hands of his enemies for thirty pieces of silver4 ,maundy ,thursday 7from ,dies mandati1 mandate ,thursday71 so called either from the command given his disciples to love one another1 or to commemorate the sacrament of ,his supper4 ,good ,friday1 so called in acknowledgment of the benefit derived from the death of ,christ4 ,the closing scenes in the life of ,christ1 the events of ,wednesday1 ,thursday and ,friday of ,holy ,week1 are events of much more importance than were ever before crowded into any one week in the history of the world4 ,the betrayal on ,wednesday1 the institution of the sacrament on ,thursday night1 also the words of our ,saviour as recorded in ,john's gospel1 from the #adth to the #agth chapters inclusive1 the agony and the bloody sweat in the garden1 the arrest and trial during ,thursday night and ,friday morning1 the crucifixion at the third hour1 the darkness that was over all the land from the sixth to the ninth hour1 and the last words of the blessed ,jesus1 ,it is finished1 7tasted death for every man72 these we say1 are events of more importance to man than were ever before crowded into any one week in the world's history4 ,the prophets who prophesied of these things1 inquired and searched diligently1 searching what1 or what manner of time the ,spirit of ,christ which was in them did signify1 when it testified beforehand the sufferings of ,christ and the glory that should follow4 ,and about an hour before this prophecy began to be fulfilled our ,saviour uttered these words3 ,verily1 verily1 ,i say unto you1 that ye shall weep and lament1 but the world shall rejoice2 and ye shall be sorrowful1 but your sorrow shall be turned into joy4 ,it was probably not more than an hour from the time these words fell from the ,saviour's lips1 that he was arrested and led away to undergo a trial2 cruel mocking and scourging1 crucifixion and death upon the cross4 ,then cometh ,joseph of ,arimathea1 bringing fine linen1 and ,nicodemus with his hundred pounds of myrrh and aloes1 and they two took the body of the ,lord ,jesus and wrapped it in the linen with the spices1 and laid it in ,joseph's own new tomb1 which he had hewn out in a rock1 wherein never man before was laid1 and rolled a great stone against the door of the sepulcher and departed4 ,thus endeth ,passion ,week4 ,while the body of ,jesus is in the sepulcher the world is rejoicing1 and the disciples are weeping and lamenting1 according to the words of the ,saviour1 ,ye shall weep and lament1 but the world shall rejoice4 ,he dies6 the friend of sinners dies6 ,lo6 ,salem's daughters weep around2 ,a solemn darkness veils the skies1 ,a sudden trembling shakes the ground4 e--,easter 7,german1 ,ostern1 ,old ,saxon ,oster1 from osten1 signifying rising17 is a church festival in commemoration of the resurrection of our ,lord from the dead4 ,but the apparent victory which the enemies of ,christ had gained was of short duration1 the rejoicing of the world did not long continue1 the remaining words of our ,saviour must needs be fulfilled3 ,but your sorrow shall be turned into joy4 ,now1 upon the first day of the week1 very early in the morning1 7,easter morning7 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 ,jesus1 but were greatly astonished when they saw that the great stone1 which they had seen rolled against the door of the sepulcher on ,friday afternoon1 was rolled away1 and an angel sitting upon it whose countenance was like lightning1 and for fear of whom the keepers did shake and become as dead men4 ,but to the women he said1 ,fear not ye2 for ,i know that ye seek ,jesus which was crucified1 ,he is not here1 for ,he is risen4 ,that you may know for a certainty that ,he is risen1 come and see the place where you saw ,him laid only a few hours ago4 ,now go quickly and tell ,his disciples that ,he is risen from the dead1 and behold ,he goeth before you into ,galilee1 there shall ye see ,him4 ,and they departed quickly from the sepulcher with fear and great joy1 and did run to carry the good news to the disciples4 ,but how much greater their joy soon after their departure when ,jesus himself met them with the comforting words1 ,be not afraid1 but go tell my brethren that they go into ,galilee1 and there shall they see ,me4 ,the subject for conversation for the past two days had been ,jesus and the crucifixion1 but now ,jesus and the resurrection4 ,some believed1 but some doubted4 ,others ran to the sepulcher and found it even as the women had said4 ,while the chief priests and elders hired the soldiers to say that the disciples came by night and stole him away while we slept4 ,but how should they know what had become of ,him if they were sleeping8 ,the truth was they were so overcome with fear by the brightness of the angels' countenance that they became as dead men1 not knowing what was transpiring around them4 ,but it was truly good tidings and great joy to the disciples of ,christ on that ,easter morning4 ,the rising ,god forsakes the tomb2 ,in vain the tomb forbids ,his rise2 ,vain the stone1 the watch1 the seal1 ,christ has burst the gates of hell2 ,death in vain forbids ,his rise2 ,christ hath opened ,paradise4 ,the spirit of ,christ in the prophets had testified beforehand the suffering of ,christ and the glory that should follow4 ,that morning and that day was not only joyful to the disciples of ,christ1 but glorious2 it was joy unspeakable and full of glory4 ,although #ahfc years have rolled around since that ,easter morning1 yet we are as much interested in what then and there transpired as were the ,marys1 and ,peter1 and ,john1 who were the first at the sepulcher1 and who were permitted the same day to see their risen ,lord1 whom having not seen1 we love2 in whom1 though now we see ,him not1 yet believing1 we as well as they rejoice with joy unspeakable and full of glory4 ,low ,sunday4 ,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 day1 whence it took the name of ,low ,sunday1 being celebrated as a feast1 but of a lower degree than ,easter day itself4 ,the next ,sunday after ,easter has been popularly1 so called in ,england1 perhaps by corruption for close1 7,pascha ,clausum7 close of ,easter4 ,dominica in ,albis1 7the ,sunday of white garments7 a title anciently given to the first ,sunday after ,easter1 because on this day those persons who had been baptized at ,easter appear for the last time in the chrysomes1 or white robes which they received at baptism4 ,these were laid up in the church as evidences of their baptismal profession4 ,rogation ,days1 7,latin rogare1 to beseech17 are the ,monday1 ,tuesday and ,wednesday after ,rogation ,sunday and before ,ascension ,day1 7,holy ,thursday47 ,about the middle of the fifth century ,mamertus1 bishop of ,vienna1 upon the prospect of a great fire that threatened his diocese1 appointed that extraordinary prayer and supplication should be offered up to ,god1 with fasting1 for averting the impending evils upon the above mentioned days2 from which supplications 7called by the ,latins rogationes7 these days have ever since been called ,rogation ,days4 ,as retained in our present calendar1 they are simply private fasts4 f--,ascension ,day1 or ,holy ,thursday1 one of the great religious festivals of the ,roman ,catholic and ,episcopal churches1 is held on the fortieth day after ,easter1 and ten days before ,whitsun ,day1 to commemorate the ,ascension of our ,lord into heaven4 ,ascension ,day has been observed at least since the year of our ,lord #fd1 and perhaps earlier4 ,saint ,augustine believed it to have been instituted either by the apostles themselves1 or the bishops immediately succeeding them4 ,expectation ,week is the whole of the interval between ,ascension ,day and ,whitsun ,day1 so called because at this time the apostles1 according to the command of our ,saviour1 continued at ,jerusalem1 in earnest prayer and expectation of the ,holy ,comforter which was to abide with them forever4 ,the ,sunday between ,ascension ,day and ,whitsun ,day is called ,expectation ,sunday4 ,pentecost1 7,greek1 ,pentecostos1 fiftieth71 a ,jewish festival2 so called because it was observed on the fiftieth day after the feast of unleavened bread1 called also the feast of weeks1 being celebrated seven weeks from the feast of the ,passover4 ,it also commemorated the giving of the law on ,mount ,sinai upon that day4 ,the origin of the ,anglo-,saxon name of ,white ,sunday1 which also occurs in ,icelandic1 is somewhat obscure1 for in the ,roman churches the ,dominica in ,albis1 7,low ,sunday1 q4 v47 so called from the white robes then worn by the persons baptized at ,easter1 has always been the ,sunday immediately following ,easter4 ,it hardly seems probable that there should be another ,sunday of ,white ,garments within six weeks4 ,in ,german it is known by the name ,pfingsten1 old ,german ,wingsten1 old ,english ,whitsun1 hence1 probably1 our word ,whitsun ,day1 not ,white ,sunday4 g--,whitsun ,day1 or ,pentecost1 is the last of the four great festivals in the ecclesiastical year1 held in commemoration of the outpouring of the ,holy ,spirit on the infant church ten days after the ,ascension4 ,among the last words of our ,saviour to the apostles on the very day that ,he was taken up1 were ,behold ,i send the promise of my ,father upon you1 but tarry ye in the city of ,jerusalem until ye be endowed with power from on high4 ,after ten days of earnest1 believing prayer1 and expectation1 suddenly1 but not unexpectedly1 there came a sound from heaven as a rushing1 mighty wind1 and it filled all the house where they were sitting1 and there appeared unto them cloven tongues like as of fire1 and it sat upon each of them2 and they were all filled with the ,holy ,ghost1 and began to speak with other tongues as the ,spirit gave them utterance2 and the multitude came together1 and were amazed1 saying one to the other what meaneth this8 ,others mocking said1 these men are full of new wine4 ,but ,peter lifted up his voice and said1 these are not drunken as ye suppose1 seeing it is but the third hour of the day1 7nine o'clock in the morning17 men are not usually drunk so early in the morning2 but this is that which the prophet ,joel eight hundred years ago said should come to pass in these last days2 the promise of the ,father1 the baptism of the ,holy ,ghost for which they had been waiting for the past ten days2 something of that glory that should follow the crucifixion1 death1 resurrection and ascension of the ,lord ,jesus into ,heaven1 the glory of the ,christian church1 of the ,christian dispensation1 and which is destined to fill the whole earth4 ,waft1 ,waft1 ye winds his story1 ,and you1 ye waters1 roll1 ,till like a sea of glory1 ,it spreads from pole to pole4 h--,trinity ,sunday1 the octave1 or eighth day of the feast of ,pentecost1 is a church festival held in commemoration of the doctrine of the ,trinity4 ,the introduction of this day into the calendar is of comparatively recent date1 it being established by ,pope ,benedict ,,xi1 in the year of our ,lord #acje4 ,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 unity1 or the one true ,god as distinguished from idols4 ,the reason for its late introduction is that in the creed of the church1 and in its psalms1 hymns1 and doxologies1 great prominence was given to this doctrine1 and it was thought that there was no need to set apart a particular day for that which was done every day4 ,this is the last of the movable feasts in the ecclesiastical year1 being held eight weeks after ,easter2 so it may happen as early as the #agth of ,may or as late as the #bjth of ,june4 ,the length of both ,epiphany and ,trinity-tide depend upon the date of ,easter4 ,as ,epiphany-tide is shortened by the early date of ,easter1 so ,trinity-tide is lengthened proportionately1 and as ,epiphany-tide is lengthened by the later date of ,easter so ,trinity-tide is shortened proportionately2 so ,trinity-tide may contain no more than #aif days nor less than #afa4 7,see tables at the close of this chapter47 ,all ,saints ,day1 or ,all hallowmass 7,anglo-,saxon all1 and halig1 holy7 a festival celebrated by the ,roman ,catholic and ,episcopal churches on the first day of ,november1 in honor of all ,saints and martyrs4 ,it was introduced into the ,western church in the beginning of the seventh century by ,boniface4 ,the number of saints being exceedingly multiplied1 it was found too burdensome to dedicate a feast day to each1 there being1 indeed1 scarcely hours enough in the year to distribute among them all4 ,it was therefore resolved to commemorate on one day all who had no particular day4 ,by order of ,gregory ,,iv1 it was celebrated on the first of ,november1 #hcd2 formerly the first of ,may was the day appointed4 ,it was introduced into ,england about #hgj1 and is still observed in the ,english and ,lutheran churches1 as well as the ,church of ,rome on the first of ,november4 ,all-,souls' ,day1 a festival held by ,roman ,catholics on the #b;d of ,november1 for special prayer in behalf of all the faithful dead4 ,it was first introduced in #iih1 by ,odilon1 ,abbot of ,clugni1 who enjoined it on his own order4 ,it was soon after adopted by neighboring churches4 ,it is the day on which1 in the ,romish church1 extraordinary masses are repeated for the relief of souls said to be in purgatory4 ,formerly on this day persons dressed in black perambulated the towns and cities1 each provided with a bell of dismal tone1 which was rung in public places by way of exhortation to the people to remember the souls in purgatory4 ,in some parts of the west of ,england it is still the custom for the village children to go around to all their neighbors souling1 as they call it1 collecting small contributions1 and singing the following verses1 taken down from two of the children themselves3 ,soul6 ,soul6 for a soul-cake1 ,pray good mistress1 for a soul-cake1 ,one for ,peter1 two for ,paul1 ,three for ,him that made us all4 ,soul6 soul6 for an apple or two2 ,if you've got no apples1 pears will do1 ,up with your kettle1 and down with your pan1 ,give me a good big one and ,i'll be gone4 ,the soul cake referred to in the verses is a sort of bun which the people used to make1 and to give to one another on the #b;d of ,november4 ,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 #ahag-ah and #ahhe-hf4 ,in the former ,easter happens at its earliest possible date1 in the latter at its latest date in this century3 ---------------------------------------- ------------------------------ ,,year #ahag-ah4 ,days in ,sundays in ,each ,season4,each ,season4 ---------------------------------------- ------------------------------ a--,advent ,sunday1 ,november #cjth2 ,advent-tide1 #be #d #ast ,ember ,week1 after ,december #acth2 ,ember ,days1 ,wednesday1 ,friday and ,saturday4 b--,christmas1 ,december #beth2 ,christmas-tide1 #ab #b c--,epiphany1 ,january #fth2 ,epiphany-tide1 #ab #a ,septuagesima ,sunday1 ,january #ahth1 #g #a ,paschal season from ,jan4 #ahth to ,march #bith1 #gj days ,sexagesima ,sunday1 ,january #beth1 #g #a ,quinquagesima ,sunday1 ,february #ast1 #c #a ,shrove-tide1 7confession time7 ,shrove ,tues41 ,feb4 #c;d4 d--,ash ,wednesday1 ,feb #dth1 ,lent begins2 ,lenten-tide1 #df #f ,first ,sunday in ,lent 7,quadragesima7 ,february #hth4 #b;d ,ember ,week after first ,sunday in ,lent2 ,ember ,days1 ,wednesday1 ,friday and ,saturday4 ,holy ,week1 the week before ,easter2 ,special ,days1 ,palm ,sunday1 ,spy ,wednesday1 ,maundy ,thursday1 and ,good ,friday1 ,march #aeth1 #ahth1 #aith and #bjth4 e--,easter ,sunday1 ,march #bb;d2 ,easter-tide1 #ci #f ,low ,sunday1 ,march #bith2 ,paschal ,season ends4 ,rogation ,sunday1 ,april #bfth2 ,rogation ,days1 the ,monday1 ,tuesday and ,wednesday after ,rogation ,sunday4 f--,ascension ,day 7,holy ,thursday71 ,april #cjth2 ,ascension-tide1 #aj #a ,expectation ,sunday1 ,first ,sunday after ,ascension1 ,may #c;d4 g--,whitsun ,day1 7,pentecost7 ,may #ajth2 ,whitsun-tide1 #g #a #c;d ,ember ,week1 after ,whitsun ,day2 ,ember ,days1 ,wednesday1 ,friday and ,saturday4 h--,trinity ,sunday1 ,may #agth2 #aif #bh ,trinity-tide1 #dth ,ember ,week1 after ,september #adth2 ,ember ,days1 ,wednesday1 ,friday and ,saturday4 ,all ,saints' ,day1 ,november #ast4 ,all ,souls' ,day1 ,november #b;d4 ---------------------------- ,appendix ,k4 #cfd #eb ---------------------------------------- ------------------------------ ---------------------------------------- ------------------------------ ,,year #ahhe-hf4 ,days in ,sundays in ,each ,season4,each ,season4 ---------------------------------------- ------------------------------ a--,advent ,sunday1 ,november #bith1 ,advent-tide1 #bf #d #ast ,ember ,week1 after ,december #acth2 ,ember ,days1 ,wednesday1 ,friday and ,saturday4 b--,christmas1 ,december #beth2 ,christmas-tide1 #ab #b c--,epiphany1 ,january #fth2 ,epiphany-tide1 #df #f ,septuagesima ,sunday1 ,february #bast1 #g #a ,paschal season1 from ,feb4 #bast to ,may #b;d1 #gj days4 ,sexagesima ,sunday1 ,february #bhth1 #g #a ,quinquagesima ,sunday1 ,march #gth1 #c #a ,shrove-tide1 7confession time7 ,shrove ,tues41 ,mar4 #ith4 d--,ash ,wednesday1 ,march #ajth1 ,lent begins2 ,lenten-tide #df #f ,first ,sunday in ,lent 7,quadragesima7 ,march #adth4 #b;d ,ember ,week after first ,sunday in ,lent2 ,ember ,days1 ,wednesday1 ,friday and ,saturday4 ,holy ,week1 the week before ,easter2 ,special ,days1 ,palm ,sunday1 ,spy ,wednesday1 ,maundy ,thursday and ,good ,friday1 ,april #ahth1 #bast1 #bb;d and #bc;d4 e--,easter ,sunday1 ,april #beth2 ,easter-tide1 #ci #f ,low ,sunday1 ,may #b;d1 ,paschal ,season ends4 ,rogation ,sunday1 ,may #cjth2 ,rogation ,days1 the ,monday1 ,tuesday and ,wednesday after ,rogation ,sunday4 f--,ascension ,day 7,holy ,thursday71 ,june #c;d2 ,ascension-tide1 #aj #a ,expectation ,sunday1 first ,sunday after ,ascension1 ,june #fth4 g--,whitsun ,day1 7,pentecost7 ,june #acth2 ,whitsun-tide1 #g #a #c;d ,ember ,week1 after ,whitsun ,day2 ,ember ,days1 ,wednesday1 ,friday and ,saturday4 h--,trinity ,sunday1 ,june #bjth2 ,trinity-tide1 #afa #bc #dth ,ember ,week1 after ,september #adth2 ,ember ,days1 ,wednesday1 ,friday and ,saturday4 ,all ,saints' ,day1 ,november #ast4 ,all ,souls' ,day1 ,november #b;d ---------------------------- ,appendix ,k4 #cfd #eb ---------------------------------------- ------------------------------ ,,chapter ,,viii4 ,,hebrew ,,calendar4 ,to the ,bible student a knowledge of the ,hebrew calendar is indispensable1 if he would know how the date of events recorded in the ,bible are made to correspond with our present ,english calendar4 ,from the exodus 7#adia ,b4 ,c47 downward1 the ,hebrew month was lunar1 and commenced invariably with the new moon4 ,dr4 ,smith1 author of ,bible ,dictionary1 says that the terms for month and moon have the same close connection in the ,hebrew language as in our own1 only the ,hebrew ,codesh 7that is new moon7 is1 perhaps1 more distinctive than the corresponding term in our language2 for it expresses not simply the idea of a lunation1 but the recurrence of a period commencing definitely with the new moon4 ,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 month1 each of the former ranging over portions of two of the latter1 still it can be shown how they may be made to coincide very nearly by a systematic method of intercalation4 ,now from new moon to new moon again1 is about #bi-a_/b days2 therefore1 the ,hebrew year consisted of #ced days1 for #bi-a_/b x #ab #ced2 so that the epact1 7which is the excess of the solar year beyond the lunar7 is eleven days4 ,hence1 had they no method of intercalation1 the commencement of their year would go back eleven days every year1 and consequently make a revolution of the seasons every thirty-three years1 for #cfe _/ #aa #cc nearly4 ,to illustrate1 let us suppose that the new moon of ,nisan1 which is the first month in the ,sacred year1 should on any given year fall on the #ajth of ,april1 then the following year it would fall on the #cjth of ,march1 which is eleven days earlier2 the second year it would fall on the #aith of ,march or twenty-two days earlier2 the third year the new moon would fall on the #hth of ,march or thirty-three days earlier1 but that would not be the new moon of ,nisan1 which cannot happen earlier than the #aath1 so the following moon which happens thirty days later on the #gth of ,april is the new moon of ,nisan4 ,hence it may be seen that by intercalating a full month every three years1 or which comes nearer to accuracy seven times in nineteen years1 restores the coincidence of the solar and the lunar year1 and consequently the moons to the same day of the month on which they fell nineteen years before4 ,the method of designating the months previous to the exodus1 was by their numerical order1 as the ancient ,hebrews had no particular name to express their month4 ,they said the first1 second and third month1 and so on4 ,no names of months appear in the ,bible until about the time of the institution of the passover1 when the ,lord spake unto ,moses and ,aaron in the land of ,egypt1 saying this month1 7,abib1 which appears to have had its origin in ,egypt17 shall be unto you the beginning of months2 it shall be the first month of the year to you4 ,the names of the months appear to belong to two distinct periods4 ,in the first place we have those peculiar to the ,jews previous to the captivity1 viz3 ,abib1 the first month in commemoration of the exodus2 ,zif1 the second1 ,ethanim1 the seventh1 and ,bul1 the eighth4 ,these names are of ,hebrew origin1 and have reference to the characteristics of the seasons1 a circumstance which clearly shows that the months1 by intercalation1 were made to return at the same period of the year4 ,thus1 ,abib was the month of the ears of corn1 that is the month in which the ears of corn became full1 or ripe on the #afth day1 that is the #b;d day of the feast of unleavened bread4 ,zif1 the month of blossoms or the bloom of flowers4 ,ethanim1 the month of gifts1 that is of fruits1 and ,bul1 the month of rain4 ,these were superceded after the captivity1 by ,nisan1 ,iyar1 ,tisri and ,hesvan1 or ,marchesvan4 ,marchesvan1 coinciding as it does with the rainy season in ,palestine1 is considered a pure ,hebrew term4 ,the modern ,jews consider it a compound word1 from mar1 drop1 and ,chesvan2 the former betokening that it was wet1 and the latter being the proper name of the month4 ,hence the name indicates the wet month4 ,in the second place we have the names of six others which appear in the ,bible subsequently to the ,babylonian captivity1 viz43 ,sivan1 the third2 ,elul1 the sixth2 ,kislev1 the ninth2 ,tebet1 the tenth2 ,sebat1 the eleventh1 and ,adar1 the twelfth4 ,there are two other months whose names do not appear in the ,bible1 viz43 ,tamuz1 the fourth1 and ,ab1 the fifth4 ,the name of the intercalary month is called ,ve-,adar1 or #b;d ,adar because placed in the calendar after ,adar and before ,nisan4 ,dr4 ,smith says these names are probably borrowed from the ,syrians in whose regular calendar we find names answering to most of them4 ,he also says it was the opinion of the ,talmudists1 that these names were introduced by the ,jews who returned from the ,babylonish captivity1 and also that they are certainly used exclusively by writers of the post-,babylonian period4 ,inasmuch as the ,hebrew months coincided with the seasons1 as we have already shown1 it follows as a matter of course1 that an additional month must have been inserted every third year1 which would bring the number up to thirteen4 ,no notice1 however1 is taken of this month in the ,bible1 neither have we reason to think that it was inserted according to any exact rule1 but it was added whenever it was discovered that the barley harvest did not coincide with the ordinary return of the month ,abib4 ,it has already been shown that in the modern ,jewish calendar the intercalary month is introduced seven times in nineteen years1 according to the ,metonic1 or lunar cycle which was adopted by the ,jews about #cfj ,a4 ,d4 ,the ,hebrew calendar is dated from the creation1 which is supposed to have taken place #cgfa years before ,christ4 ,hence1 to find the number of cycles elapsed since the creation1 also the number in the cycle1 we have the following rule3 ,add #cgfa to the date1 divide the sum by nineteen2 the quotient is the number of cycles1 and the remainder is the number in the cycle4 ,should there be no remainder1 the proposed year is1 of course1 the last or nineteenth of the cycle4 ,thus1 for the year #ahhc1 we have #ahhc #cgfa _/ #ai #big1 remainder #a2 therefore1 #big is the number of cycles1 and #a the number in the cycle4 ,again1 for the year #ahic1 we have #ahic #cgfa _/ #ai #big1 remainder #aa2 therefore #big is the number of cycles1 and #aa the number in the cycle4 ,again for the year #aija1 we have #aija #cgfa _/ #ai #bih1 remainder #j2 therefore #bih is the number of cycles1 and #ai the last of the cycle4 ,hence it may be seen that the present cycle commenced with #ahhc1 that #aa is the number in the cycle for the present year #ahic1 also that the cycle ends with #aija2 so that the next cycle commences with #aijb4 ,if the remainder after dividing by nineteen be #c1 #f1 #h1 #aa1 #ad1 #ag or #ai 7#j71 the year is intercalary or embolismic1 consisting of #chd days2 if otherwise it is ordinary1 containing only #ced days2 so that in a cycle of nineteen years1 we have twelve ordinary years of #ced days each1 and seven embolismic years of #chd days each4 ,but1 in either case1 the year is sometimes made a day more1 and sometimes a day less1 in order that certain festivals may fall on proper days of the week for their due observance4 ,hence the ordinary year may consist of #cec1 #ced or #cee days1 and the embolismic year of #chc1 #chd or #che days4 ,in the modern ,jewish calendar the ,new ,year commences with the new moon of ,tisri1 which may happen as early as the #eth of ,september or as late as the #eth of ,october4 ,the new moon of ,nisan1 which is the first month in the ,sacred year1 may happen as early as the #aath of ,march or as late as the #aath of ,april4 ,it should be borne in mind that the names of the months ,abib1 ,zif1 ,ethanim and ,bul were superceded after the captivity1 by ,nisan1 ,iyar1 ,tisri and ,hesvan or ,marchesvan2 also the name of the third month in the civil year1 ,chisleu in the ,bible1 ,kislev in the modern ,jewish calendar4 ,in table ,no4 #a we have the names of the months in numerical order1 also the number of days in each month4 ,though the months consist of #cj and #bi days alternately1 yet1 in the embolismic year1 ,adar1 which in common years has #bi days1 is given #cj days1 and #b;d ,adar #bi2 so that two months of #cj days come together4 ,table ,no4 #b shows the earliest and the latest possible date of the new moons of each of the months respectively4 ,,table #a4 ,,hebrew ,,months4 ,sacred ,year4 ,civil ,year4 ,nisan #cj ,tisri #cj ,iyar #bi ,hesvan #bi ,sivan #cj ,kislev #cj ,tamuz #bi ,tebet #bi ,ab #cj ,sebat #cj ,elul #bi ,adar #cj ,tisri #cj #b;d ,adar1 ,embolismic #bi ,hesvan #bi ,nisan #cj ,kislev #cj ,iyar #bi ,tebet #bi ,sivan #cj ,sebat #cj ,tamuz #bi ,adar #cj ,ab #cj #b;d ,adar1 ,embolismic #bi ,elul #bi ,,table ,,ii4 ,,hebrew ,,months4 ,nisan1 ,march #aath or ,april #aath ,iyar1 ,april #aath ,may #ajth ,sivan1 ,may #ajth ,june #ith ,tamuz1 ,june #ith ,july #ith ,ab1 ,july #ith ,august #gth ,elul1 ,august #gth ,september #eth ,tisri1 ,september #eth ,october #eth ,hesvan1 ,october #fth ,november #dth ,kislev1 ,november #dth ,december #c;d ,tebet1 ,december #c;d ,january #b;d ,sebat1 ,january #c;d ,february #ajth ,adar1 ,february #ajth ,march #abth ,the charts on the three following pages are used to illustrate the correspondence of the ,hebrew months with our own4 ,each chart represents the ecliptic1 which is the apparent path of the ,sun or real path of the ,earth1 also the names of the months as they occur in their seasons4 ,the figures represent the days of the month on which the new moons of the ,hebrew calendar fall4 ,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 years4 ,hence it may be seen that by intercalating a month every three years the new moons are restored1 very nearly1 to the place they occupied three years before4 ,,chart ,i4 ,illustration3 ,this chart represents the day of the month on which all the new moons fall in the year #ahia-ib4 ,the sacred year commenced with the new moon of ,nisan on the #ith of ,april1 and the civil year with the new moon of ,tisri on the #c;d of ,october1 #ahia1 and ended respectively with the #bhth of ,march and the #bast of ,september1 #ahib4 ,,chart ,,ii4 ,illustration3 ,this chart represents the day of the month on which all the new moons fall in the year #ahib-ic4 ,it may be here seen that the year begins and ends about eleven days earlier than the year preceding1 also that all the new moons fall eleven days earlier than they did in the preceding year4 ,,chart ,,iii4 ,illustration3 ,this chart represents the year #ahic-id4 ,though the year begins about eleven days earlier than the preceding1 viz43 the #agth of ,march1 yet it being the year in which a #b;d ,adar is intercalated1 instead of falling back eleven days1 the beginning of the following year is carried forward #bj days1 making a year of #chd days2 so that the year #ahid-ie will commence with ,april #e4 ,in #ahia we commenced with ,april #i4 ,it will be #ai years before we commence on the #ith of ,april again4 ,,appendix4 ,a4--,,page #ab4 ,authors differ in regard to the length of the solar year4 ,one gives #cfe days1 #e hours1 #dg minutes and #ea4e seconds2 another1 #cfe days1 #e hours1 #dh minutes and #df seconds2 and still another1 #cfe days1 #e hours1 #dh minutes and #di4fb seconds4 ,in this work the last has been accepted as the true length of the solar year1 and all calculations have been made accordingly4 ,b4--,,page #ai4 ,there is an apparent discrepancy among authors in regard to the intercalary day4 ,while one asserts that it was between the #bdth and #beth of ,february1 another equally reliable1 says that the #beth was the sexto calendas and the #bdth was the bis-sexto calendas of the ,julian calendar4 ,now it should be borne in mind that the ,julian calendar is the basis of our own1 and is identical with it in the number of months in the year1 and in the number of days in the month4 ,also when the method of numbering the days from the beginning of the month was adopted1 the intercalation was made to correspond with the intercalary day in the ,julian calendar4 ,as in the ,julian calendar there were twice the sixth day1 so in the reformed calendar there were twice the #bdth day1 which was equivalent to #bi days in ,february4 ,when the calendar was again corrected1 making the #bith the intercalary day1 then the #bdth corresponded with the bis-sexto calendas of the ,julian calendar4 ,this reconciles the apparent discrepancy4 ,while one author refers to the calendar in which the ,julian rule of intercalation is adopted1 another refers to the calendar when so corrected as to make the #bith of ,february the intercalary day4 ,see following table3 ---------------------------------------- ------------------------------ ,,julian ,,method ,,modern ,,method ,,of ,,intercalation4 ,,of ,,intercalation4 ---------------------------------------- ------------------------------ #a ,cal4 ,calendae #a ,cal4 ,calendae #b #d ,quarto ,nonas #b #d ,quarto ,nonas #c #c ,tertio ,nonas #c #c ,tertio ,nonas #d #b ,pridie ,nonas #d #b ,pridie ,nonas #e ,nomes ,nonae #e ,nomes ,nonae #f #h ,octavo ,idus #f #h ,octavo ,idus #g #g ,septimo ,idus #g #g ,septimo ,ides #h #f ,sexto ,idus #h #f ,sexto ,idus #i #e ,quinto ,idus #i #e ,quinto ,idus #aj #d ,quarto ,idus #aj #d ,quarto ,idus #aa #c ,tertio ,idus #aa #c ,tertio ,idus #ab #b ,pridie ,idus #ab #b ,pridie ,idus #ac ,ides ,idus #ac ,ides ,idus #ad #af ,sextodecimo ,calendas #ad #af ,sextodecimo ,calendas #ae #ae ,quintodecimo ,calendas #ae #ae ,quintodecimo ,calendas #af #ad ,quartodecimo ,calendas #af #ad ,quartodecimo ,calendas #ag #ac ,tertiodecimo ,calendas #ag #ac ,tertiodecimo ,calendas #ah #ab ,duodecimo ,calendas #ah #ab ,duodecimo ,calendas #ai #aa ,undecimo ,calendas #ai #aa ,undecimo ,calendas #bj #aj ,decimo ,calendas #bj #aj ,decimo ,calendas #ba #i ,nono ,calendas #ba #i ,nono ,calendas #bb #h ,octavo ,calendas #bb #h ,octavo ,calendas #bc #g ,septimo ,calendas #bc #g ,septimo ,calendas #bd #f ,bis-,sexto ,calendas #bd #f ,bis-sexto ,calendas #bd #f ,sexto ,calendas #be #f ,sexto ,calendas #be #e ,quinto ,calendas #bf #e ,quinto ,calendas #bf #d ,quarto ,calendas #bg #d ,quarto ,calendas #bg #c ,tertio ,calendas #bh #c ,tertio ,calendas #bh #b ,pridie ,calendas #bi #b ,pridie ,calendas ---------------------------------------- -------------------------- ,c4--,,page #bj4 ,the city where the great council was convened in #cbe is not in ,france1 as some have supposed1 that being a more modern city of the same orthography1 but pronounced ,nees4 ,the city which is so frequently referred to in this work is in ,bythinia1 one of the provinces of ,asia ,minor1 situated about #ed miles southeast of ,constantinople1 of the same orthography as the former1 but pronounced ,ni'ce1 and was so named by ,lysimachus1 a ,greek general1 about #cjj years before ,christ1 in honor of his wife ,nicea4 ,d4--,,page #bc4 ,between the #bc;d and #bdth of ,february1 #df years before ,christ1 there was intercalated a month of #bc days according to an established method1 but still the civil year was in advance of the solar year by #fg days2 so that when the ,earth in her annual revolutions should arrive to that point of the ecliptic marked the #bb;d of ,october1 it would be the #ast day of ,january in the ,roman year4 ,caesar and his astronomers1 knowing this fact and fixing on the #ast day of ,january1 #de years before ,christ and #gji from the foundation of ,rome1 for the reformed calendar to take effect1 were under the necessity of intercalating two months1 together consisting of #fg days4 ,now1 as the civil year would end on the #bb;d of ,october1 true or solar time1 it would be reckoned in the old calendar the #ast day of ,january2 so they let the old calendar come to a stand while the ,earth performs #fg diurnal revolutions1 and thereby restored the concurrence of the solar and the civil year4 ,as an illustration1 let us suppose that in a certain shop where hangs a regulator are two clocks to be regulated4 ,both are set with the regulator at #h a4 m4 to see how they will run for ten consecutive hours4 ,it was found that when it was #f p4 m41 by the first clock1 it was #e3ej by the regulator1 the clock having gained one minute every hour4 ,to rectify this discrepancy we must intercalate #aj minutes by stopping the clock until it is #f by the regulator4 ,by this means the coincidence is restored1 and the time lost in the preceding hours is now reckoned in this last hour1 making it to consist of #gj minutes4 ,by this it may be seen how ,caesar reformed the ,roman calendar4 ,the ,roman year was too short1 by reason of which the calendar was thrown into confusion1 being #ij days in advance of the true time1 so that ,december1 ,january and ,february took the place in the seasons of ,september1 ,october and ,november1 and ,september1 ,october and ,november the place of ,june1 ,july and ,august4 ,to make the correction he must stop the old ,roman clock 7the calendar7 while the ,earth performs #ij diurnal revolutions to restore the concurrence of the solar and the civil year1 making the year #df ,b4 ,c4 to consist of #dde days4 ,it was also found that when it was #f p4 m41 by the regulator1 it was only #e3ej by the second clock1 it having lost one minute every hour4 ,to rectify this discrepancy we must suppress #aj minutes1 calling it #f p4 m41 turning the hands of the clock to coincide with the regulator1 making the last hour to consist of only #ej minutes1 too much time having been reckoned in the preceding hours4 ,it may be seen by this illustration1 how ,gregory corrected the ,julian calendar1 the ,julian year was too long1 consequently behind true or solar time1 so that when the correction was made in #aehb1 the ten days gained had to be suppressed to restore the coincidence1 making the year to consist of only #cee days4 ,as the solar year consists of #cfe days and a fraction1 ,caesar intended to retain the concurrence of the solar and the civil year by intercalating a day every four years2 but this made the year a little too long1 by reason of which it became necessary1 in #aehb1 to rectify the error1 and by adopting the ,gregorian rule1 three intercalations are suppressed every #djj years2 so that by a series of intercalations and suppressions1 our calendar may be preserved in its present state of perfection4 ,e4--,,page #bc4 ,as the day and the civil year always commence at the same instance1 so they must end at the same instance2 and as the solar year always ends with a fraction1 not only of a day1 but of an hour1 a minute and even a second2 so there is no rule of intercalation by which the solar and the civil year can be made to coincide exactly4 ,but the discrepancy is only a few hours in a hundred years1 and that is so corrected by the ,gregorian rule of intercalation that it would amount to a little more than a day in #d1jjj years2 and by the improved method less than a day in #ajj1jjj years4 ,f4--,,page #bf4 ,it has been stated that by adopting the ,julian rule of intercalation1 time was gained2 it has also been stated that by the same rule time was lost4 ,now both are true4 ,time is gained in that there is too much time in a given year1 in other words1 the year is too long2 but what is gained in a given year is lost to the following year4 ,as an illustration let us take the case of the supposed solar year of #cfe days1 and the civil year of #cff4 ,the civil year would gain one day every year1 or be too long by one day2 but the one day gained is lost to the following years1 and if continued #ca years1 when the ,earth is in that part of its orbit marked the #ast day of ,january #cb1 the civil year would reckon the #ast day of ,december #ca2 so that in the thirty-one years would reckon thirty-one days too much1 and before the civil year is completed1 the ,earth will have passed on in its orbit to a point marked the #ast day of ,february4 ,now to reform such a calendar1 we would have to suppress or drop the thirty-one days1 by calling the #ast day of ,december the #ast day of ,january1 and thus the month of ,december would disappear from the calendar in the year #ca1 making a year of only eleven months1 consisting of #ccd days4 ,if this method be continued #ib years1 there would be gained #ib days1 to the loss of #ib days in the year #ib4 ,if the calendar be now reformed by suppressing #ib days1 calling the #ast day of ,october1 #ib1 the #ast day of ,january1 #ic1 then ,october1 ,november and ,december would disappear from the calendar in the year #ib2 and if continued #cfe years there would be crowded into #cfd years1 #cfd days too much2 gained to the #cfd years to the total loss of the year #cfe1 passing from #cfd to #cff2 #cfe disappearing from the calendar4 ,g4--,,page #ej4 ,an era is a fixed point of time from which a series of years is reckoned4 ,among the nations of the ,earth there are no less than twenty-five different eras2 but the most of them are not of enough importance to be mentioned here4 ,attention is particularly called to the ,roman era which commenced with the building of the city of ,rome #gec years before ,christ4 ,also the ,mahometan era1 or the era of the ,hegira1 employed in ,turkey1 ,persia and ,arabia1 which is dated from the flight of ,mahomet from ,mecca to ,medina1 which was ,thursday night1 the #aeth of ,july1 ,a4 ,d41 #fbb1 and it commenced on ,friday1 the day following4 ,but there is a point from which all computation originally commenced1 namely1 the creation of man4 ,such an era is called the ,mundane era4 ,now there are different ,mundane eras--the common ,mundane era #d1jjd ,b4 ,c41 the ,grecian ,mundane era #e1eih ,b4 ,c41 and the ,jewish ,mundane era #c1gfa ,b4 ,c4 ,all these commence computation from the same point1 but differ in regard to the time which has elapsed since their computation commenced4 ,god's people used the ,mundane era1 until the ,great ,creator appeared among us1 as one of us1 in the person of our ,lord ,jesus ,christ1 to accomplish the great work of redemption2 then ,his name was introduced as the turning point of the ages1 the starting point of computation4 ,this was done by ,dionysius ,exiguus in the year of our ,lord about #edj1 known at that time as the ,dionysian1 as well as the ,christian era1 and was first used in historical works by the venerable ,bede early in the eighth century4 ,it was a great thought of the little monk 7whether so called from his humility or littleness of stature is unknown71 to view ,christ as the turning point of the ages1 and to introduce this view into chronology4 ,all honor to him who introduced it1 and to the nations which have approved1 for thus honoring the ,great ,redeemer4 ,dionysius probably did not know1 neither is it now known for a certainty the year of ,christ's birth1 but it is evident1 however1 from the best authorities1 that the era commenced at least five years too late1 and probably more4 ,h4--,,page #eg4 ,it is recorded that1 in the time of ,numa1 the vernal equinox fell on the #beth of ,march1 and that ,julius ,caesar restored it to the #beth1 when he reformed the ancient ,roman calendar in the year #df ,b4 ,c4 ,it is also recorded that in less than #djj years from that time1 at the meeting of the ,council of ,nice in #cbe1 it had fallen back to the #bast--four days in less than #djj years4 ,now there is an error somewhere1 for it is found by actual computation that the discrepancy between the solar and the ,julian year is about three days in #djj years4 ,it certainly is true that the vernal equinox fell on the #bast in #cbe1 and was restored to that place by ,gregory in #aehb2 since which time it has been made to fall on the #bast by the ,gregorian rule of intercalation4 ,again it is stated by the same author that the discrepancies in time from ,caesar to ,gregory is thirteen days1 from the ,council of ,nice to ,gregory ten days2 now #aj #d #ad4 ,while our author states it is thirteen days1 he also states it is fourteen days2 a discrepancy of one day4 ,the mistake evidently is in making the #beth instead of the #bdth1 the date of the vernal equinox in the time of ,caesar1 consequently a difference of four days instead of three from ,caesar to the ,council of ,nice4 ,i4--,,page #ei4 ,the concurrence of the solar and the civil year was restored by ,gregory in #aehb1 or #afjj is the same in computation2 but the discrepancy between civil and solar time is #aa minutes and #aj4ch seconds every year1 which in #ajj years will amount to #ah hours1 and #cg4c minutes2 reckoned in round numbers #ah hours1 and is represented on the chart1 hours behind time #ah4 ,the intercalary day or #bd hours being suppressed in #agjj1 causes the civil year to be #f hours in advance of the solar1 and is represented on the chart #f hours in advance4 ,now this discrepancy of #ah hours for the next #ajj years1 will cause the civil year in #ahjj to be #ab hours behind2 again suppressing the intercalation it will be #ab hours in advance4 ,in #aijj it will be #f hours behind1 but the correction makes #ah hours in advance4 ,the #ah hours gained the next #ajj years restores the coincidence in the year #bjjj and so on1 the solar and the civil year being made to coincide very nearly every #djj years4 ,from close examination it will become evident that the solar and the civil year coincide twice every #djj years1 though no account is made of it in computation4 ,from #f hours in advance in #agjj1 the civil year falls back to #ab hours behind the solar in #ahjj1 consequently they must coincide in #agcc4 ,again from #ab hours in advance in #ahjj1 it falls back to #f hours behind the solar in #aijj1 consequently they must coincide again in #ahfg4 ,discrepancy between ,julian and solar time in--#a year is 7#cfe;d4 #f;h47 - 7#cfe;d4 #e;h4 #dhm4 #di4fbs47 7#aam4 #aj4chs47 #ajj years is 7#aam4 #aj4chs47 x #ajj 7#ah;h4 #cg4c47 #djj 7#ah;h4 #cg4cm47 x #d 7#c;d4 #b;h4 #bi4bm47 #d1jjj 7#c;d4 #b;h4 #bi4bm47 x #aj 7#ca;d4 #j;h4 #ebm47 #ajj1jjj 7#ca;d4 #j;h4 #ebm47 x #be 7#ggc;d4 #ba;h4 #djm47 ,discrepancy between ,gregorian and solar time in-- #a year is 4#cgcm4 #ajj years is 4#cgcm4 x #ajj #cg4cm4 #djj years #cg4cm4 x #d #b;h4 #bi4bm4 #d1jjj 7#b;h4 #bi4bm47 x #aj #a;d4 #j;h4 #ebm4 #ajj1jjj 7#a;d4 #j;h4 #ebm47 x #be #be;d4 #ba;h4 #djm4 ,discrepancy between corrected ,gregorian and solar time in-- #d1jjj years is 7#a;d4 #j;h4 #ebm47 - #a day #ebm4 #ajj1jjj 7#ebm4 x #be7 #ba;h4 #djm4 ,j4--,,page #hi4 ,lilius1 author of the ,extended ,table of ,epacts1 says1 when the full moon falls on the #ajth of ,march1 the following moon1 which happens #bi days later1 is the paschal moon1 making the #ahth of ,april its latest possible date4 ,for1 says he1 because of the double epact that occurs on the #dth and #eth of ,april that lunation has only #bi days4 ,it may have been very convenient for ,lilius1 in his peculiar method of determining the date of the paschal moon1 to give to that lunation only #bi days2 but nevertheless1 when he did so1 it was at the expense of accuracy1 for he makes a difference of #ab days in the date of the paschal moon of that year1 and the year preceding1 and only #aj days difference between that year and the succeeding year2 whereas the difference is uniformly #aa days from year to year through the whole cycle of #ai years4 ,by referring to the table on the #ic;d page1 it will be seen that1 in fixing the date of the paschal moon1 six times in a cycle of #ai years the full moon falls before the #bast of ,march1 and in every instance except this one the following moon is reckoned by ,lilius #cj days later4 ,by this uniform method of determining the date of the paschal moon1 we make the #aith of ,april instead of the #ahth1 its latest possible date2 so it should be borne in mind that whenever the #aith of ,april is the date of the paschal moon1 as indicated in the tables commencing with the #ic;d page1 that ,lilius1 and probably most1 if not all other authors1 have the #ahth4 ,now it is admitted that notwithstanding the cumbersome apparatus employed by ,lilius in his calculations1 the conditions of the problem are not always satisfied1 nor is it possible that they can be always satisfied by any similar method of proceeding4 ,we admit that none of these calculations are perfectly exact1 but the sum of the solar and lunar inequalities is compensated in the whole period1 or corrections made at the end of certain periods1 not by interrupting the order of a uniform method during the cycle of #ai years4 ,now the table of epacts was introduced by ,lilius himself1 making the excess of the solar year beyond the lunar1 in round numbers #aa days4 ,then why interrupt this order every #ai years1 for a period of #aad years2 that is from #aeif to #agaj1 by making the epact #ab days for one year1 and the following year only #aj8 ,after which1 from #agaj to #aijj1 a period of #aij years1 according to ,lilius' own calculations1 the epact is uniformly #aa days1 coinciding exactly with the calculations made in this work4 ,then again after the year #aijj1 he gives to that particular lunation1 in every lunar cycle for a period of #cjd years1 only #bi days2 and having done so1 he is under the necessity of giving only #bi days to another lunation in the same cycle1 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 cycle4 ,by reference to the #ajast page1 opposite the year #aije1 it will be seen that the date of the paschal moon is the #aith of ,april4 ,lilius1 by giving to that lunation only #bi days1 makes its date the #ahth2 and then again in the year #aiaf1 lest he should make the paschal moon fall twice on the #ahth of ,april in the course of a lunar cycle1 7a thing which cannot really occur7 he for the first time in more than #djj years1 gives only #bi days to a second lunation in the same cycle and of course to all the cycles in the period of #cjd years4 ,now the epacts for a lunar cycle of #ai years are represented thus3 #bf -- #j1 #aa1 #bb1 #c1 #ad1 #be1 #f1 #ag1 #bh1 #i1 #bj #bg -- #a1 #ab1 #bc1 #d1 #ae1 #bf1 #g1 #ah ,the number #bf placed over the #be shows ,lilius' first error in giving to that lunation only #bi days4 ,he thereby makes a difference of #ab days between the epact #ad and #bf1 and only #aj between #bf and #f4 ,he now has two epacts of the same number #bf4 ,in order to get out of the dilemma he makes that #bg1 by giving to another lunation only #bi days4 ,k4--,,page #abb-c4 ,it will probably be noticed that according to the showing in the tables the ecclesiastical year contains only #cfd days4 ,the reason for this is1 that ,advent ,sunday1 which is the first day of the year1 happens one day earlier every year until it occurs on the #bgth of ,november1 its earliest possible date2 then the first ,sunday after the #bfth of ,november1 which is ,advent ,sunday1 falls on the #c;d of ,december1 its latest possible date1 so that the year begins six days later1 making a year of #cga days4 ,then there is the loss of a day every year until ,advent ,sunday again falls on the #bgth of ,november and so on4 ,hence1 did the civil year always consist of #cfe days1 then the ecclesiastical year would always contain either #cfd or #cga days4 ,but as every fourth year contains #cff days1 this order is so interrupted that sometimes the first ,sunday falls on the #b;d instead of the #c;d of ,december2 so that the year begins only five days later1 making a year of only #cgj days4 ,hence the ecclesiastical year may consist of either #cfd1 #cgj or #cga days4 ,but five times out of six it will contain only #cfd days4 ,l4--,,page #hc4 ,but why did the ,pope1 in correcting the ,julian calendar in #aehb1 not correct the whole error of thirteen days8 ,why did he leave the three days uncorrected8 ,this question has been asked an hundred times1 but a correct answer has never yet been given4 ,some say that the ,pope did according to his best ability1 and would make us believe that neither he nor his astronomers knew what the error was4 ,this is not true1 for history records the fact of the error1 and just what that error was4 ,he simply did not want to correct the three days1 and for good reasons1 which we shall endeavor to show2 reasons which every churchman ought to know4 ,when ,caesar formed his calendar1 #df ,b4 ,c41 the vernal equinox fell on the #bdth of ,march4 ,at the meeting of the ,council of ,nice1 in #cbe1 it had fallen back to the #bast1 the error being three days in about #djj years4 ,now it should be borne in mind that the ,julian calendar was the only one in use at that time1 and for the next #abeg years1 when in #aehb1 it was corrected by ,pope ,gregory ,,xiii4 ,easter1 and all the movable feasts1 had been unsettled during the #abeg years intervening1 from the ,council of ,nice to ,gregory1 on account of the errors of the ,julian calendar4 ,the ,easter question had been the cause of a good deal of discussion between the ,eastern and ,western churches during the second and third centuries1 as they could not agree on the day of the week on which that event should be celebrated4 ,the ,western churches observed the nearest ,sunday to the full moon of ,nisan4 ,the ,asiatics1 on the other hand1 adopted the #adth of ,nisan upon which to commemorate the crucifixion1 and observed the festival of ,easter on the third day following1 upon whatever day of the week that might fall4 ,finally1 the ,council of ,nice was convened1 and the matter came before that council1 and a reconciliation was accomplished4 ,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 equinox1 and that the #bast of ,march should be accounted the day of the vernal equinox4 ,it has already been shown that the error in the ,julian calendar is three days in #djj years2 so that in #djj years from the ,council of ,nice the vernal equinox had fallen back to the #ahth of ,march2 in #hjj years it had fallen back to the #aeth2 in #abeg years1 that is in #aehb1 it fell on the #aath4 ,still the #bast of ,march1 by the only calendar in use at that time1 was accounted the date of the vernal equinox1 by which date ,easter was determined1 so that1 in #aehb1 when it was the #bast by the calendar1 the correct date was the #cast4 ,hence1 the error had been increasing at the rate of three days every #djj years until in #aehb it amounted to ten days4 ,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 ,easter1 so he drops the ten days and restores the vernal equinox to the #bast of ,march1 its date at the meeting of the ,council of ,nice in #cbe1 the date by which ,easter day was determined4 ,he not only made the correction1 but he so reformed the calendar that the solar and the civil year are now made to coincide very nearly4 ,had he dropped the thirteen days1 the vernal equinox would have been restored to the #bdth of ,march1 its date in the time of ,caesar1 and the #bdth would still be its date4 ,but the ,council of ,nice decided that the #bast should be the date by which ,easter day should be determined4 ,hence the reason for dropping the ten days instead of the thirteen is evident2 and it is also evident that the ,pope acted understandingly when he made the correction in #aehb4 ,,errata4 ,on #east page1 ninth line from the bottom of the page1 instead of #adec _/ #dc #fc1 should be #adec _/ #d #cfc4 ,on #gfth page1 twelfth line from the top of the page1 #cef should be #cfe4 ,,the ,,columbus ,,celebration4 ,,the ,,wellsboro ,,man ,,who ,,brought ,,about ,,the ,,change ,,in ,,the ,,date4 ,state ,superintendent ,d4 ,j4 ,waller1 in the ,school ,journal4 ,who brought about the change in the date8 ,it was down in the books as ,october #abth4 ,the ,committee of the ,national ,educational ,association issued circulars to the country to observe that day4 ,congress solemnly resolved that that day should be celebrated throughout the land4 ,the ,commissioners of the ,world's ,fair fixed upon ,october #ab1 as dedication-day1 and sent out invitations to the exercises4 ,suddenly there was a change4 ,heralded by no newspaper discussion1 preceded by no exhaustive treatise1 without any authoritative decree1 a change was made to ,october #ba4 ,the following facts are indisputable4 ,an aged retired minister in the ,methodist ,episcopal ,church1 living in ,wellsboro1 ,tioga ,county1 ,pa41 author of a little book entitled ,our ,calendar1 ,rev4 ,george ,nichols ,packer1 saw the error4 ,he possessed the confidence of ,judge ,henry ,w4 ,williams1 of the ,supreme ,court of ,pennsylvania4 ,after laying the facts before him1 he secured through him the approval by the several ,justices composing that body1 of an effort to change to the proper date1 ,october #bast4 ,equipped with this approval1 he secured the endorsement of his project by ,governor ,pattison and some of the heads of the ,executive departments at ,harrisburg4 ,he then went to ,washington1 gained an audience with the ,president1 laid the subject before the member of ,congress from his district1 and went before the ,congressional ,committee4 ,the evidence in support of the proposition was so presented that it could not be successfully disputed4 ,congressman ,w4 ,a4 ,stone skillfully enlisted influential collegiates in an effort to correct the error already widely spread4 ,the correction by the ,national ,legislature was in time to have its influence upon ,president ,harrison1 who named ,october #ba in his proclamation1 as the day to be observed1 and ,boston and ,chicago fell into line4 ,all honor to ,rev4 ,george ,nichols ,packer1 of ,wellsboro1 ,tioga ,county1 ,pennsylvania4 ,transcriber's ,notes3 ,passages in italics are indicated by italics4 ,punctuation has been corrected without note4 ,corrections noted in the ,errata section have been applied to the text4 ,the following misprints have been corrected3 aad corrected to and 7page #h7 leap-year corrected to leap-years 7page #de7 missing the added 7page #de7 #aiic corrected to #agic 7page #fc7 co-incide standardized to coincide 7page #ga7 ,caesar standardized to ,caesar 7page #ga7 conseqently corrected to consequently 7page #gd7 #agcf corrected to #agcg 7page #if7 countenace corrected to countenance 7page #aad7 ,other than the corrections listed above1 inconsistencies in spelling and hyphenation have been retained from the original4 ,on page #cg1 #c #djj is presented with a space as in the original text4