,transcriber's note ,a list of the changes made can be found at the end of the book4 ,formatting and special characters are indicated as follows3 italic bold gesperrt ,,remarks ,,upon ,,the ,,solar ,,and ,,the ,,lunar ,,years1 ,the ,cycle of #ai ,years1 commonly called ,,the ,,golden ,,number1 ,,the ,,epact1 ,and a ,method of finding the ,time of ,easter1 as it is now observed in most ,parts of ,europe4 ,being ,part of a ,,letter from ,the ,right ,honourable ,,george ,,earl ,,of ,,macclesfield to ,martin ,folkes ,esq2 ,president of the ,royal ,society1 and by him communicated to the same1 ,may #aj4 #agej4 ,,london3 ,printed for ,,charles ,,davis1 ,printer to the ,royal ,society4 ,m4,,dcc4,,li4 ,a ,,table1 shewing1 by means of the ,golden ,numbers1 the several ,days on which the ,paschal ,limits or ,full ,moons1 according to the ,gregorian ,account1 have already happened1 or will hereafter happen2 from the ,reformation of the ,calendar in the ,year of our ,lord #aehb1 to the ,year #daii inclusive4 ,to find the ,day on which the ,paschal ,limit or ,full ,moon falls in any given ,year2 ,look1 in the ,column of ,golden ,numbers belonging to that ,period of ,time wherein the given ,year is contained1 for the ,golden ,number of that ,year2 over-against which1 in the same ,line continued to the ,column intitled ,paschal ,full ,moons1 you will find the ,day of the ,month1 on which the ,paschal ,limit or ,full ,moon happens in that ,year4 ,and the ,sunday next after that ,day is ,easter ,day in that ,year1 according to the ,gregorian ,account4 ---------------------------------------- ------------------- ,golden ,numbers from the ,year #aehc to #afii1 and so on to #daii1 all inclusive4 ---------------------------------------- -------- #aehcagjjaijjbbjjbcjjbdjjbejjbfjjbijjcaj jcdjjcejj to to to to to to to to to to to to #afiiahiibaiibbiibciibdiibeiibhiicjiicci icdiiceii ---------------------------------------- -------- #c #ad 44 #f #ag #f #ag 44 #i 44 #a #ab 44 #c #ad 44 #f 44 #f #ag 44 #i 44 #a #aa 44 #c #ad 44 #ad 44 #f #ag 44 #i 44 44 #aa 44 #c #ad #c #ad 44 #f #ag 44 #i #ai 44 #aa 44 #c 44 #c #ad 44 #f #ag 44 #h #ai 44 #aa 44 #aa 44 #c #ad 44 #f #ag 44 #h #ai 44 #aa 44 #aa 44 #c #ad 44 #f #af 44 #h #ai 44 #ai 44 #aa 44 #c #ad 44 #e #af 44 #h #ai #h #ai 44 #aa 44 #c #ad 44 #e #af 44 #h 44 #h #ai 44 #aa 44 #c #ac 44 #e #af 44 #af 44 #h #ai 44 #aa 44 #b #ac 44 #e #af #e #af 44 #h #ai 44 #aa 44 #b #ac 44 #e 44 #e #af 44 #h #ai 44 #aj 44 #b #ac 44 #ac 44 #e #af 44 #h #ai 44 #aj 44 #b #ac #b #ac 44 #e #af 44 #h #ah 44 #aj 44 #b 44 #b #ac 44 #e #af 44 #g #ah 44 #aj 44 #aj 44 #b #ac 44 #e #af 44 #g #ah 44 #aj 44 #aj 44 #b #ac 44 #e #ae 44 #g #ah 44 #ah 44 #aj 44 #b #ac 44 #d #ae 44 #g #ah #g #ah 44 #aj 44 #b #ac 44 #d #ae 44 #g 44 #g #ah 44 #aj 44 #b #ab 44 #d #ae 44 #ae 44 #g #ah 44 #aj 44 #a #ab 44 #d #ae #d #ae 44 #g #ah 44 #aj 44 #a #ab 44 #d 44 #d #ae 44 #g #ah 44 #i 44 #a #ab 44 #ab 44 #d #ae 44 #g #ah 44 #i 44 #a #ab #a #ab 44 #d #ae 44 #g #ag 44 #i 44 #a 44 #a #ab 44 #d #ae 44 #f #ag #ag #i 44 #i 44 #a #ab #ab #d #ae #ad #f #f #ag #i #ag #i #i #a #a #ab #d ---------------------------------------- -------- ---------------------------------------- ----------------- ,golden ,numbers from the ,year #aehc to #afii1 ,paschal and so on to #daii1 all inclusive4 ,full ,moons4 ---------------------------------------- ------------ #cfjjcgjjchjjdajj ,days of the to to to to ,month1 and #cfiicgiidjiidaii ,sunday ,letters ---------------------------------------- ------------ #a #ab 44 #d ,march #ba4 ,c 44 #a #ab 44 #bb4 ,d #i 44 #a #ab #bc4 ,e 44 #i 44 #a #bd4 ,f #ag 44 #i 44 #be4 ,g #f #ag 44 #i #bf4 ,a 44 #f #ag 44 #bg4 ,b #ad 44 #f #ag #bh4 ,c #c #ad 44 #f #bi4 ,d 44 #c #ad 44 #cj4 ,e #aa 44 #c #ad #ca4 ,f 44 #aa 44 #c ,april #a4 ,g #ai 44 #aa 44 #b4 ,a #h #ai 44 #aa #c4 ,b 44 #h #ai 44 #d4 ,c #af 44 #h #ai #e4 ,d #e #af 44 #h #f4 ,e 44 #e #af 44 #g4 ,f #ac 44 #e #af #h4 ,g #b #ac 44 #e #i4 ,a 44 #b #ac 44 #aj4 ,b #aj 44 #b #ac #aa4 ,c 44 #aj 44 #b #ab4 ,d #ah 44 #aj 44 #ac4 ,e #g #ah 44 #aj #ad4 ,f 44 #g #ah 44 #ae4 ,g #ae 44 #g #ah #af4 ,a #d #ae #ae #g #ag4 ,b #ab #d #d #ae #ah4 ,c #ai4 ,d #bj4 ,e #ba4 ,f #bb4 ,g #bc4 ,a #bd4 ,b #be4 ,c ---------------------------------------- ------------- ,remarks upon the ,solar and the ,lunar ,years1 the ,cycle of #ai ,years1 commonly called the ,golden ,number1 the ,epact1 and a ,method of finding the ,time of ,easter1 as it is now observed in most ,parts of ,europe4 ,being ,part of a ,letter from the ,right ,honourable ,george ,earl of ,macclesfield to ,martin ,folkes ,esq2 ,president of the ,royal ,society4 ,of the ,solar ,year4 ,read ,may #aj4 #agej4 ,,the mean ,tropical ,solar ,year1 or that mean ,space of ,time wherein the ,sun1 or ,earth1 after departing from any ,point of the ,ecliptic returns to the same again1 consists1 according to ,dr4 ,halley's ,tables1 of #cfe;d1 #e;h1 #dh1 #ee3 ,which is less by #aa1 #e1 than the mean ,julian ,year1 consisting of #cfe;d1 #f;h1 #j1 #j4 ,hence the ,equinoxes and ,solstices anticipate1 or come earlier than the ,julian ,account supposes them to do by #aa1 #e1 in each mean ,julian ,year2 or #dd1 #bj in every four2 or #c;d1 #a;h1 #ec1 #bj1 in every four hundred ,julian ,years4 ,in order to correct this ,error in the ,julian ,year1 the ,authors of the ,gregorian ,method of regulating the ,year1 when they reformed the ,calendar in the ,beginning of ,october #aehb1 directed that three intercalary ,days should be omitted or dropped in every four hundred ,years2 by reckoning all those ,years1 whose ,date consists of a ,number of entire ,hundreds not divisible by #d1 such as #agjj1 #ahjj1 #aijj1 #bajj1 c4 to be only ,common1 and not ,bissextile or ,leap ,years1 as they would otherwise have been2 and consequently omitting the intercalary ,days1 which1 according to the ,julian ,account1 should have been inserted in the ,month of ,february in those ,years4 ,but at the same time they order'd that every fourth hundredth ,year1 consisting of a ,number of entire ,hundreds1 divisible by #d1 such as #afjj1 #bjjj1 #bdjj1 #bhjj1 c4 should still be consider'd as ,bissextile or ,leap ,years1 and1 of consequence1 that one ,day should be intercalated as usual in those ,years4 ,this ,correction1 however1 did not entirely remove the ,error3 ,for the ,equinoxes and ,solstices still anticipate #a;h1 #ec1 #bj in every four hundred ,gregorian ,years4 ,but that ,difference is so inconsiderable as not to amount to twenty-four ,hours1 or to one whole ,day1 in less than #ejhb ,gregorian ,years4 ,of the ,lunar ,year1 ,cycle of #ai ,years1 and the ,epact4 ,the ,space of ,time betwixt one mean ,conjunction of the ,moon with the ,sun and the next following1 or a mean ,synodical ,month1 is equal to #bi;d1 #ab;h1 #dd1 #c1 #b1 #ef;,,iv according to ,mr4 ,pound's ,tables of mean ,conjunctions4 ,the ,common ,lunar ,year consists of #ab such ,months4 ,the ,intercalary or ,emboliman ,year consists of #ac such ,months4 ,in each ,cycle of #ai ,lunar ,years1 there are #ab ,common1 and #g ,intercalary or ,emboliman ,years1 making together #bce ,synodical ,months4 ,it was thought1 at the time of the ,general ,council of ,nice1 which was holden in the ,year of our ,lord #cbe1 that #ai ,julian ,solar ,years were exactly equal to such a ,cycle of #ai ,lunar ,years1 or to #bce ,synodical ,months2 and therefore1 that1 at the ,end of #ai ,years1 the ,new ,moons or ,conjunctions would happen exactly at the same ,times1 as they did #ai ,years before3 ,and upon this ,supposition it was1 that1 some time afterwards1 the several ,numbers of that ,cycle1 commonly called the ,golden ,numbers1 were prefixed to all those ,days in the ,calendar1 on which the ,new ,moons then happened in the respective ,years corresponding to those ,numbers2 it being imagined1 that whensoever any of those ,numbers should for the future be the ,golden ,number of the ,year1 the ,new ,moons would invariably happen on those ,days in the several ,months1 to which that ,number was prefixed4 ,but this was a ,mistake3 d h ,for #ai ,julian ,solar ,years contain #fici1 #ah1 #j1 #j1 #j ,whereas #bce ,synodical ,months contain only #fici1 #af1 #ca1 #ef1 #cj ---------------------- ,and are therefore less than #ai ,julian ,solar ,years by #j1 #a1 #bh1 #c1 #cj4 ,this ,difference amounts to a whole ,day very nearly in #caj4g ,years1 the ,new ,moons anticipating1 or falling earlier1 by #bd ,hours in that ,space of ,time1 than they did before3 ,and therefore now in the ,year #agej1 the ,new ,moons happen above four ,days and a half sooner1 than the ,times pointed out by the ,golden ,numbers in the ,calendar4 ,in order therefore to preserve a sort of regular ,correspondence betwixt the ,solar and the ,lunar ,years1 and to make the ,golden ,numbers1 prefixed to the ,days of the ,month1 useful for determining the ,times of the ,new ,moons1 it would be necessary1 when once those ,golden ,numbers should have been prefixed to the proper ,days1 to make them anticipate a ,day at the ,end of every #caj4g ,years1 as the ,moons will actually have done2 that is to set them back one ,day1 by prefixing each of them to the ,day preceding that1 against which they before stood4 ,but as such a ,rule would neither be so easily comprehended or retained in ,memory1 as if the ,alteration was to be made at the ,end or at the ,beginning of complete ,centuries of ,years2 the ,rule would be much more fit for ,practice1 and keep sufficiently near to the ,truth1 if those ,numbers should be set back nine ,days in the ,space of #bhjj ,years2 by setting them back one ,day1 first at the ,end of #djj ,years1 and then at the ,end of every #cjj ,years for eight times successively3 whereby they would be set back1 in the whole1 nine ,days in #bhjj ,years4 ,after which they must again be set one ,day back at the ,end of #djj ,years1 and so on1 as in the preceding #bhjj ,years4 ,by which means the ,golden ,numbers would always point out the mean ,times of the ,new ,moons1 within a ,day of the ,truth4 ,it is plain however that the ,lunar ,year will have lost one ,day more than ordinary1 with respect to the ,solar ,year1 whenever the ,new ,moons shall have anticipated a whole ,day2 as they will have done at those times1 when it is necessary that the ,golden ,numbers should1 by the ,rule just now given1 be set back one ,day3 and consequently the ,epact1 for that and the succeeding ,years1 must exceed by an ,unit the several corresponding ,epacts of the preceding #ai ,years4 ,for the ,epact is the ,difference1 in whole ,days1 betwixt the common ,julian ,solar and the ,lunar ,year2 the former being reckoned to consist of #cfe1 and the latter of only #ced ,days4 ,if therefore the ,solar and the ,lunar ,year at any time should commence on the same ,day1 the ,solar would1 at the ,end of the ,year1 have exceeded the ,lunar by #aa ,days2 which ,number #aa would be the ,epact of the next ,year3 #bb would be the ,epact of the ,year following1 and #cc the ,epact of the ,year after that1 the ,epacts increasing yearly by #aa4 ,but as often as this yearly ,addition makes the ,epact exceed #cj1 those #cj are rejected as making an intercalary ,month1 and only the ,excess of the ,epact above #cj is accounted the true ,epact for that ,year4 ,thus when the ,epact would amount to #ca1 #cb1 #cc1 #cd1 c4 the #cj is rejected1 and the ,epact becomes #a1 #b1 #c1 #d1 c4 ,since therefore the ,lunar ,year will have lost a ,day more than ordinary1 in respect of the ,solar ,year1 whenever it is necessary to set the ,golden ,numbers one ,day back1 as was before observed2 it follows1 that the ,epact must at the same time be increased by an ,unit more than usual3 the ,difference betwixt the ,solar and the ,lunar ,year having been just so much greater than usual4 ,that is1 #ab must be added1 instead of #aa1 to the ,epact of the preceding1 in order to form what will be the ,epact of the then present ,year4 ,which ,addition of an ,unit extraordinary to one ,epact will occasion all the subsequent ,epacts 7which will follow each other in the usual manner1 each exceeding the foregoing by #aa7 to be greater by an ,unit than their respectively corresponding ,epacts of the preceding #ai ,years4 ,if therefore1 instead of the ,golden ,numbers1 the ,epacts of the several ,years were prefixed1 in the manner the ,gregorians have done1 to the ,days of the ,calendar1 in order to denote the ,days on which the ,new ,moons fall in those ,years whereof those ,numbers are the ,epacts2 there would never be ,occasion to shift the ,places of those ,epacts in the ,calendar2 since the ,augmentation by an ,unit extraordinary of the ,epacts themselves would answer the ,purpose1 and keep all tolerably right4 ,thus in a very easy ,method may the ,course of the ,new ,moons be pointed out1 either by the ,golden ,numbers1 or by the ,epacts1 according to the ,julian ,account or ,manner of adjusting the ,year1 which goes on regular and uniform without any ,variation4 ,but the regulating these things for those who use the ,gregorian ,account1 is an ,affair of more ,intricacy2 and for them it will require more ,consideration to determine1 when the ,epacts are to be more than ordinarily augmented1 and at what ,times they are to continue in their usual ,course2 nay1 to know when they are not only not to be extraordinarily augmented1 but also when they are to be diminished by an ,unit1 by increasing one of them by #aj only instead of #aa as usual3 and this happens much oftener with the ,gregorians1 than the increasing one of them by #ab instead of #aa4 ,for1 in every ,gregorian ,solar ,year1 whose ,date consists of any ,number of entire ,hundreds not divisible by #d1 it is supposed that the ,equinox has anticipated one whole ,day2 and therefore one ,day1 that which ought to be the intercalary one1 is omitted2 and consequently the preceding ,solar ,year1 where one ,day was lost1 exceeded the ,lunar ,year by #aj ,days only instead of #aa4 ,in order therefore to adapt the before-mention'd ,rule to the ,gregorian ,account1 and to know in what ,years the ,epacts should either be extraordinarily augmented or diminished1 and the ,golden ,numbers should either be set backwards or forwards in the ,calendar2 the following ,rules and ,directions must be observed4 ,first4 ,that in the ,years #ahjj1 #bajj1 #bgjj1 #cjjj1 c4 where the ,number of entire ,hundreds is divisible by #c1 but not by #d1 the ,gregorian ,solar1 as well as the ,lunar ,year1 will have lost a ,day2 and consequently the ,difference betwixt them will be the same as usual3 ,therefore in those ,years there must be no ,alteration1 either in the ,epacts or the ,golden ,numbers2 but the former must go on in the same manner1 and the latter stand prefixed to the same ,days in the ,calendar1 for another1 as they did for the last hundred ,years4 #b;dly4 ,the like will happen in the ,years #bjjj1 #bhjj1 #cbjj1 c4 where the ,number of entire ,hundreds is divisible by #d1 but not by #c3 ,for neither the ,gregorian ,solar nor the ,lunar ,year is to be altered2 and therefore the ,epacts must go on1 and the ,golden ,numbers stand1 as they did before4 ,but1 #c;dly1 ,in the ,years #bdjj1 and #cfjj1 whose ,number of entire ,hundreds is divisible both by #c and #d1 the ,gregorian ,solar ,year goes on as usual1 and the ,lunar ,year has lost a ,day4 ,the ,difference therefore betwixt them being #ab1 the ,epact of the preceding ,year must be augmented by that ,number instead of #aa1 in order to form the ,epact of the then present ,year2 whereby a new ,set of ,epacts will be introduced1 exceeding their precedent corresponding ,epacts by an ,unit3 ,and the ,golden ,numbers must be set one ,day back in the ,calendar4 #dthly and lastly1 ,in the ,years #aijj1 #bbjj1 #bcjj1 #bejj1 c4 where the ,number of ,hundreds is divisible neither by #c nor #d2 the ,gregorian ,solar ,year having lost one ,day1 and the ,lunar none1 the ,difference betwixt them being only #aj2 that ,number only1 and not #aa1 is to be added to the ,epact of the preceding1 in order to form the ,epact of that1 the then present ,year2 whereby a new ,set of ,epacts will be introduced1 all of them less by an ,unit than their precedent corresponding ,epacts3 ,and the ,golden ,numbers must be set a ,day forwarder in the ,calendar2 that is1 be prefixed to the ,day following that1 against which they stood in the precedent hundred ,years4 ,this ,method would preserve a sort of ,regularity betwixt the ,solar and the ,lunar ,years2 and1 by means of the ,rules and ,directions before-mentioned1 the ,days of the ,new ,moons might be pointed out1 either by the ,golden ,numbers or by the ,epacts1 placed in the ,calendar for that ,purpose2 according to the ,julian ,account for ever1 and according to the ,gregorian ,account till the ,year #daii inclusive1 after which there must be some little ,variation made in the four last ,precepts or ,rules1 but it would be to little ,purpose now1 to attempt the framing of a new ,set of ,rules for so distant a ,time4 ,the ,gregorians have chosen to make use of the ,epacts to determine the ,days of the ,new ,moons1 and follow pretty nearly the ,rules prescribed above2 except that they order the ,epacts to have an additional ,augmentation of an ,unit eight times in #bejj ,years1 beginning with the ,year #ahjj1 as at the ,end of #djj ,years2 to which #djj ,years if there be added three times seven hundred1 or #bajj ,years1 the ,period of #bejj ,years will be completed in the ,year #cijj4 ,after which they do not make their extraordinary ,augmentation of an ,unit in the ,epacts1 till at the ,end of another ,term of #djj ,years2 which defers that ,augmentation from the ,year #dbjj to the ,year #dcjj4 ,and this is the ,reason that the ,rules above delivered will require a ,variation in the ,year #dbjj2 whereas it is directed in this ,paper that the ,epacts should be augmented1 or 7which is the same thing7 the ,golden ,numbers be set back in the ,calendar nine times in #bhjj ,years4 ,this arises from the ,gregorians supposing1 that the ,difference betwixt #ai ,solar and as many ,lunar ,years would not amount to a whole ,day in less than #cab ,years and a half2 whereas it has appeared above1 that it would amount to a whole ,day in #caj4g ,years4 ,but although the ,rule prescribed in this ,paper comes much nearer to the ,truth1 yet the ,error in either ,case is very inconsiderable1 being so small as not to amount to a whole ,day in many thousand ,years2 and therefore is not worth regarding4 ,a ,method of finding the ,time of ,easter1 as it is observed in most ,parts of ,europe4 ,from what has been already said1 a ,method may be obtained1 for fixing1 with sufficient ,exactness1 the ,time of the ,celebration of the ,feast of ,easter1 which is governed by the ,vernal ,equinox1 and by the ,age of the ,moon nearest to it4 ,the former whereof1 when once rightly adjusted1 may 7by the ,corrections mentioned in that ,part of this ,paper which relates to the ,solar ,year7 be made to continue to fall at very near the same time with1 or at most not to differ a whole ,day from the true ,equinox3 and the same ,rules and ,directions1 which1 as was before shewn1 would1 without any great ,error1 point out the ,times of the first ,day of the ,moon1 would with equal ,certainty point out the fourteenth1 fifteenth1 or any other3 ,and thus the ,times of the ,oppositions or the ,full ,moons might be as well marked out thereby1 as those of the ,conjunctions or the ,new ,moons4 ,i shall not at present take notice of the ,canon of the ,council of ,nice1 in the ,year of our ,lord #cbe1 which directs the ,time of celebrating the ,feast of ,easter1 or of the ,reasons upon which that ,canon was founded4 ,nor shall ,i endeavour to explain the ,rule now in ,use in the ,church of ,england for finding ,easter3 ,for1 besides that such an ,explanation would extend this ,paper to an improper ,length1 those ,points have already been treated of by several much abler ,hands1 and particularly by our ,countryman the learned ,dr4 ,prideaux4 ,nor is it my ,intention to enter far into the ,methods used by the ,gregorians1 or those of the ,church of ,rome1 or by any other ,nations or ,countries1 for finding the ,time of that ,feast4 ,as to our own1 ,i shall only observe1 that the ,method now used in ,england1 for finding the fourteenth ,day of the ,moon1 or the ,ecclesiastical ,full ,moon1 on which ,easter dependeth1 is1 by ,process of ,time1 become considerably erroneous3 as the ,golden ,numbers1 which were placed in the ,calendar1 to point out the ,days on which the ,new ,moons fall in those ,years of which they are respectively the ,golden ,numbers1 do now stand several ,days later in the same than those ,new ,moons do really happen4 ,which ,error1 as was before observed1 arises from the ,anticipation of the ,moons since the ,time of the ,council of ,nice3 ,and as the ,vernal ,equinox has also anticipated eleven ,days since that time2 neither that ,equinox1 nor the ,new ,moons1 do now happen on those ,days upon which the ,church of ,england supposes them so to happen4 ,when ,pope ,gregory ,,xiii4 reformed the ,julian ,solar ,year1 he likewise made a ,correction as to the ,time of celebrating the ,feast of ,easter1 by placing the ,epacts 7which he directed to be made use of for the future instead of the ,golden ,numbers7 much nearer to the true ,times of the ,new ,moons than the ,golden ,numbers then stood in the old ,calendar3 ,i say1 much nearer to the true ,times2 because in fact the ,epacts1 as placed by him1 were not prefixed to the exact ,days upon which the ,new ,moons then truly fell4 ,and this was done with ,design1 and for a ,reason which it is not material to the ,purpose of this ,paper to mention4 ,but the ,church of ,england1 and that of ,rome or the ,gregorians1 do still agree in this2 that both of them mark 7the former by the ,golden ,numbers1 and the latter by the ,epacts corresponding to them7 the ,days on which their ,ecclesiastical ,new ,moons are supposed to happen3 ,and that fourteenth ,day of the ,moon inclusive1 or that ,full ,moon1 which falls upon1 or next after1 the #bast ,day of ,march1 is the ,paschal ,limit or ,full ,moon to both3 ,and the ,sunday next following that ,limit or ,full ,moon1 is by both ,churches celebrated as ,easter ,day4 ,but the #bast of ,march being reckoned1 according to the ,gregorian ,account or the ,new ,style1 eleven ,days sooner than by the ,julian ,account or the ,old ,style1 which is still in ,use amongst us2 and their ,ecclesiastical ,new ,moons being three ,days earlier than those of the ,church of ,england2 it happens that although the ,church of ,england and that of ,rome often do1 yet more frequently they do not1 celebrate the ,feast of ,easter upon the same natural ,day4 ,it might however be easier for both1 and could occasion no ,inconvenience1 now that ,almanacks1 which tell the exact ,times of the ,new ,moons1 are in most ,peoples ,hands2 if all the ,golden ,numbers and ,epacts now prefixed to those ,days of the ,calendar1 in our ,book of ,common ,prayer1 and in the ,roman ,breviary1 on which the respective ,ecclesiastical ,new ,moons happen1 were omitted in the ,places where they now stand2 and were set only against those fourteenth ,days of the ,moon1 or those ,full ,moons1 which happen betwixt the #bast ,day of ,march and the #ahth of ,april1 both inclusive4 ,since no fourteenth ,day or ,full ,moon1 which happens before the #bast of ,march1 or after the #ahth ,day of ,april1 can have any ,share in fixing the ,time of ,easter4 ,by which means the ,trouble of counting to the fourteenth ,day1 and the ,mistakes which sometimes arise therefrom1 would be avoided4 ,we do as yet in ,england follow the ,julian ,account or the ,old ,style in the ,civil ,year2 as also the ,old ,method of finding those ,moons upon which ,easter depends3 ,both of which have been shewn to be very erroneous4 ,if therefore this ,nation should ever judge it proper to correct the ,civil ,year1 and to make it conformable to that of the ,gregorians1 it would surely be adviseable to correct the ,time of the ,celebration of the ,feast of ,easter likewise1 and to bring it to the same ,day upon which it is kept and solemnized by the ,inhabitants of the greatest ,part of ,europe1 that is1 by those who follow the ,gregorian ,account4 ,for tho' ,i am aware1 that their ,method of finding the ,time of ,easter is not quite exact1 but is liable to some ,errors2 yet ,i apprehend1 that all other practicable ,methods of doing it would be so too3 ,and if they were more free from ,error1 they would probably be more intricate1 and harder to be understood by ,numbers of ,people1 than the ,method of determining that ,feast either by a ,cycle of ,epacts1 as is practiced by the ,gregorians1 or by that of #ai ,years or the ,golden ,numbers1 in the manner proposed in the following ,part of this ,paper3 ,and it is of no small ,importance1 that a ,matter of so general a ,concern1 as the ,method of finding ,easter is1 should be within the ,reach of the ,generality of ,mankind1 at least as far as the ,nature of the thing will admit4 ,for which ,reason1 in case the ,legislature of this ,country should before the ,year #aijj1 think fit to make our ,civil ,year correspond with that of the ,gregorians1 and also to celebrate all the future ,feasts of ,easter upon the same ,days upon which they celebrate them2 this last ,particular might be easily effected1 without altering the ,rule of the ,church of ,england for the finding of that ,feast3 ,and this only by advancing the ,golden ,numbers1 prefixed to certain ,days in the ,calendar1 #h ,days forwarder for the ,new ,moons1 or #ba ,days forwarder for the fourteenth ,days or ,full ,moons1 than they now stand in our ,calendar4 ,in order to explain this1 it must be observed1 that the ,gregorian ,account or the ,new ,style is eleven ,days forwarder than the ,julian ,account or the ,old ,style1 which we still make use of2 that is1 the last ,day of any of our ,months is the eleventh ,day of their next succeeding ,month4 ,if therefore their ,ecclesiastical ,new ,moons fell on the same ,days with those of the ,church of ,england1 the ,golden ,number #ad1 which now stands against the last ,day of ,february in our that is the ,julian ,calendar1 should1 when we should have adopted the ,gregorian ,calendar1 be prefixed to the #aath ,day of ,march4 ,but since their ,ecclesiastical ,new ,moons happen #c ,days earlier than our ,ecclesiastical ,new ,moons at present do2 so much should be deducted from those #aa ,days1 by which the ,golden ,numbers ought otherwise to be advanced2 and the ,golden ,number #ad should not be placed against the #aath1 but the #hth ,day of ,march3 ,which being reckoned the first ,day of the ,moon1 if we count on to the fourteenth ,day of the same inclusive1 that would be found to fall on the a #bast ,day of ,march2 on which ,day the ,gregorian ,paschal ,limit or ,full ,moon will happen when the ,golden ,number is #ad4 ,and the like ,course should be taken with the rest of the #ai ,golden ,numbers2 which ought to be placed #h ,days forwarder than they now stand1 if they are to point out the ,new ,moon2 or #ba ,days forwarder than they are at present1 if they are to mark the fourteenth ,day of the ,moon or the ,full ,moon3 ,the latter of which1 as has been shewn1 would be more eligible1 than to prefix those ,numbers to the ,days on which the ,new ,moons happen4 ,thus may the ,rule and ,method now used in the ,church of ,england1 be most easily adapted to shew the ,time of ,easter1 as it is observed by the ,gregorians1 till the ,year #aijj2 at which ,time1 and at the other proper succeeding ,times1 if the ,golden ,numbers in the ,calendar shall either be advanced or set backward a ,day1 according the foregoing ,rules and ,directions for that ,purpose1 they will continue to shew us the ,new or the ,full ,moons1 of the ,church of ,rome or the ,gregorian ,calendar with great ,exactness1 till the ,year #daii3 when1 as has been already mentioned1 there must be a little ,variation made in those ,rules and ,directions4 ,there is however one ,exception to those ,general ,rules and ,directions1 which will be taken notice of in the next ,paragraph4 ,upon these ,principles ,i framed the ,table accompanying this ,paper1 and shewing1 by means of the ,golden ,numbers1 all the ,gregorian ,paschal ,limits or ,full ,moons1 from the ,reformation of the ,calendar1 c4 by ,pope ,gregory to the ,year #daii inclusive4 ,which ,space of ,time is therein divided into sixteen unequal ,portions or ,periods2 at the ,beginning of each of which1 all the ,golden ,numbers1 when once they shall have been properly placed in the ,calendar1 must either be advanced or set back one ,day1 with respect to the ,place where they stood in the preceding ,period1 agreeably to the foregoing ,rules3 ,except those ,numbers which shall happen to stand against the #dth and #eth of ,april to shew the ,paschal ,new ,moons1 or against the #agth and #ahth of the same ,month to mark out the ,paschal ,full ,moons2 both which ,numbers at some ,times1 and only one of them at others1 must keep the same ,place for that1 which was allotted to them in the immediately preceding ,period4 ,in order to determine at what ,times1 and on what ,occasions1 this ,exception is to take ,place2 let it be observed1 that1 in the ,months of ,january1 ,march1 ,may1 and some others in our present ,calendar1 as well as in the ,table above mentioned1 some of the ,golden ,numbers stand double or in ,pairs1 and follow one the other immediately2 whilst others1 on the contrary1 generally stand single and by themselves4 ,now1 when any of those ,pairs1 or two ,numbers which usually accompany each other1 happen1 in pursuance of the foregoing ,rules1 to be prefixed the one to the #dth and the other to the #eth of ,april for the ,new ,moons1 or the one to the #agth and the other to the #ahth of ,april for the ,paschal ,limits or ,full ,moons3 ,and when any of those ,numbers1 which generally stand single1 are prefixed1 according to the said ,rules1 to the #eth of ,april for the ,new ,moons1 or to the #ahth for the ,full ,moons3 ,in these ,cases those ,pairs or single ,numbers that are so situated2 must not be set forward or advanced at the ,beginning of the next ,period1 but must keep their ,places during another ,period1 if the foregoing ,rules direct all the ,golden ,numbers to be advanced a ,day2 which must be complied with in respect to all the other ,golden ,numbers1 except those so situated as above4 ,instances whereof may be seen in the ,table1 under the respective ,periods beginning with the ,years #aijj1 #bfjj1 #cajj1 and #chjj4 ,but if1 in ,conformity to the foregoing ,rules1 all the ,golden ,numbers are to be set one ,day backward2 those ,pairs or single ,numbers1 tho' situated as is above-mentioned1 must not keep their ,places1 but must move one ,day backward like all the other ,golden ,numbers2 as they may be seen to do in the ,periods beginning with the ,years #bdjj and #cfjj4 ,to give a plain and intelligible ,account of the ,reason1 on which the ,directions now given with respect to this ,exception are founded1 would extend this ,paper1 already too long1 far beyond its due and proper ,bounds4 ,i shall therefore content myself with observing1 that it depends chiefly upon the ,nature of the ,menses ,pleni and ,menses ,cavi1 into which the ,lunar ,year is usually divided3 and that1 in order to make use of the ,golden ,numbers for finding the ,time of the ,gregorian ,easter1 it will be necessary not only to conform to the general ,rules laid down in the former ,part of this ,paper2 but also to follow the ,directions just now given1 with respect to the above-mentioned ,exception to those general ,rules4 ,but ,i should not do ,justice to ,peter ,davall of the ,middle ,temple1 ,esq2 ,secretary of the ,royal ,society1 did ,i not here acknowledge1 that1 before ,i had so fully considered these ,matters as ,i have since done1 ,i had the first ,hint of applying the ,golden ,numbers to find the ,gregorian ,paschal ,limit or full ,moon1 from him2 who has since that time composed and drawn up ,tables1 c4 which may possibly be of considerable and general ,use in this ,nation hereafter4 ,,finis4 ,transcriber's ,note ,variable spelling and hyphenation have been retained4 ,minor punctuation inconsistencies have been silently repaired4 ,corrections4 ,the first line indicates the original1 the second the correction4 p4 #g what ,years the ,epacts should either be extraordinariy what ,years the ,epacts should either be extraordinarily