Calendars 2

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0><script type="text/javascript" src="http://hb.lycos.com/hb.js"></script> <script type="text/javascript" src="http://ratings.lycos.com/ratings/lycosRating.js.php"></script> <script type="text/javascript"><![CDATA[//><!]]></script> <script type="text/javascript" src="http://scripts.lycos.com/catman/init.js"></script> <script type="text/javascript" src="http://members.tripod.com/adm/ad/code-start.js"></script> <script type="text/javascript" src="http://members.tripod.com/adm/ad/code-middle.js"></script> <script type="text/javascript" src="http://members.tripod.com/adm/ad/code-end.js"></script> <noscript> <img src="http://members.tripod.com/adm/img/common/ot_noscript.gif?rand=240560" alt="" width="1" height="1" />  <iframe frameborder="0" marginwidth="0" marginheight="0" scrolling="no" width="728" height="90" src="http://ad.yieldmanager.com/st?ad_type=iframe&ad_size=728x90&section=209094"></iframe>  </noscript> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" height=125 BGCOLOR="#996699" TEXT="#080000" bgproperties="fixed" background="040467d1erlcll.gif"> <div> <FONT SIZE="5" COLOR="#FFFFFF" FACE="Arial" ><B>2001: The Beginning of the 21st Century and the Third Millennium</b></FONT><B>     </b><B>|     </b><A HREF="index.htm" TARGET="_top" TITLE="2001: The Beginning of the 21st Century "><U><B>home</b></U></A></div> <div> <B>Calendars 2</b>   |   <A HREF="id53.htm" TARGET="_top" TITLE="Calendars 3"><U>Calendars 3</U></A>   |   <A HREF="id54.htm" TARGET="_top" TITLE="Calendars 4"><U>Calendars 4</U></A></div> <div> </div> </td> </tr><tr> <td valign="top" height=355 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> Calendars 2</div> <div> <B> <A NAME="2_9__what_is_easter_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9. What is Easter?</b></div> <bR> <div> In the Christian world, Easter (and the days immediately preceding it) is the celebration of the death and resurrection of Jesus in (approximately) AD 30.</div> <bR> <bR> <div> <B> <A NAME="2_9_1__when_is_easter___short_answer_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9.1. When is Easter? (Short answer)</b></div> <bR> <div> Easter Sunday is the first Sunday after the first full moon after vernal equinox.</div> <bR> <bR> <div> <B> <A NAME="2_9_2__when_is_easter___long_answer_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9.2. When is Easter? (Long answer)</b></div> <bR> <div> The calculation of Easter is complicated because it is linked to (an inaccurate version of) the Hebrew calendar.</div> <bR> <div> Jesus was crucified immediately before the Jewish Passover, which is a celebration of the Exodus from Egypt under Moses. Celebration of Passover started on the 14th or 15th day of the (spring) month of Nisan. Jewish months start when the moon is new, therefore the 14th or 15th day of the month must be immediately after a full moon.</div> <bR> <div> It was therefore decided to make Easter Sunday the first Sunday after the first full moon after vernal equinox. Or more precisely: Easter Sunday is the first Sunday after the <U>official</U> full moon on or after the <U>official</U> vernal equinox.</div> <bR> <div> The official vernal equinox is always 21 March.</div> <bR> <div> The official full moon may differ from the 'real' full moon by one or two days.</div> <bR> <div> (Note, however, that historically, some countries have used the 'real' (astronomical) full moon instead of the official one when calculating Easter. This was the case, for example, of the German Protestant states, which used the astronomical full moon in the years 1700-1776. A similar practice was used Sweden in the years 1740-1844 and in Denmark in the 1700s.)</div> <bR> <div> The full moon that precedes Easter is called the Paschal full moon. Two concepts play an important role when calculating the Paschal full moon: The Golden Number and the Epact. They are described in the following sections.</div> <bR> <div> The following sections give details about how to calculate the date for Easter. Note, however, that while the Julian calendar was in use, it was customary to use tables rather than calculations to determine Easter. The following sections do mention how to calcuate Easter under the Julian calendar, but the reader should be aware that this is an attempt to express in formulas what was originally expressed in tables. The formulas can be taken as a good indication of when Easter was celebrated in the Western Church from approximately the 6th century.</div> <bR> <bR> <div> <B> <A NAME="2_9_3__what_is_the_golden_number_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9.3. What is the Golden Number?</b></div> <bR> <div> Each year is associated with a Golden Number.</div> <bR> <div> Considering that the relationship between the moon's phases and the days of the year repeats itself every 19 years (as described in section 1), it is natural to associate a number between 1 and 19 with each year. This number is the so-called Golden Number. It is calculated thus:</div> <bR> <div> <I>GoldenNumber = (year mod 19)+1</I></div> <bR> <div> New moon will fall on (approximately) the same date in two years with the same Golden Number.</div> <bR> <bR> <div> <B> <A NAME="2_9_4__what_is_the_epact_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9.4. What is the Epact?</b></div> <bR> <div> Each year is associated with an Epact.</div> <bR> <div> The Epact is a measure of the age of the moon (i.e. the number of days that have passed since an 'official' new moon) on a particular date.</div> <bR> <div> <I>In the Julian calendar, 8 + the Epact is the age of the moon at the start of the year</I></div> <div> <I>In the Gregorian calendar, the Epact is the age of the moon at the start of the year</I></div> <bR> <div> The Epact is linked to the Golden Number in the following manner:</div> <bR> <div> Under the Julian calendar, 19 years were assumed to be exactly an integral number of synodic months, and the following relationship exists between the Golden Number and the Epact:</div> <bR> <div> <I>Epact = (11 * (GoldenNumber-1)) mod 30 </I></div> <bR> <div> If this formula yields zero, the Epact is by convention frequently designated by the symbol * and its value is said to be 30. Weird?</div> <div> Maybe, but people didn't like the number zero in the old days.</div> <bR> <div> Since there are only 19 possible golden numbers, the Epact can have only 19 different values: 1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 18, 20,22, 23, 25, 26, 28, and 30.</div> <bR> <div> The Julian system for calculating full moons was inaccurate, and under the Gregorian calendar, some modifications are made to the simple relationship between the Golden Number and the Epact.</div> <bR> <div> In the Gregorian calendar the Epact should be calculated thus (the divisions are integer divisions, in which remainders are discarded):</div> <div>         </div> <div> <I>1) Use the Julian formula:</I></div> <div> <I>      Epact = (11 * (GoldenNumber-1)) mod 30</I></div> <bR> <div> <I>2) Adjust the Epact, taking into account the fact that 3 out of 4centuries have one leap year less than a Julian century:</I></div> <div> <I>        Epact = Epact - (3*century)/4</I></div> <bR> <div> <I>   (For the purpose of this calculation century=20 is used for the</I></div> <div> <I>   years 1900 through 1999, and similarly for other centuries,</I></div> <div> <I>   although this contradicts the rules in section 2.10.3.)</I></div> <bR> <div> <I>3) Adjust the Epact, taking into account the fact that 19 years is not exactly an integral number of synodic months:</I></div> <div> <I>        Epact = Epact + (8*century + 5)/25</I></div> <bR> <div> <I>   (This adds one to the Epact 8 times every 2500 years.)</I></div> <bR> <div> <I>4) Add 8 to the Epact to make it the age of the moon on 1 January:</I></div> <div> <I>        Epact = Epact + 8</I></div> <bR> <div> <I>5) Add or subtract 30 until the Epact lies between 1 and 30.</I></div> <bR> <div> In the Gregorian calendar, the Epact can have any value from 1 to 30.</div> <bR> <div> <I>Example: What was the Epact for 1992?</I></div> <bR> <div> <I>GoldenNumber = 1992 mod 19 + 1 = 17</I></div> <div> <I>1) Epact = (11 * (17-1)) mod 30 = 26</I></div> <div> <I>2) Epact = 26 - (3*20)/4 = 11</I></div> <div> <I>3) Epact = 11 + (8*20 + 5)/25 = 17</I></div> <div> <I>4) Epact = 17 + 8 = 25</I></div> <div> <I>5) Epact = 25</I></div> <bR> <div> <I>The Epact for 1992 was 25.</I></div> <bR> <bR> <div> <B> <A NAME="2_9_5__how_does_one_calculate_easter"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9.5. How does one calculate Easter then?</b></div> <bR> <div> To find Easter the following algorithm is used:</div> <bR> <div> 1) Calculate the Epact as described in the previous section.</div> <bR> <div> 2) For the Julian calendar: Add 8 to the Epact. (For the Gregorian</div> <div>    calendar, this has already been done in step 4 of the calculation of</div> <div>    the Epact). Subtract 30 if the sum exceeds 30.</div> <bR> <div> 3) Look up the Epact (as possibly modified in step 2) in this table to</div> <div>    find the date for the Paschal full moon:</div> <bR> <div> <TABLE BORDER="2" CELLPADDING="2" CELLSPACING="1" WIDTH="514" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Epact</div> </tD> <tD VALIGN=TOP><NOBR><div> Full Moon</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> Epact</div> </tD> <tD VALIGN=TOP><NOBR><div> Full Moon</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> Epact</div> </tD> <tD VALIGN=TOP WIDTH="112"><div> Full Moon</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 1</div> </tD> <tD VALIGN=TOP><NOBR><div> 12 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 11</div> </tD> <tD VALIGN=TOP><NOBR><div> 02 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 21</div> </tD> <tD VALIGN=TOP WIDTH="112"><div> 23 March</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 2</div> </tD> <tD VALIGN=TOP><NOBR><div> 11 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 12</div> </tD> <tD VALIGN=TOP><NOBR><div> 01 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 22</div> </tD> <tD VALIGN=TOP WIDTH="112"><div> 22 March</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 3</div> </tD> <tD VALIGN=TOP><NOBR><div> 10 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 13</div> </tD> <tD VALIGN=TOP><NOBR><div> 31 March</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 23</div> </tD> <tD VALIGN=TOP WIDTH="112"><div> 21 March</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 4</div> </tD> <tD VALIGN=TOP><NOBR><div> 09 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 14</div> </tD> <tD VALIGN=TOP><NOBR><div> 30 March</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 24</div> </tD> <tD VALIGN=TOP WIDTH="112"><div> 18 April</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 5</div> </tD> <tD VALIGN=TOP><NOBR><div> 08 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 15</div> </tD> <tD VALIGN=TOP><NOBR><div> 29 March</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 25</div> </tD> <tD VALIGN=TOP><NOBR><div> 18 or 17 April</div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 6</div> </tD> <tD VALIGN=TOP><NOBR><div> 07 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 16</div> </tD> <tD VALIGN=TOP><NOBR><div> 28 March</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 26</div> </tD> <tD VALIGN=TOP WIDTH="112"><div> 17 April</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 7</div> </tD> <tD VALIGN=TOP><NOBR><div> 06 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 17</div> </tD> <tD VALIGN=TOP><NOBR><div> 27 March</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 27</div> </tD> <tD VALIGN=TOP WIDTH="112"><div> 16 April</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 8</div> </tD> <tD VALIGN=TOP><NOBR><div> 05 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 18</div> </tD> <tD VALIGN=TOP><NOBR><div> 26 March</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 28</div> </tD> <tD VALIGN=TOP WIDTH="112"><div> 15 April</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 9</div> </tD> <tD VALIGN=TOP><NOBR><div> 04 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 19</div> </tD> <tD VALIGN=TOP><NOBR><div> 25 March</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="112"><div> 14 April</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 10</div> </tD> <tD VALIGN=TOP><NOBR><div> 03 April</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 20</div> </tD> <tD VALIGN=TOP><NOBR><div> 24 March</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="71"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="112"><div> 13 April</div> </tD> </tR> </TABLE></div> <bR> <bR> <div> 4) Easter Sunday is the first Sunday following the above full moon  date. If the full moon falls on a Sunday, Easter Sunday is the</div> <div>    following Sunday.</div> <bR> <div> An Epact of 25 requires special treatment, as it has two dates in the above table. There are two equivalent methods for choosing the correct full moon date:</div> <bR> <div> A) Choose 18 April, unless the current century contains years with an epact of 24, in which case 17 April should be used.</div> <bR> <div> B) If the Golden Number is > 11 choose 17 April, otherwise choose 18 April.</div> <bR> <div> The proof that these two statements are equivalent is left as an exercise to the reader.</div> <bR> <div> Example: When was Easter in 1992?</div> <bR> <div> In the previous section we found that the Golden Number for 1992 was 17 and the Epact was 25. Looking in the table, we find that the Paschal full moon was either 17 or 18 April. By rule B above, we choose 17 April because the Golden Number > 11.</div> <bR> <div> 17 April 1992 was a Friday. Easter Sunday must therefore have been 19 April.</div> <bR> <bR> <div> <B> <A NAME="2_9_6__isn_t_there_a_simpler_way_to"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9.6. Isn't there a simpler way to calculate Easter?</b></div> <bR> <div> This is an attempt to boil down the information given in the previous sections (the divisions are integer divisions, in which remainders are discarded):</div> <bR> <div> G = year mod 19</div> <bR> <div> For the Julian calendar:</div> <div>     I = (19*G + 15) mod 30</div> <div>     J = (year + year/4 + I) mod 7</div> <bR> <div> For the Gregorian calendar:</div> <div>     C = year/100</div> <div>     H = (C - C/4 - (8*C+13)/25 + 19*G + 15) mod 30</div> <div>     I = H - (H/28)*(1 - (H/28)*(29/(H + 1))*((21 - G)/11))</div> <div>     J = (year + year/4 + I + 2 - C + C/4) mod 7</div> <bR> <div> Thereafter, for both calendars:</div> <div> L = I - J</div> <div> EasterMonth = 3 + (L + 40)/44</div> <div> EasterDay = L + 28 - 31*(EasterMonth/4)</div> <bR> <bR> <div> This algorithm is based in part on the algorithm of Oudin (1940) as quoted in <I>'Explanatory Supplement to the Astronomical Almanac', P. Kenneth Seidelmann, editor.</I></div> <bR> <div> People who want to dig into the workings of this algorithm, may be interested to know that</div> <div>     G is the Golden Number-1</div> <div>     H is 23-Epact (modulo 30)</div> <div>     I is the number of days from 21 March to the Paschal full moon</div> <div>     J is the weekday for the Paschal full moon (0=Sunday, 1=Monday,</div> <div>       etc.)</div> <div>     L is the number of days from 21 March to the Sunday on or before</div> <div>       the Paschal full moon (a number between -6 and 28)</div> <bR> <bR> <div> <B> <A NAME="2_9_7__is_there_a_simple_relationship"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9.7. Is there a simple relationship between two consecutive Easters?</b></div> <bR> <div> Suppose you know the Easter date of the current year, can you easily find the Easter date in the next year? No, but you can make a qualified guess.</div> <bR> <div> If Easter Sunday in the current year falls on day X and the next year is not a leap year, Easter Sunday of next year will fall on one of the following days: X-15, X-8, X+13 (rare), or X+20.</div> <bR> <div> If Easter Sunday in the current year falls on day X and the next year is a leap year, Easter Sunday of next year will fall on one of the following days: X-16, X-9, X+12 (extremely rare), or X+19. (The jump X+12 occurs only once in the period 1800-2099, namely when going from</div> <div> 2075 to 2076.)</div> <bR> <div> If you combine this knowledge with the fact that Easter Sunday never falls before 22 March and never falls after 25 April, you can narrow the possibilities down to two or three dates.</div> <bR> <bR> <div> <B> <A NAME="2_9_8__how_frequently_are_the_dates_for"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9.8. How frequently are the dates for Easter repeated?</b></div> <bR> <div> The sequence of Easter dates repeats itself every 532 years in the Julian calendar. The number 532 is the product of the following numbers:</div> <bR> <div> <I>19 (the Metonic cycle or the cycle of the Golden Number)</I></div> <div> <I>28 (the Solar cycle, see </I><A HREF="id50_2_4__what_is_the_solar_cycle_.htm" TARGET="_top" TITLE="More on calendars"><U><I>section 2.4</I></U></A><I>)</I></div> <bR> <div> The sequence of Easter dates repeats itself every 5,700,000 years in the Gregorian calendar. The number 5,700,000 is the product of the following numbers:</div> <bR> <div> <I>19 (the Metonic cycle or the cycle of the Golden Number)</I></div> <div> <I>400 (the Gregorian equivalent of the Solar cycle, see </I><A HREF="id50_2_4__what_is_the_solar_cycle_.htm" TARGET="_top" TITLE="More on calendars"><U><I>section 2.4</I></U></A><I>)</I></div> <div> <I>25 (the cycle used in step 3 when calculating the Epact)</I></div> <div> <I>30 (the number of different Epact values)</I></div> <bR> <bR> <div> <B> <A NAME="2_9_9__what_about_greek_easter_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9.9. What about Greek Easter?</b></div> <bR> <div> The Greek Orthodox Church does not always celebrate Easter on the same day as the Catholic and Protestant countries. The reason is that the Orthodox Church uses the Julian calendar when calculating Easter. This is case even in the churches that otherwise use the Gregorian calendar.</div> <bR> <div> When the Greek Orthodox Church in 1923 decided to change to the Gregorian calendar (or rather: a Revised Julian Calendar), they chose to use the astronomical full moon as the basis for calculating Easter, rather than the 'official' full moon described in the previous sections. And they chose the meridian of Jerusalem to serve as definition of when a Sunday starts. However, except for some sporadic use the 1920s, this system was never adopted in practice.</div> <bR> <bR> <div> <B> <A NAME="2_9_10__what_will_happen_after_2001_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.9.10. What will happen after 2001?</b></div> <bR> <div> At at meeting in Aleppo, Syria (5-10 March 1997), organised by the World Council of Churches and the Middle East Council of Churches, representatives of several churches and Christian world communions suggested that the discrepancies between Easter calculations in the Western and the Eastern churches could be resolved by adopting astronomically accurate calculations of the vernal equinox and the full moon, instead of using the algorithm presented in <A HREF="#2_9_5__how_does_one_calculate_easter" TITLE="Calendars 2"><U>section 2.9.5</U></A>. The meridian of Jerusalem should be used for the astronomical calculations.</div> <bR> <div> The new method for calculating Easter should take effect from the year 2001. In that year the Julian and Gregorian Easter dates coincide (on 15 April Gregorian/2 April Julian), and it is therefore a reasonable starting point for the new system.</div> <bR> <div> Whether this new system will actually be adopted, remains to be seen. So the answer to the question heading this section is: I don't know.</div> <bR> <div> If the new system is introduced, churches using the Gregorian calendar will hardly notice the change. Only once during the period 2001-2025 will these churches note a difference: In 2019 the Gregorian method gives an Easter date of 21 April, but the proposed new method gives 24 March.</div> <bR> <div> Note that the new method makes an Easter date of 21 March possible. This date was not possible under the Julian or Gregorian algorithms.(Under the new method, Easter will fall on 21 March in the year 2877)</div> <bR> <div>  <A NAME="2_10__how_does_one_count_years_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></div> <div> <B>2.10. How does one count years?</b></div> <bR> <div> In about AD 523, the papal chancellor, Bonifatius, asked a monk by the name of Dionysius Exiguus to devise a way to implement the rules from the Nicean council (the so-called 'Alexandrine Rules') for general use.</div> <bR> <div> Dionysius Exiguus (in English known as Denis the Little) was a monk from Scythia, he was a canon in the Roman curia, and his assignment was to prepare calculations of the dates of Easter. At that time it was customary to count years since the reign of emperor Diocletian; but in his calculations Dionysius chose to number the years since the birth of Christ, rather than honour the persecutor Diocletian.</div> <bR> <div> Dionysius (wrongly) fixed Jesus' birth with respect to Diocletian's reign in such a manner that it falls on 25 December 753 AUC (ab urbe condita, i.e. since the founding of Rome), thus making the current era start with AD 1 on 1 January 754 AUC.</div> <bR> <div> How Dionysius established the year of Christ's birth is not known (see section <A HREF="#2_10_1__how_did_dionysius_date_christ_s" TITLE="Calendars 2"><U>2.10.1</U></A> for a couple of theories). Jesus was born under the reign of king Herod the Great, who died in 750 AUC, which means that Jesus could have been born no later than that year. Dionysius' calculations were disputed at a very early stage.</div> <bR> <div> When people started dating years before 754 AUC using the term 'Before Christ', they let the year 1 BC immediately precede AD 1 with no intervening year zero. </div> <bR> <div> Note, however, that astronomers frequently use another way of numbering the years BC. Instead of 1 BC they use 0, instead of 2 BC they use -1, instead of 3 BC they use -2, etc.</div> <bR> <div> See also <A HREF="#2_10_2__was_jesus_born_in_the_year_0_" TITLE="Calendars 2"><U>section 2.10.2</U></A>.</div> <bR> <div> It is frequently claimed that it was the venerable Bede (673-735) who introduced BC dating. This is probably not true.</div> <bR> <div> In this section I have used AD 1 = 754 AUC. This is the most likely equivalence between the two systems. However, some authorities state that AD 1 = 753 AUC or 755 AUC. This confusion is not a modern one, it appears that even the Romans were in some doubt about how to count the years since the founding of Rome.</div> <bR> <bR> <div> <B> <A NAME="2_10_1__how_did_dionysius_date_christ_s"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.10.1. How did Dionysius date Christ's birth?</b></div> <bR> <div> There are quite a few theories about this. And many of the theories are presented as if they were indisputable historical fact.</div> <bR> <div> Here are two theories that I personally consider likely:</div> <bR> <div> 1. According to the Gospel of Luke (3:1 & 3:23) Jesus was "about  thirty years old" shortly after "the fifteenth year of the reign of</div> <div>    Tiberius Caesar". Tiberius became emperor in AD 14. If you combine these numbers you reach a birthyear for Jesus that is strikingly</div> <div>    close to the beginning of our year reckoning. This may have been the basis for Dionysius' calculations.</div> <bR> <div> 2. Dionysius' original task was to calculate an Easter table. In the Julian calendar, the dates for Easter repeat every 532 years (see</div> <div>    <A HREF="#2_9_8__how_frequently_are_the_dates_for" TITLE="Calendars 2"><U>section 2.9.8</U></A>). The first year in Dionysius' Easter tables is AD 532. Is it a coincidence that the number 532 appears twice here? Or</div> <div>    did Dionysius perhaps fix Jesus' birthyear so that his own Easter tables would start exactly at the beginning of the second Easter</div> <div>    cycle after Jesus' birth?</div> <bR> <bR> <div> <B> <A NAME="2_10_2__was_jesus_born_in_the_year_0_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.10.2. Was Jesus born in the year 0?</b></div> <bR> <div> No.</div> <bR> <div> There are two reasons for this:</div> <div> - There is no year 0.</div> <div> - Jesus was born before 4 BC.</div> <bR> <div> The concept of a year "zero" is a modern myth (but a very popular one). Roman numerals do not have a figure designating zero, and treating zero as a number on an equal footing with other numbers was not common in the 6th century when our present year reckoning was established by Dionysius Exiguus (see <A HREF="#2_10__how_does_one_count_years_" TITLE="Calendars 2"><U>section 2.10</U></A>). Dionysius let the year AD 1 start one week after what he believed to be Jesus' birthday.</div> <bR> <div> Therefore, AD 1 follows immediately after 1 BC with no intervening year zero. So a person who was born in 10 BC and died in AD 10, would have died at the age of 19, not 20.</div> <bR> <div> Furthermore, Dionysius' calculations were wrong. The Gospel of Matthew tells us that Jesus was born under the reign of king Herod the Great, and he died in 4 BC. It is likely that Jesus was actually born around 7 BC. The date of his birth is unknown; it may or may not be 25 December.</div> <bR> <bR> <div> <B> <A NAME="2_10_3__when_does_the_3rd_millenium"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.10.3. When does the 3rd millenium start?</b></div> <bR> <div> The first millennium started in AD 1, so the millennia are counted in this manner:</div> <bR> <div> 1st millennium:        1-1000</div> <div> 2nd millennium: 1001-2000</div> <div> 3rd millennium:  2001-3000</div> <bR> <div> Thus, the 3rd millennium and, similarly, the 21st century start on 1 Jan 2001.</div> <bR> <div> This is the cause of some heated debate, especially since some dictionaries and encyclopaedias say that a century starts in years that end in 00. Furthermore, the change 1999/2000 is obviously much more spectacular than the change 2000/2001.</div> <bR> <div> A few compromises:</div> <bR> <div> Any 100-year period is a century. Therefore the period from 23 June 1998 to 22 June 2098 is a century. So please feel free to celebrate the start of a century any day you like!</div> <bR> <div> Although the 20th century started in 1901, the 1900s started in 1900. Similarly, we can celebrate the start of the 2000s in 2000 and the start of the 21st century in 2001.</div> <bR> <div> Finally, let's take a lesson from history:</div> <div> When 1899 became 1900 people celebrated the start of a new century.</div> <div> When 1900 became 1901 people celebrated the start of a new century.</div> <div> Two parties! Let's do the same thing again!</div> <bR> <bR> <div> <B> <A NAME="2_10_4__what_do_ad_bc_ce_and_bce"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.10.4. What do AD, BC, CE, and BCE stand for?</b></div> <bR> <div> Years before the birth of Christ are in English traditionally identified using the abbreviation BC ('Before Christ').</div> <bR> <div> Years after the birth of Christ are traditionally identified using the abbreviation AD ('Anno Domini', that is, 'In the Year of the Lord').</div> <bR> <div> Some people, who want to avoid the reference to Christ that is implied in these terms, prefer the abbreviations BCE ('Before the Common Era' or 'Before the Christian Era') and CE ('Common Era' or 'Christian Era').</div> <bR> <bR> <div> <B> <A NAME="2_11__what_is_the_indiction_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.11. What is the Indiction?</b></div> <bR> <div> The Indiction was used in the middle ages to specify the position of a year in a 15 year taxation cycle. It was introduced by emperor Constantine the Great on 1 September 312 and ceased to be used in 1806.</div> <bR> <div> The Indiction may be calculated thus:</div> <div>         Indiction = (year + 2) mod 15 + 1</div> <bR> <div> The Indiction has no astronomical significance.</div> <bR> <div> The Indiction did not always follow the calendar year. Three different Indictions may be identified:</div> <bR> <div> 1) The Pontifical or Roman Indiction, which started on New Year's Day (being either 25 December, 1 January, or 25 March).</div> <div> 2) The Greek or Constantinopolitan Indiction, which started on 1 September.</div> <div> 3) The Imperial Indiction or Indiction of Constantine, which started on 24 September.</div> <bR> <bR> <div> <B> <A NAME="2_12__what_is_the_julian_period_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.12. What is the Julian Period?</b></div> <bR> <div> The Julian period (and the Julian day number) must not be confused with the Julian calendar. </div> <bR> <div> The French scholar Joseph Justus Scaliger (1540-1609) was interested in assigning a positive number to every year without having to worry about BC/AD. He invented what is today known as the 'Julian Period'.</div> <bR> <div> The Julian Period probably takes its name from the Julian calendar, although it has been claimed that it is named after Scaliger's father, the Italian scholar Julius Caesar Scaliger (1484-1558).</div> <bR> <div> Scaliger's Julian period starts on 1 January 4713 BC (Julian calendar) and lasts for 7980 years. AD 1999 is thus year 6712 in the Julian period. After 7980 years the number starts from 1 again.</div> <bR> <div> Why 4713 BC and why 7980 years? Well, in 4713 BC the Indiction (see <A HREF="#2_11__what_is_the_indiction_" TITLE="Calendars 2"><U>section 2.11</U></A>), the Golden Number (see <A HREF="#2_9_3__what_is_the_golden_number_" TITLE="Calendars 2"><U>section 2.9.3</U></A>) and the Solar Number (see <A HREF="id50_2_4__what_is_the_solar_cycle_.htm" TARGET="_top" TITLE="More on calendars"><U>section 2.4</U></A>) were all 1. The next times this happens is 15x19x28=7980 years later, in AD 3268.</div> <bR> <div> Astronomers have used the Julian period to assign a unique number to every day since 1 January 4713 BC. This is the so-called Julian Day (JD). JD 0 designates the 24 hours from noon UTC on 1 January 4713 BC to noon UTC on 2 January 4713 BC.</div> <bR> <div> This means that at noon UTC on 1 January AD 2000, JD 2,451,545 will start.</div> <bR> <div> This can be calculated thus:</div> <bR> <div> <I>From 4713 BC to AD 2000 there are 6712 years.</I></div> <div> <I>In the Julian calendar, years have 365.25 days, so 6712 years correspond to 6712*365.25=2,451,558 days. Subtract from this</I></div> <div> <I>the 13 days that the Gregorian calendar is ahead of the Julian calendar, and you get 2,451,545.</I></div> <bR> <div> Often fractions of Julian day numbers are used, so that 1 January AD 2000 at 15:00 UTC is referred to as JD 2,451,545.125.</div> <bR> <div> Note that some people use the term 'Julian day number' to refer to any numbering of days. NASA, for example, use the term to denote the number of days since 1 January of the current year.</div> <bR> <bR> <div> <B> <A NAME="2_12_1__is_there_a_formula_for"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.12.1. Is there a formula for calculating the Julian day number?</b></div> <bR> <div> Try this one (the divisions are integer divisions, in which remainders are discarded):</div> <bR> <div>    a = (14-month)/12</div> <div>    y = year+4800-a</div> <div>    m = month + 12*a - 3</div> <bR> <div>   For a date in the Gregorian calendar:</div> <div>    JDN = day + (153*m+2)/5 + y*365 + y/4 - y/100 + y/400 - 32045</div> <bR> <div>   For a date in the Julian calendar:</div> <div>    JDN = day + (153*m+2)/5 + y*365 + y/4 - 32083</div> <bR> <bR> <div> JDN is the Julian day number that starts at noon UTC on the specified date.</div> <bR> <div> The algorithm works fine for AD dates. If you want to use it for BC dates, you must first convert the BC year to a negative year (e.g., 10 BC = -9). The algorithm works correctly for all dates after 4800 BC, i.e. at least for all positive Julian day numbers.</div> <bR> <div> To convert the other way (i.e., to convert a Julian day number, JDN, to a day, month, and year) these formulas can be used (again, the divisions are integer divisions):</div> <bR> <div>   For the Gregorian calendar:</div> <div>      a = JDN + 32044</div> <div>      b = (4*a+3)/146097</div> <div>      c = a - (b*146097)/4</div> <bR> <div>   For the Julian calendar:</div> <div>      b = 0</div> <div>      c = JDN + 32082</div> <bR> <div>   Then, for both calendars:</div> <div>      d = (4*c+3)/1461</div> <div>      e = c - (1461*d)/4</div> <div>      m = (5*e+2)/153</div> <bR> <div>      day   = e - (153*m+2)/5 + 1</div> <div>      month = m + 3 - 12*(m/10)</div> <div>      year  = b*100 + d - 4800 + m/10</div> <bR> <bR> <div> <B> <A NAME="2_12_2__what_is_the_modified_julian_day"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.12.2. What is the modified Julian day number?</b></div> <bR> <div> Sometimes a modified Julian day number (MJD) is used which is 2,400,000.5 less than the Julian day number. This brings the numbers into a more manageable numeric range and makes the day numbers change at midnight UTC rather than noon.</div> <bR> <div> MJD 0 thus started on 17 Nov 1858 (Gregorian) at 00:00:00 UTC.</div> <bR> <bR> <div> <B> <A NAME="2_13__what_is_the_correct_way_to_write"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>2.13. What is the correct way to write dates?</b></div> <bR> <div> The answer to this question depends on what you mean by 'correct'. Different countries have different customs.</div> <bR> <div> Most countries use a day-month-year format, such as:</div> <div> 25.12.1998   25/12/1998   25/12-1998   25.XII.1998</div> <bR> <div> In the U.S.A. a month-day-year format is common:</div> <div> 12/25/1998   12-25-1998</div> <bR> <div> International standard IS-8601 mandates a year-month-day format, namely either 1998-12-25 or 19981225.</div> <bR> <div> In all of these systems, the first two digits of the year are frequently omitted:</div> <div> 25.12.98   12/25/98   98-12-25   </div> <bR> <div> This confusion leads to misunderstandings. What is 02-03-04? To most people it is 2 Mar 2004; to an American it is 3 Feb 2004; and to a person using the international standard it would be 4 Mar 2002.</div> <bR> <div> If you want to be sure that people understand you, it is recommended to:</div> <div> - write the month with letters instead of numbers, and</div> <div> - write the years as 4-digit numbers.</div> <bR> <div>  <A NAME="3__the_hebrew_calendar"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></div> <div> <B>3. The Hebrew Calendar</b></div> <bR> <div> The current definition of the Hebrew calendar is generally said to have been set down by the Sanhedrin president Hillel II in approximately AD 359. The original details of his calendar are, however, uncertain.</div> <bR> <div> The Hebrew calendar is used for religious purposes by Jews all over the world and is the official calendar of Israel.</div> <bR> <div> The Hebrew calendar is a combined solar/lunar calendar, in that it strives to have its years coincide with the tropical year and its months coincide with the synodic months. This is a complicated goal, and the rules for the Hebrew calendar are correspondingly fascinating.</div> <bR> <bR> <div> <B> <A NAME="3_1__what_does_a_hebrew_year_look_like_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>3.1. What does a Hebrew year look like?</b></div> <bR> <div> An ordinary (non-leap) year has 353, 354, or 355 days.</div> <div> A leap year has 383, 384, or 385 days.</div> <div> The three lengths of the years are termed 'deficient', 'regular',and 'complete', respectively.</div> <bR> <div> An ordinary year has 12 months, a leap year has 13 months.</div> <bR> <div> Every month starts (approximately) on the day of a new moon.</div> <bR> <div> The months and their lengths are:</div> <bR> <div> <I> <TABLE BORDER="2" CELLPADDING="2" CELLSPACING="1" WIDTH="627" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Name</div> </tD> <tD VALIGN=TOP><NOBR><div> Length in a deficient year</div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> Length in a regular year</div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> Length in a complete year</div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Tishri</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 ><NOBR><div> Heshvan</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Kislev</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Tevet</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Shevat</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Adar 1</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Adar 2</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Nisan</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Iyar</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Sivan</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 ><NOBR><div> Tammuz</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Av</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 30</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 30</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> Elul</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 29</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 29</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 ><NOBR><div> TOTAL:</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="179"><div> 353 or 383</div> </tD> <tD VALIGN=TOP WIDTH="165"><div> 354 or 384</div> </tD> <tD VALIGN=TOP WIDTH="179"><div> 355 or 385</div> </tD> </tR> </TABLE></I></div> <bR> <div> The month Adar I is only present in leap years. In non-leap years Adar II is simply called 'Adar'.</div> <bR> <div> Note that in a regular year the numbers 30 and 29 alternate; a complete year is created by adding a day to Heshvan, whereas a deficient year is created by removing a day from Kislev.</div> <bR> <div> The alteration of 30 and 29 ensures that when the year starts with a new moon, so does each month.</div> <bR> <bR> <div> <B> <A NAME="3_2__what_years_are_leap_years_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>3.2. What years are leap years?</b></div> <bR> <div> A year is a leap year if the number year mod 19 is one of the following: 0, 3, 6, 8, 11, 14, or 17.</div> <bR> <div> The value for year in this formula is the 'Anno Mundi' described in <A HREF="#3_8__how_does_one_count_years_" TITLE="Calendars 2"><U>section 3.8</U></A>.</div> <bR> <bR> <div> <B> <A NAME="3_3__what_years_are_deficient_regular"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>3.3. What years are deficient, regular, and complete?</b></div> <bR> <div> That is the wrong question to ask. The correct question to ask is: When does a Hebrew year begin? Once you have answered that question (see <A HREF="#3_6__when_does_a_hebrew_year_begin_" TITLE="Calendars 2"><U>section 3.6</U></A>), the length of the year is the number of days between 1 Tishri in one year and 1 Tishri in the following year.</div> <bR> <bR> <div> <B> <A NAME="3_4__when_is_new_year_s_day_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>3.4. When is New Year's day?</b></div> <bR> <div> That depends. Jews have 4 different days to choose from:</div> <bR> <div> 1 Tishri:  "Rosh HaShanah". This day is a celebration of the creation of the world and marks the start of a new calendar year. This will be the day we shall base our calculations on in the following sections.</div> <bR> <div> 15 Shevat: "Tu B'shevat". The new year for trees, when fruit tithes should be brought.</div> <bR> <div> 1 Nisan:   "New Year for Kings". Nisan is considered the first month, although it occurs 6 or 7 months after the start of the calendar year.</div> <bR> <div> 1 Elul:    "New Year for Animal Tithes (Taxes)".</div> <bR> <div> Only the first two dates are celebrated nowadays.</div> <bR> <div>  <A NAME="3_5__when_does_a_hebrew_day_begin_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></div> <div> <B>3.5. When does a Hebrew day begin?</b></div> <bR> <div> A Hebrew-calendar day does not begin at midnight, but at either sunset or when three medium-sized stars should be visible, depending on the religious circumstance.</div> <bR> <div> Sunset marks the start of the 12 night hours, whereas sunrise marks the start of the 12 day hours. This means that night hours may be longer or shorter than day hours, depending on the season.</div> <bR> <bR> <div> <B> <A NAME="3_6__when_does_a_hebrew_year_begin_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>3.6. When does a Hebrew year begin?</b></div> <bR> <div> The first day of the calendary year, Rosh HaShanah, on 1 Tishri is determined as follows:</div> <bR> <div> 1) The new year starts on the day of the new moon that occurs about 354 days (or 384 days if the previous year was a leap year) after</div> <div> 1 Tishri of the previous year</div> <bR> <div> 2) If the new moon occurs after noon on that day, delay the new year by one day. (Because in that case the new crescent moon will not be visible until the next day.)</div> <bR> <div> 3) If this would cause the new year to start on a Sunday, Wednesday, or Friday, delay it by one day. (Because we want to avoid that</div> <div> Yom Kippur (10 Tishri) falls on a Friday or Sunday, and that Hoshanah Rabba (21 Tishri) falls on a Sabbath (Saturday)).</div> <bR> <div> 4) If two consecutive years start 356 days apart (an illegal year length), delay the start of the first year by two days.</div> <bR> <div> 5) If two consecutive years start 382 days apart (an illegal year length), delay the start of the second year by one day.</div> <bR> <div> Note: Rule 4 can only come into play if the first year was supposed to start on a Tuesday. Therefore a two day delay is used rather that a one day delay, as the year must not start on a Wednesday as stated in rule 3.</div> <bR> <bR> <div> <B> <A NAME="3_7__when_is_the_new_moon_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>3.7. When is the new moon?</b></div> <bR> <div> A calculated new moon is used. In order to understand the calculations, one must know that an hour is subdivided into 1080 'parts'.</div> <bR> <div> The calculations are as follows:</div> <bR> <div> The new moon that started the year AM 1, occurred 5 hours and 204 parts after sunset (i.e. just before midnight on Julian date 6 October 3761 BC).</div> <bR> <div> The new moon of any particular year is calculated by extrapolating from this time, using a synodic month of 29 days 12 hours and 793 parts.</div> <bR> <div> Note that 18:00 Jerusalem time (15:39 UT) is used instead of sunset in all these calculations.</div> <bR> <bR> <div> <B> <A NAME="3_8__how_does_one_count_years_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></b><B>3.8. How does one count years?</b></div> <bR> <div> Years are counted since the creation of the world, which is assumed to have taken place in 3761 BC. In that year, AM 1 started (AM = Anno Mundi = year of the world).</div> <bR> <div> In the year AD 1999 we have witnessed the start of Hebrew year AM 5760.</div> <bR> <bR> <div> <A HREF="id53.htm" TARGET="_top" TITLE="Calendars 3"><U>Continued</U></A></div> <bR> </td> </tr></table></body>