# Rambam - 3 Chapters a Day

## Kiddush HaChodesh - Chapter Six, Kiddush HaChodesh - Chapter Seven, Kiddush HaChodesh - Chapter Eight

## Kiddush HaChodesh - Chapter Six

When [the new moon] was sanctified [based on the testimony of witnesses regarding] the sighting of the moon, the court would calculate the time of the conjunction of the sun and the moon in an exact manner, as the astronomers do.1 [This enabled them] to know whether or not the moon would be sighted.

The first level of these calculations represent approximations of the time of the conjunction, and their accuracy is not great. This approximation of the time of the conjunction is calculated according to the mean rates of movements.2 The time of the conjunction as calculated in this manner is referred to as the *molad*.

The essentials of the calculations that are used when a court to sanctify [the new moon based on the testimony of witnesses of] the sighting [of the moon] does not exist - i.e., the calculations we use today - are referred to as *ibbur*. To explain:

בִזְמַן שֶׁעוֹשִׂין עַל הָרְאִיָּה הָיוּ מְחַשְּׁבִין וְיוֹדְעִין שָׁעָה שֶׁיִּתְקַבֵּץ בּוֹ הַיָּרֵחַ עִם הַחַמָּה בְּדִקְדּוּק הַרְבֵּה כְּדֶרֶךְ שֶׁהָאִיצְטַגְנִינִין עוֹשִׂין. כְּדֵי לֵידַע אִם יֵרָאֶה הַיָּרֵחַ אוֹ לֹא יֵרָאֶה. וּתְחִלַּת אוֹתוֹ הַחֶשְׁבּוֹן הוּא הַחֶשְׁבּוֹן שֶׁמְּחַשְּׁבִין אוֹתוֹ בְּקֵרוּב וְיוֹדְעִין שְׁעַת קִבּוּצָם בְּלֹא דִּקְדּוּק אֶלָּא בְּמַהֲלָכָם הָאֶמְצָעִי הוּא הַנִּקְרָא מוֹלָד. וְעִקְּרֵי הַחֶשְׁבּוֹן שֶׁמְּחַשְּׁבִין בִּזְמַן שֶׁאֵין שָׁם בֵּית דִּין שֶׁיִּקְבְּעוּ בּוֹ עַל הָרְאִיָּה וְהוּא חֶשְׁבּוֹן שֶׁאָנוּ מְחַשְּׁבִין הַיּוֹם הוּא הַנִּקְרָא עִבּוּר:

Day and night are constantly considered a twenty-four hour composite, [on the average:] twelve [hours] of daylight and twelve [hours] of night. An hour can be divided into 1080 units. This number was chosen because it can be divided in half, into fourths, eighths, thirds, sixths, ninths, and tenths.3 Each of these fractions contains many of these units.

בהַיּוֹם וְהַלַּיְלָה אַרְבַּע וְעֶשְׂרִים שָׁעוֹת בְּכָל זְמַן. שְׁתֵּים עֶשְׂרֵה בַּיּוֹם וּשְׁתֵּים עֶשְׂרֵה בַּלַּיְלָה. וְהַשָּׁעָה מְחֻלֶּקֶת לְאֶלֶף וּשְׁמוֹנִים חֲלָקִים. וְלָמָּה חִלְּקוּ הַשָּׁעָה לְמִנְיָן זֶה. לְפִי שֶׁמִּנְיָן זֶה יֵשׁ בּוֹ חֲצִי וּרְבִיעַ וּשְׁמִינִית וּשְׁלִישׁ וּשְׁתוּת וְתֵשַׁע וְחֹמֶשׁ וְעִשּׂוּר. וְהַרְבֵּה חֲלָקִים יֵשׁ לְכָל אֵלּוּ הַשֵּׁמוֹת:

According to this calculation, [the interval] between one conjunction of the moon and the sun and the subsequent conjunction according to their mean movement is twenty-nine full days, twelve hours of the thirtieth day, and 793 units of the thirteenth hour. This is the interval between one conjunction and the next, [and thus,] the length of a lunar month.

גמִשֶּׁיִּתְקַבֵּץ הַיָּרֵחַ וְהַחַמָּה לְפִי חֶשְׁבּוֹן זֶה עַד שֶׁיִּתְקַבְּצוּ פַּעַם שְׁנִיָּה בְּמַהֲלָכָם הָאֶמְצָעִי. תִּשְׁעָה וְעֶשְׂרִים יוֹם וּשְׁתֵּים עֶשְׂרֵה שָׁעוֹת מִיּוֹם שְׁלֹשִׁים מִתְּחִלַּת לֵילוֹ. וּשְׁבַע מֵאוֹת וּשְׁלֹשָׁה וְתִשְׁעִים חֲלָקִים מִשְּׁעַת שְׁלֹשׁ עֶשְׂרֵה. וְזֶה הוּא הַזְּמַן שֶׁבֵּין כָּל מוֹלָד וּמוֹלָד וְזֶה הוּא חָדְשָׁהּ שֶׁל לְבָנָה:

[Accordingly,] an [ordinary] lunar year, which includes twelve of these months, would include three hundred fifty-four days, eight hours, and eight hundred seventy-six units.

A leap year, which would include thirteen of these months, would include three hundred eighty-three days, twenty-one hours, and five hundred eighty-nine units.

A solar year is three hundred sixty-five days and six hours.4 Thus, a solar year exceeds an [ordinary] lunar year by ten days, twenty-one hours, and two hundred and four units.

דשָׁנָה שֶׁל לְבָנָה אִם תִּהְיֶה שְׁנֵים עָשָׂר חֹדֶשׁ מֵחֳדָשִׁים אֵלּוּ יִהְיֶה כְּלָלָהּ שְׁלֹשׁ מֵאוֹת יוֹם וְאַרְבָּעָה וַחֲמִשִּׁים יוֹם וּשְׁמוֹנֶה שָׁעוֹת וּשְׁמוֹנֶה מֵאוֹת וְשִׁשָּׁה וְשִׁבְעִים חֲלָקִים. וְאִם תִּהְיֶה מְעֻבֶּרֶת וְתִהְיֶה הַשָּׁנָה שְׁלֹשָׁה עָשָׂר חֹדֶשׁ יִהְיֶה כְּלָלָהּ שְׁלֹשׁ מֵאוֹת וּשְׁמוֹנִים וּשְׁלֹשָׁה יוֹם וְאַחַת וְעֶשְׂרִים שָׁעוֹת וַחֲמֵשׁ מֵאוֹת וְתִשְׁעָה וּשְׁמוֹנִים חֲלָקִים. וּשְׁנַת הַחַמָּה הִיא שְׁלֹשׁ מֵאוֹת חֲמִשָּׁה וְשִׁשִּׁים יוֹם וְשֵׁשׁ שָׁעוֹת. נִמְצָא תּוֹסֶפֶת שְׁנַת הַחַמָּה עַל שְׁנַת הַלְּבָנָה עֲשָׂרָה יָמִים וְאַחַת וְעֶשְׂרִים שָׁעוֹת וּמָאתַיִם וְאַרְבָּעָה חֲלָקִים:

When the days of a lunar month are counted in groups of seven, according to the weekly cycle, there is a remainder of one day, twelve hours, and 793 units (in numerical terms, 1 - 12 - 793). This is the remainder for a lunar month.

Similarly, when the days of a lunar year are counted in groups of seven, according to the weekly cycle, there is a remainder of four days, eight hours, and 876 units (in numerical terms, 4 - 8 - 876). This is the remainder for an ordinary lunar year. The remainder for a leap year will be five days, twenty-one hours, and 589 units (in numerical terms, 5 - 21 - 589).

הכְּשֶׁתַּשְׁלִיךְ יְמֵי חֹדֶשׁ הַלְּבָנָה שִׁבְעָה שִׁבְעָה שֶׁהֵן יְמֵי הַשָּׁבוּעַ. יִשָּׁאֵר יוֹם אֶחָד וּשְׁתֵּים עֶשְׂרֵה שָׁעוֹת וּשְׁבַע מֵאוֹת וּשְׁלֹשָׁה וְתִשְׁעִים חֲלָקִים. סִימָן לָהֶם אי''ב תשצ''ג. וְזוֹ הִיא שְׁאֵרִית חֹדֶשׁ הַלְּבָנָה. וְכֵן כְּשֶׁתַּשְׁלִיךְ יְמֵי שְׁנַת הַלְּבָנָה שִׁבְעָה שִׁבְעָה. אִם שָׁנָה פְּשׁוּטָה הִיא יִשָּׁאֵר מִמֶּנָּה אַרְבָּעָה יָמִים וּשְׁמוֹנֶה שָׁעוֹת וּשְׁמוֹנֶה מֵאוֹת וְשִׁשָּׁה וְשִׁבְעִים חֲלָקִים. סִימָן לָהֶם ד''ח תתע''ו. וְזוֹ הִיא שְׁאֵרִית שָׁנָה פְּשׁוּטָה. וְאִם שָׁנָה מְעֵבֶּרֶת הִיא תִּהְיֶה שְׁאֵרִיתָהּ חֲמִשָּׁה יָמִים וְאַחַת וְעֶשְׂרִים שָׁעוֹת וַחֲמֵשׁ מֵאוֹת וְתִשְׁעָה וּשְׁמוֹנִים חֲלָקִים. סִימָן לָהֶם הכ''א תקפ''ט:

When you know the time of the conjunction [of the sun and the moon] for any particular month, and add 1 - 12 - 793, you will arrive at the time of the conjunction of the following month. Thus, you will be able to determine on which day of the week and at which hour it will take place, and how many units of that hour will have passed.5

וכְּשֶׁיִּהְיֶה עִמְּךָ יָדוּעַ מוֹלַד חֹדֶשׁ מִן הֶחֳדָשִׁים וְתוֹסִיף עָלָיו אי''ב תשצ''ג יֵצֵא מוֹלָד שֶׁאַחֲרָיו. וְתֵדַע בְּאֵי זֶה יוֹם מִימֵי הַשָּׁבוּעַ וּבְאֵי זוֹ שָׁעָה וּבְכַמָּה חֲלָקִים יִהְיֶה:

What is implied? If the conjunction [of the moon and the sun] for the month of Nisan takes place on Sunday, five hours and 107 units after sunrise (in numerical terms 1 - 56 - 107), by adding the remainder for a lunar month, 1 - 12 - 793, you will be able to determine that the conjunction for the month of Iyar will take place on Tuesday night, five hours and 900 units after nightfall (in numerical terms, 3 - 5 - 900). One may follow this same method [of calculation] month after month for eternity.

זכֵּיצַד. הֲרֵי שֶׁהָיָה מוֹלַד נִיסָן בְּאֶחָד בְּשַׁבָּת בְּחָמֵשׁ שָׁעוֹת בַּיּוֹם וּמֵאָה וְשִׁבְעָה חֲלָקִים סִימָן לָהֶם אהק''ז. כְּשֶׁתּוֹסִיף עָלָיו שְׁאֵרִית חֹדֶשׁ הַלְּבָנָה וְהוּא אי''ב תשצ''ג. יֵצֵא מוֹלַד אִיָּר בְּלֵיל שְׁלִישִׁי חָמֵשׁ שָׁעוֹת בַּלַּיְלָה וּתְשַׁע מֵאוֹת חֲלָקִים. סִימָן לָהֶם ג''ה תת''ק. וְעַל דֶּרֶךְ זוֹ עַד סוֹף הָעוֹלָם חֹדֶשׁ אַחַר חֹדֶשׁ:

Similarly, if you know the time of the conjunction for a particular year and you add its remainder - either the remainder of an ordinary year or the remainder of a leap year - to the time of the conjunction, you will determine the time of the conjunction of the following year. This method [of calculation] may be followed year after year for eternity.

The first conjunction from which we begin, the conjunction of the first year of creation, was on Monday night, 5 hours and 204 units after nightfall7 (in numerical terms, 2 - 5 - 204). This is the starting point for these calculations.

חוְכֵן כְּשֶׁיִּהְיֶה עִמְּךָ יָדוּעַ מוֹלַד שָׁנָה זוֹ וְתוֹסִיף שְׁאֵרִיתָהּ עַל יְמֵי הַמּוֹלָד. אִם פְּשׁוּטָה הִיא שְׁאֵרִית הַפְּשׁוּטָה וְאִם מְעֻבֶּרֶת הִיא שְׁאֵרִית הַמְעֻבֶּרֶת. יֵצֵא לְךָ מוֹלַד שָׁנָה שֶׁלְּאַחֲרֶיהָ. וְכֵן שָׁנָה אַחַר שָׁנָה עַד סוֹף הָעוֹלָם. וְהַמּוֹלָד הָרִאשׁוֹן שֶׁמִּמֶּנּוּ תַּתְחִיל הוּא מוֹלַד שֶׁהָיָה בַּשָּׁנָה הָרִאשׁוֹנָה שֶׁל יְצִירָה. וְהוּא הָיָה בְּלֵיל שֵׁנִי חָמֵשׁ שָׁעוֹת בַּלַּיְלָה וּמָאתַיִם וְאַרְבָּעָה חֲלָקִים. סִימָן לָהֶם בהר''ד וּמִמֶּנּוּ הוּא תְּחִלַּת הַחֶשְׁבּוֹן:

In all the calculations to determine the time of the conjunction, when the remainder [of one period] should be added to another remainder, [the following principles should be adhered to:] When a sum of 1080 units is reached, it should be counted as an hour, and added to the number of the hours. When a sum of twenty-four hours is reached, it should be counted as a day, and added to the number of days. When the number of days is greater than seven, [all multiples of] seven should be subtracted from the sum, and the remainder be focused on.

For the purpose of our calculations is not to know the number of days, but rather to know on which day of the week, and at what hour and after how many units will the conjunction take place.

טבְּכָל הַחֶשְׁבּוֹנוֹת הָאֵלּוּ שֶׁתֵּדַע מֵהֶן הַמּוֹלָד. כְּשֶׁתּוֹסִיף שְׁאֵרִית עִם שְׁאֵרִית. כְּשֶׁיִּתְקַבֵּץ מִן הַחֲלָקִים אֶלֶף וּשְׁמוֹנִים תַּשְׁלִים שָׁעָה אַחַת וְתוֹסִיף אוֹתָהּ לְמִנְיַן הַשָּׁעוֹת. וּכְשֶׁיִּתְקַבֵּץ מִן הַשָּׁעוֹת אַרְבַּע וְעֶשְׂרִים תַּשְׁלִים יוֹם וְתוֹסִיף מִמֶּנּוּ לְמִנְיַן הַיָּמִים. וּכְשֶׁיִּתְקַבֵּץ מִן הַיָּמִים יוֹתֵר עַל שִׁבְעָה תַּשְׁלִיךְ שִׁבְעָה מִן הַמִּנְיָן וְתַנִּיחַ הַשְּׁאָר. שֶׁאֵין אָנוּ מְחַשְּׁבִין לֵידַע מִנְיַן הַיָּמִים אֶלָּא לֵידַע בְּאֵי זֶה יוֹם מִימֵי הַשָּׁבוּעַ וּבְאֵי זֶה שָׁעָה וְאֵי זֶה חֵלֶק יִהְיֶה הַמּוֹלָד:

[The fixed calendar is structured in] a nineteen-year cycle, including seven leap years and twelve ordinary years. This is called a *machzor*.

Why was this [structure] chosen? Because when you total the number of days in twelve ordinary years and seven leap years together with their hours and their units, counting all [sums of] 1080 units as an hour, [all sums of] twenty-four hours as a day, and adding them to the number of days, the total will equal nineteen solar years, each of these years being 365 days and six hours.

The difference between the days of the solar calendar [and the lunar calendar] will be only one hour and 485 units (in numerical terms, 1 - 485).8

יכָּל תְּשַׁע עֶשְׂרֵה שָׁנָה שֶׁיִּהְיוּ מֵהֶן שֶׁבַע שָׁנִים מְעֵבָּרוֹת וּשְׁתֵּים עֶשְׂרֵה פְּשׁוּטוֹת נִקְרָא מַחֲזוֹר. וְלָמָּה סָמַכְנוּ עַל מִנְיָן זֶה. שֶׁבִּזְמַן שֶׁאַתָּה מְקַבֵּץ מִנְיַן יְמֵי שְׁתֵּים עֶשְׂרֵה שָׁנָה פְּשׁוּטוֹת וְשֶׁבַע מְעֵבָּרוֹת וּשְׁעוֹתֵיהֶן וְחֶלְקֵיהֶן וְתַשְׁלִים כָּל אֶלֶף וּשְׁמֹנִים חֲלָקִים שָׁעָה. וְכָל אַרְבַּע וְעֶשְׂרִים שָׁעוֹת יוֹם. וְתוֹסִיף לְמִנְיַן הַיָּמִים. תִּמְצָא הַכּל תְּשַׁע עֶשְׂרֵה שָׁנָה מִשְּׁנֵי הַחַמָּה שֶׁכָּל שָׁנָה מֵהֶן שְׁלֹשׁ מֵאוֹת וַחֲמִשָּׁה וְשִׁשִּׁים יוֹם וְשֵׁשׁ שָׁעוֹת בְּשָׁוֶה. וְלֹא יִשָּׁאֵר מִמִּנְיַן יְמֵי הַחַמָּה בְּכָל תְּשַׁע עֶשְׂרֵה שָׁנָה חוּץ מִשָּׁעָה אַחַת וְאַרְבַּע מֵאוֹת וּשְׁמוֹנִים וַחֲמִשָּׁה חֲלָקִים. סִימָן לָהֶם אתפ''ה:

Thus, in such a [nineteen-year] cycle, the months are lunar months, and the years are solar years. The seven leap years in each cycle should be the following: The third year of the cycle, the sixth year, the eighth year, the eleventh year, the fourteenth year, the seventeenth year, the nineteenth year9 (in numbers, 3, 6, 8, 11, 14, 17, 19).

יאנִמְצָא בְּמַחֲזוֹר שֶׁהוּא כָּזֶה הֶחֳדָשִׁים כֻּלָּם חָדְשֵׁי הַלְּבָנָה וְהַשָּׁנִים שְׁנֵי הַחַמָּה. וְהַשֶּׁבַע שָׁנִים הַמְעֻבָּרוֹת שֶׁבְּכָל מַחֲזוֹר וּמַחֲזוֹר לְפִי חֶשְׁבּוֹן זֶה הֵם שָׁנָה שְׁלִישִׁית מִן הַמַּחֲזוֹר וְשִׁשִּׁית וּשְׁמִינִית וּשְׁנַת אַחַת עֶשְׂרֵה וּשְׁנַת אַרְבַּע עֶשְׂרֵה וּשְׁנַת שְׁבַע עֶשְׂרֵה וּשְׁנַת י''ט. סִימָן לָהֶם גו''ח י''א י''ד י''ז י''ט:

When you add the remainders of each of the twelve ordinary years, [the remainder of each year] being 4 - 8 - 876, and the remainders of the seven leap years, [the remainder of each year] being 5 - 21 - 589, and then divide the entire sum in groups of seven, there is a remainder of two days, sixteen hours, and 595 units (in numerical terms, 2 - 16 - 595). This is the remainder of a [nineteen-year] cycle.

יבכְּשֶׁתְּקַבֵּץ שְׁאֵרִית כָּל שָׁנָה מִשְּׁתֵּים עֶשְׂרֵה שָׁנָה הַפְּשׁוּטוֹת שֶׁהִיא ד''ח תתע''ו. וּשְׁאֵרִית כָּל שָׁנָה מִשֶּׁבַע שָׁנִים הַמְעֻבָּרוֹת שֶׁהִיא הכ''א תקפ''ט. וְתַשְׁלִיךְ הַכּל שִׁבְעָה שִׁבְעָה יִשָּׁאֵר שְׁנֵי יָמִים וְשֵׁשׁ עֶשְׂרֵה שָׁעוֹת וַחֲמֵשׁ מֵאוֹת וַחֲמִשָּׁה וְתִשְׁעִים חֲלָקִים. סִימָן לָהֶם בי''ו תקצ''ה. וְזֶה הוּא שְׁאֵרִית הַמַּחֲזוֹר:

When you know the time of the conjunction of the beginning of a [nineteen-year] cycle, by adding 2 - 16 - 595 to it you will be able to determine the beginning of the next [nineteen-year] cycle, and similarly all the [subsequent nineteen-year] cycles for eternity. As stated above, the conjunction [marking] the beginning of the first [nineteen-year] cycle took place on 2 - 5 - 204. [The expression,] the conjunction of a year refers to the conjunction of the month of Tishrei for that year.10

יגכְּשֶׁיִּהְיֶה לְךָ יָדוּעַ מוֹלַד תְּחִלַּת מַחֲזוֹר וְתוֹסִיף עָלָיו בי''ו תקצ''ה. יָצָא לְךָ תְּחִלַּת הַמַּחֲזוֹר שֶׁאַחֲרָיו וְכֵן מוֹלַד כָּל מַחֲזוֹר וּמַחֲזוֹר עַד סוֹף הָעוֹלָם. וּכְבָר אָמַרְנוּ שֶׁמּוֹלַד תְּחִלַּת הַמַּחֲזוֹר הָרִאשׁוֹן הָיָה לבהר''ד. וּמוֹלַד הַשָּׁנָה הוּא מוֹלַד תִּשְׁרֵי שֶׁל אוֹתָהּ הַשָּׁנָה:

Using the above method, it is possible to know the conjunction [marking] the beginning of any particular year, or any particular month, whether for the years that have passed or for the years to come.

What is implied? One should take the number of years that have passed until Tishrei of the [desired] year and group them in nineteen- year cycles. Thus, one will be able to determine the number of nineteen-year cycles that have passed and the number of years that have passed within the [nineteen-year] cycle that has not been completed [until the desired year]. One should add 2 - 16 - 595 for each cycle, 4 - 8 - 876 for every ordinary year of the cycle that has not been completed, and 5 - 21 - 589 for every leap year [of the cycle that has not been completed].

One should then add together the entire sum, calculating [the groups of 1080] units as hours, the [groups of 24] hours as days, and the groups of seven days [as weeks]. [By adding] the remainder of the days, hours, and units [to 2 - 5 - 204], one can determine the time of the conjunction of the desired year.

ידוּבַדֶּרֶךְ הַזֹּאת תֵּדַע מוֹלַד כָּל שָׁנָה וְשָׁנָה שֶׁתִּרְצֶה. וּמוֹלַד כָּל חֹדֶשׁ וְחֹדֶשׁ שֶׁתִּרְצֶה. מִשָּׁנִים שֶׁעָבְרוּ אוֹ מִשָּׁנִים שֶׁעֲתִידִים לָבֹא. כֵּיצַד. תִּקַּח שְׁנֵי יְצִירָה שֶׁעָבְרוּ וְגָמְרוּ וְתַעֲשֶׂה אוֹתָם מַחֲזוֹרִין שֶׁל תְּשַׁע עֶשְׂרֵה תְּשַׁע עֶשְׂרֵה שָׁנָה עַד תִּשְׁרֵי שֶׁל אוֹתָהּ הַשָּׁנָה. וְתֵדַע מִנְיַן הַמַּחֲזוֹרִין שֶׁעָבְרוּ וּמִנְיַן הַשָּׁנִים שֶׁעָבְרוּ מִמַּחֲזוֹר שֶׁעֲדַיִן לֹא נִשְׁלַם. וְתִקַּח לְכָל מַחֲזוֹר וּמַחֲזוֹר בי''ו תקצ''ה. וּלְכָל שָׁנָה וְשָׁנָה פְּשׁוּטָה מִשְּׁנֵי הַמַּחֲזוֹר שֶׁלֹּא נִשְׁלַם ד''ח תתע''ו. וּלְכָל שָׁנָה מְעֵבֶּרֶת הכ''א תקפ''ט. וּתְקַבֵּץ הַכּל וְתַשְׁלִים הַחֲלָקִים שָׁעוֹת. וְתַשְׁלִים הַשָּׁעוֹת יָמִים. וְהַיָּמִים תַּשְׁלִיכֵם שִׁבְעָה שִׁבְעָה. וְהַנִּשְׁאָר מִן הַיָּמִים וּמִן הַשָּׁעוֹת וְהַחֲלָקִים הוּא מוֹלַד שָׁנָה הַבָּאָה שֶׁתִּרְצֶה לֵידַע מוֹלָדָהּ:

The time of the conjunction of a year determined through the above method is the conjunction of Rosh Chodesh Tishrei. By adding 1 - 12 - 793 to this figure, one can determine the conjunction of Marcheshvan, and by adding 1 - 12 - 793 to [the conjunction of] Marcheshvan, one can determine the conjunction of Kislev. Similarly, one can determine the conjunction of all subsequent months for eternity.

טומוֹלַד הַשָּׁנָה שֶׁיֵּצֵא בְּחֶשְׁבּוֹן זֶה הוּא מוֹלַד רֹאשׁ חֹדֶשׁ תִּשְׁרֵי. וּכְשֶׁתּוֹסִיף עָלָיו אי''ב תשצ''ג יֵצֵא מוֹלַד מַרְחֶשְׁוָן. וּכְשֶׁתּוֹסִיף עַל מַרְחֶשְׁוָן אי''ב תשצ''ג יֵצֵא מוֹלַד כִּסְלֵו. וְכֵן לְכָל חֹדֶשׁ וְחֹדֶשׁ זֶה אַחַר זֶה עַד סוֹף הָעוֹלָם:

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The term conjunction refers to the point when the sun, the moon and the earth are positioned in that order in a direct line. Therefore, as seen from the earth, the moon does not reflect the light of the sun. [When the sun and the moon have the same latitude (see Chapter 16) - i.e., when they are in the same plane - a conjunction is the cause of a solar eclipse. Ordinarily, however, there is a difference in latitude, and an alignment of this nature does not cause an eclipse.]

Our translation differs from the standard published text of the *Mishneh Torah*, and is based on the version found in authoritative manuscripts and early printings.

The term mean rate of movement refers to the average movement of the sun or the moon in angular degrees over a particular period. To explain: It was easy to calculate the number of conjunctions between one solar eclipse and another. Afterwards, this number would be multiplied by 360 (the number of degrees in a circle) and then divided by the number of years, months, days, or hours (depending on the mean one wanted to reach) that had passed between the two eclipses.

In fact, however, the sun - and to a much greater extent, the moon - would deviate from this mean rate of movement - i.e., the position in which they are located in the heavens differs from the position that would be reached by calculating the mean rate of progress. As is explained in the succeeding chapters, there are various ways of correcting and adjusting these mean calculations so that the actual position of these celestial bodies can be determined.

The only integer that cannot be divided into this sum is seven. The commentaries have noted that the number 360 also can be divided into all the fractions mentioned by the Rambam and question why he did not use this smaller figure.

See Chapter 9, Halachah 1, which explains that there are two views concerning whether this is an approximation or an exact figure. See also Chapter 10, Halachah 6.

As mentioned above, the Rambam is speaking about an average figure. Accordingly, this figure alone is not sufficient for the calculations of when the moon can be sighted. It is useful for structuring the fixed calendar, as explained in this and the following chapter.

*Kinat Eliyahu* suggests that the Rambam should have stated 1 - 17, since five hours after sunrise is seventeen hours after the beginning of the day.

*Tosafot, Rosh HaShanah* 8 a,b, explains that this follows the view of Rabbi Eliezer (*Rosh HaShanah* 10b), who states that the world was created in Tishrei. According to this conception, the conjunction for Rosh HaShanah, the day of Adam's creation, was the fourteenth hour of Friday (the second hour after sunrise). Since the first day of creation was the twenty-fifth of Elul, the year prior to that of Adam's creation is also significant. To calculate the conjunction of that year, we subtract the remainder of an ordinary year - 4 days, 8 hours, and 876 units - from six days and fourteen hours. This produces the figure cited by the Rambam.

As mentioned in Halachah 4, each ordinary lunar year is 10 days, 21 hours, and 204 units shorter than a solar year. Thus, the difference between the 12 ordinary lunar years of a nineteen-year cycle and the corresponding solar years is 130 days, 14 hours, and 288 units.

A lunar leap year is 18 days, 15 hours, and 589 units longer than a solar year. Thus, the difference between the seven leap years of a nineteen-year cycle and the corresponding solar years is 130 days, 12 hours, and 883 units. When this sum is subtracted from the figure mentioned in the previous paragraph, the remainder mentioned by the Rambam is reached.

As explained in Chapter 10, Halachah 1, there is another reckoning, which maintains that the nineteen-year cycle produces a more exact interrelation between the two calendars.

By structuring the pattern in this manner, an interrelation [albeit not a totally exact one] is established between the lunar and solar calendars in each of the years. After several years in which the number of days of the solar calendar exceeds those of the lunar calendar, a leap year reverses that pattern and establishes an approximate equivalence. In this way, we ensure that the Pesach is always celebrated after the vernal equinox.

This point of clarification is necessary, because there are certain halachic matters regarding which Nisan is considered the beginning of the year.

The term conjunction refers to the point when the sun, the moon and the earth are positioned in that order in a direct line. Therefore, as seen from the earth, the moon does not reflect the light of the sun. [When the sun and the moon have the same latitude (see Chapter 16) - i.e., when they are in the same plane - a conjunction is the cause of a solar eclipse. Ordinarily, however, there is a difference in latitude, and an alignment of this nature does not cause an eclipse.]

Our translation differs from the standard published text of the *Mishneh Torah*, and is based on the version found in authoritative manuscripts and early printings.

The term mean rate of movement refers to the average movement of the sun or the moon in angular degrees over a particular period. To explain: It was easy to calculate the number of conjunctions between one solar eclipse and another. Afterwards, this number would be multiplied by 360 (the number of degrees in a circle) and then divided by the number of years, months, days, or hours (depending on the mean one wanted to reach) that had passed between the two eclipses.

In fact, however, the sun - and to a much greater extent, the moon - would deviate from this mean rate of movement - i.e., the position in which they are located in the heavens differs from the position that would be reached by calculating the mean rate of progress. As is explained in the succeeding chapters, there are various ways of correcting and adjusting these mean calculations so that the actual position of these celestial bodies can be determined.

The only integer that cannot be divided into this sum is seven. The commentaries have noted that the number 360 also can be divided into all the fractions mentioned by the Rambam and question why he did not use this smaller figure.

See Chapter 9, Halachah 1, which explains that there are two views concerning whether this is an approximation or an exact figure. See also Chapter 10, Halachah 6.

As mentioned above, the Rambam is speaking about an average figure. Accordingly, this figure alone is not sufficient for the calculations of when the moon can be sighted. It is useful for structuring the fixed calendar, as explained in this and the following chapter.

*Kinat Eliyahu* suggests that the Rambam should have stated 1 - 17, since five hours after sunrise is seventeen hours after the beginning of the day.

*Tosafot, Rosh HaShanah* 8 a,b, explains that this follows the view of Rabbi Eliezer (*Rosh HaShanah* 10b), who states that the world was created in Tishrei. According to this conception, the conjunction for Rosh HaShanah, the day of Adam's creation, was the fourteenth hour of Friday (the second hour after sunrise). Since the first day of creation was the twenty-fifth of Elul, the year prior to that of Adam's creation is also significant. To calculate the conjunction of that year, we subtract the remainder of an ordinary year - 4 days, 8 hours, and 876 units - from six days and fourteen hours. This produces the figure cited by the Rambam.

As mentioned in Halachah 4, each ordinary lunar year is 10 days, 21 hours, and 204 units shorter than a solar year. Thus, the difference between the 12 ordinary lunar years of a nineteen-year cycle and the corresponding solar years is 130 days, 14 hours, and 288 units.

A lunar leap year is 18 days, 15 hours, and 589 units longer than a solar year. Thus, the difference between the seven leap years of a nineteen-year cycle and the corresponding solar years is 130 days, 12 hours, and 883 units. When this sum is subtracted from the figure mentioned in the previous paragraph, the remainder mentioned by the Rambam is reached.

As explained in Chapter 10, Halachah 1, there is another reckoning, which maintains that the nineteen-year cycle produces a more exact interrelation between the two calendars.

By structuring the pattern in this manner, an interrelation [albeit not a totally exact one] is established between the lunar and solar calendars in each of the years. After several years in which the number of days of the solar calendar exceeds those of the lunar calendar, a leap year reverses that pattern and establishes an approximate equivalence. In this way, we ensure that the Pesach is always celebrated after the vernal equinox.

This point of clarification is necessary, because there are certain halachic matters regarding which Nisan is considered the beginning of the year.

## Kiddush HaChodesh - Chapter Seven

[Rosh Chodesh is generally instituted on the day of the conjunction. Nevertheless,] Rosh Chodesh Tishrei1 should never be established on a Sunday, a Wednesday, or a Friday - in symbols, אד"ו - although, according to these calculations, [the conjunction for the month will occur on these days]. Instead, when the conjunction for the month of Tishrei occurs on any of these three days, Rosh Chodesh should be established on the following day.2

What is implied? When the conjunction occurs on Sunday, Rosh Chodesh Tishrei should be established on Monday. When the conjunction occurs on Wednesday, Rosh Chodesh Tishrei should be established on Thursday. When the conjunction occurs on Friday, Rosh Chodesh Tishrei should be established on the Sabbath.3

אאֵין קוֹבְעִין לְעוֹלָם רֹאשׁ חֹדֶשׁ תִּשְׁרֵי לְפִי חֶשְׁבּוֹן זֶה לֹא בְּאֶחָד בְּשַׁבָּת וְלֹא בִּרְבִיעִי בְּשַׁבָּת וְלֹא בְּעֶרֶב שַׁבָּת. סִימָן לָהֶם אד''ו. אֶלָּא כְּשֶׁיִּהְיֶה מוֹלַד תִּשְׁרֵי בְּאֶחָד מִשְּׁלֹשָׁה יָמִים הָאֵלּוּ קוֹבְעִין רֹאשׁ חֹדֶשׁ בַּיּוֹם שֶׁלְּאַחֲרָיו. כֵּיצַד. הֲרֵי שֶׁהָיָה הַמּוֹלָד בְּאֶחָד בְּשַׁבָּת קוֹבְעִין רֹאשׁ חֹדֶשׁ תִּשְׁרֵי יוֹם שֵׁנִי. וְאִם הָיָה הַמּוֹלָד בִּרְבִיעִי קוֹבְעִין רֹאשׁ חֹדֶשׁ יוֹם חֲמִישִׁי. וְאִם הָיָה הַמּוֹלָד בְּשִׁשִּׁי קוֹבְעִין רֹאשׁ חֹדֶשׁ בִּשְׁבִיעִי:

Similarly, if the conjunction [for the month of Tishrei]4 takes place at noon or after noon, Rosh Chodesh should be established on the following day.5

What is implied? When the conjunction takes place on Monday, six hours after daybreak or later, Rosh Chodesh is established on Tuesday. If, however, the conjunction takes place before noon, even if only a single unit prior, Rosh Chodesh is established on the day of the conjunction, provided that day is neither Sunday, Wednesday, nor Friday.

בוְכֵן אִם יִהְיֶה הַמּוֹלָד בַּחֲצִי הַיּוֹם אוֹ לְמַעְלָה מֵחֲצִי הַיּוֹם קוֹבְעִין רֹאשׁ חֹדֶשׁ בַּיּוֹם שֶׁלְּאַחֲרָיו. כֵּיצַד. הֲרֵי שֶׁהָיָה הַמּוֹלָד בְּיוֹם שֵׁנִי בְּשֵׁשׁ שָׁעוֹת בַּיּוֹם אוֹ יֶתֶר עַל שֵׁשׁ שָׁעוֹת קוֹבְעִין רֹאשׁ חֹדֶשׁ בִּשְׁלִישִׁי. וְאִם יִהְיֶה הַמּוֹלָד קֹדֶם חֲצִי הַיּוֹם אֲפִלּוּ בְּחֵלֶק אֶחָד קוֹבְעִין רֹאשׁ הַחֹדֶשׁ בְּאוֹתוֹ יוֹם הַמּוֹלָד עַצְמוֹ. וְהוּא שֶׁלֹּא יִהְיֶה אוֹתוֹ הַיּוֹם מִימֵי אד''ו:

When the conjunction takes place at noon or after noon, and [Rosh Chodesh Tishrei would be] postponed to the following day - if that following day is either Sunday, Wednesday, or Friday, Rosh Chodesh is postponed again, and is established on the third day after the conjunction.

What is implied? If the conjunction takes place on the Sabbath after noon (in numbers, 7 - 186), in such a year Rosh Chodesh should be established on Monday.7 Similarly, if the conjunction takes place on Tuesday at noon or after noon, Rosh Chodesh should be established on Thursday.

גכְּשֶׁיִּהְיֶה הַמּוֹלָד בַּחֲצִי הַיּוֹם אוֹ אַחַר חֲצוֹת וְיִדָּחֶה לַיּוֹם שֶׁלְּאַחֲרָיו. אִם יִהְיֶה יוֹם שֶׁלְּאַחֲרָיו מִימֵי אד''ו הֲרֵי זֶה נִדְחֶה לְשֶׁלְּאַחֲרָיו וְיִהְיֶה רֹאשׁ הַחֹדֶשׁ קָבוּעַ בִּשְׁלִישִׁי מִיּוֹם הַמּוֹלָד. כֵּיצַד. הֲרֵי שֶׁיִּהְיֶה הַמּוֹלָד בְּשַׁבָּת בַּחֲצוֹת סִימָן זי''ח קוֹבְעִין רֹאשׁ הַחֹדֶשׁ בַּשָּׁנָה שֶׁמּוֹלָדָהּ כָּזֶה בְּשֵׁנִי בְּשַׁבָּת. וְכֵן אִם הָיָה הַמּוֹלָד בִּשְׁלִישִׁי בַּחֲצוֹת אוֹ אַחַר חֲצוֹת קוֹבְעִין רֹאשׁ הַחֹדֶשׁ בַּחֲמִישִׁי בְּשַׁבָּת:

In an ordinary year, when the conjunction [of the month] of Tishrei falls on the night of the third day,8 nine hours and 204 units (in numbers, 3 - 9 - 204) or more after nightfall, Rosh Chodesh is postponed, and instead of being established on Tuesday, it is established on Thursday.9

דמוֹלַד תִּשְׁרֵי שֶׁיָּצָא בְּחֶשְׁבּוֹן זֶה בְּלֵיל שְׁלִישִׁי בְּתֵשַׁע שָׁעוֹת בַּלַּיְלָה וּמָאתַיִם וְאַרְבָּעָה חֲלָקִים מִשָּׁעָה עֲשִׂירִית סִימָנָהּ ג''ט ר''ד. אוֹ יוֹתֵר עַל זֶה. אִם הָיְתָה שָׁנָה פְּשׁוּטָה דּוֹחִין אֶת רֹאשׁ הַחֹדֶשׁ וְאֵין קוֹבְעִים אוֹתוֹ בִּשְׁלִישִׁי בְּשָׁנָה זוֹ אֶלָּא בַּחֲמִישִׁי בְּשַׁבָּת:

A similar situation [may arise] in a year that follows a leap year: If the conjunction for Tishrei takes place on Monday, three hours and 589 units or more after daybreak (in numbers, 2 - 1510 - 589), Rosh Chodesh is not established on Monday, but on Tuesday.11

הוְכֵן אִם יָצָא מוֹלַד תִּשְׁרֵי בְּיוֹם שֵׁנִי בְּשָׁלֹשׁ שָׁעוֹת בְּיוֹם וְתקפ''ט חֲלָקִים מִשָּׁעָה רְבִיעִית. סִימָנָהּ בט''ו תקפ''ט. אוֹ יֶתֶר עַל כֵּן. אִם הָיְתָה אוֹתָהּ הַשָּׁנָה מוֹצָאֵי הַמְעֻבֶּרֶת שֶׁהָיְתָה הַשָּׁנָה הַסְּמוּכָה לָהּ שֶׁעָבְרָה מְעֻבֶּרֶת. אֵין קוֹבְעִין רֹאשׁ הַחֹדֶשׁ בְּשֵׁנִי בְּשָׁנָה זוֹ אֶלָּא בִּשְׁלִישִׁי:

If, however, the conjunction of an ordinary year occurs [even] one unit earlier - i.e., were it to be 3 - 9 - 203 or earlier - [Rosh Chodesh] should be established on Tuesday, [rather than postponed until Thursday as mentioned above].

Similarly, if the conjunction of a year following a leap year occurs [even] one unit earlier - i.e., were it to be 2 - 15 - 588 or earlier - [Rosh Chodesh] should be established on Monday.

Thus, the way to determine [the day on which] Rosh Chodesh Tishrei will be established according to these calculations is as follows: One should first determine the day [of the week], the hour of the day - or night - and the number of units of the hour when the conjunction takes place. The day of the conjunction will be the day of Rosh Chodesh, except in the following instances:

a) [The conjunction] takes place on Sunday, Wednesday, or Friday;

b) The conjunction takes place at noon or after noon;

c) In an ordinary year, [the conjunction] takes place on the night of the third day, after 204 units of the tenth hour have passed, or later [that day];

d) In an ordinary year that follows a leap year, the conjunction takes place on Monday past 589 units of the fourth hour after daybreak has passed or later [that day].

If the conjunction occurs in one of these four instances, [Rosh Chodesh] is not established on the day of the conjunction, but rather on the day that follows, or on the day following that, as explained.

והָיָה מוֹלַד הַשָּׁנָה הַפְּשׁוּטָה שֶׁאָמַרְנוּ שֶׁתִּדָּחֶה לַחֲמִישִׁי פָּחוֹת חֵלֶק אֶחָד. כְּגוֹן שֶׁיָּצָא סִימָנָהּ ג''ט ר''ג אוֹ פָּחוֹת מִזֶּה. קוֹבְעִין אוֹתָהּ בִּשְׁלִישִׁי. וְכֵן אִם הָיָה מוֹלַד מוֹצָאֵי הָעִבּוּר בְּיוֹם שֵׁנִי פָּחוֹת חֵלֶק. כְּגוֹן שֶׁהָיָה סִימָנָהּ בט''ו תקפ''ח אוֹ פָּחוֹת מִזֶּה. קוֹבְעִין אוֹתָהּ בְּשֵׁנִי. נִמְצָא דֶּרֶךְ קְבִיעַת רֹאשׁ חֹדֶשׁ תִּשְׁרֵי לְפִי חֶשְׁבּוֹן זֶה כָּךְ הוּא. תַּחְשֹׁב וְתֵדַע הַמּוֹלָד בְּאֵי זֶה יוֹם יִהְיֶה וּבְכַמָּה שָׁעוֹת מִן הַיּוֹם אוֹ מִן הַלַּיְלָה וּבְכַמָּה חֲלָקִים מִן הַשָּׁעָה. וְיוֹם הַמּוֹלָד הוּא יוֹם הַקְּבִיעָה לְעוֹלָם. אֶלָּא אִם כֵּן הָיָה בְּאֶחָד בְּשַׁבָּת אוֹ בִּרְבִיעִי אוֹ בְּעֶרֶב שַׁבָּת. אוֹ אִם הָיָה הַמּוֹלָד בַּחֲצוֹת הַיּוֹם אוֹ אַחַר חֲצוֹת. אוֹ אִם הָיָה בר''ד חֲלָקִים מִשָּׁעָה עֲשִׂירִית מִלֵּיל שְׁלִישִׁי אוֹ יוֹתֵר עַל זֶה וְהָיְתָה שָׁנָה פְּשׁוּטָה. אוֹ שֶׁהָיָה הַמּוֹלָד בתקפ''ט חֲלָקִים מִשָּׁעָה רְבִיעִית מִיּוֹם שֵׁנִי וְהָיְתָה הַשָּׁנָה פְּשׁוּטָה שֶׁאַחַר הַמְעֵבֶּרֶת. שֶׁאִם יֶאֱרַע בְּאֶחָד מֵאַרְבָּעָה דְּבָרִים הָאֵלּוּ אֵין קוֹבְעִין בְּיוֹם הַמּוֹלָד אֶלָּא בַּיּוֹם שֶׁלְּאַחֲרָיו אוֹ שֶׁלְּאַחַר אַחֲרָיו כַּדֶּרֶךְ שֶׁבֵּאַרְנוּ:

Why is [Rosh HaShanah] not established [on the day of the conjunction] when it falls on Sunday, Wednesday, or Friday? Because these calculations determine the conjunction of the sun and the moon only according to their mean [rate of] progress, and do not [necessarily] reflect the true position [of the sun and the moon in the celestial sphere], as explained. Therefore, they instituted that [on] one day [Rosh Chodesh] would be established and on the following day it would be postponed, so that they would ascertain the day when the true conjunction takes place.12

What is implied? [When according to our calculations, the conjunction occurs on] Tuesday, we establish [Rosh Chodesh]. [When it occurs] on Wednesday, we postpone it. [When it occurs] on Thursday, we establish [Rosh Chodesh]. [When it occurs] on Friday, we postpone it. [When it occurs] on the Sabbath, we establish [Rosh Chodesh]. [When it occurs] on Sunday, we postpone it. [When it occurs] on Monday, we establish [Rosh Chodesh].

זוּמִפְּנֵי מָה אֵין קוֹבְעִין בְּחֶשְׁבּוֹן זֶה בִּימֵי אד''ו. לְפִי שֶׁהַחֶשְׁבּוֹן הַזֶּה הוּא לְקִבּוּץ הַיָּרֵחַ וְהַשֶּׁמֶשׁ בְּהִלּוּכָהּ הָאֶמְצָעִי לֹא בַּמָּקוֹם הָאֲמִתִּי כְּמוֹ שֶׁהוֹדַעְנוּ. לְפִיכָךְ עָשׂוּ יוֹם קְבִיעָה וְיוֹם דְּחִיָּה כְּדֵי לִפְגֹּעַ בְּיוֹם קִבּוּץ הָאֲמִתִּי. כֵּיצַד. בִּשְׁלִישִׁי קוֹבְעִין בִּרְבִיעִי דּוֹחִין. בַּחֲמִישִׁי קוֹבְעִין בְּשִׁשִּׁי דּוֹחִין. בְּשַׁבָּת קוֹבְעִין אֶחָד בְּשַׁבָּת דּוֹחִין. בְּשֵׁנִי קוֹבְעִין:

This same principle, that the calculations are based on the mean rate of progress, is also the motivating factor for the other four reasons for the postponement [of Rosh Chodesh]. As proof of this, there are times when [according to the calculations] the conjunction takes place on Tuesday, and [Rosh Chodesh] is postponed until Thursday,13 and yet the moon will not be seen Thursday night, nor even Friday night. This indicates that the true conjunction of the sun and the moon did not take place until Thursday.

חוְעִקַּר שְׁאָר הָאַרְבַּע דְּחִיּוֹת אֵלּוּ הוּא זֶה הָעִקָּר שֶׁאָמַרְנוּ שֶׁהַחֶשְׁבּוֹן הַזֶּה בְּמַהֲלָךְ אֶמְצָעִי. וּרְאָיָה לַדָּבָר שֶׁהַמּוֹלָד יִהְיֶה בְּלֵיל שְׁלִישִׁי וְיִדָּחֶה לַחֲמִישִׁי פְּעָמִים רַבּוֹת לֹא יֵרָאֶה יָרֵחַ בְּלֵיל חֲמִישִׁי וְלֹא בְּלֵיל שִׁשִּׁי מִכְּלַל שֶׁלֹּא נִתְקַבְּצוּ הַשֶּׁמֶשׁ וְהַיָּרֵחַ קִבּוּץ אֲמִתִּי אֶלָּא בַּחֲמִישִׁי:

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Which is also Rosh HaShanah.

The Rambam mentions the reason for postponing Rosh Chodesh in Halachah 7.

The first day of Rosh HaShanah is therefore celebrated frequently on Monday, Thursday, and the Sabbath, for the holiday is held on these days when the conjunction falls on the day itself or on the previous day. The first day of Rosh HaShanah is rarely celebrated on Tuesday, for the probability of the conjunction falling on that day is merely one out of seven, half that of the other days.

The principle mentioned in this halachah - and indeed, in the entire chapter - applies to Rosh Chodesh Tishrei alone, and not to the other months.

This condition is referred to as a *molad zaken*, literally, "an aged conjunction." The rationale for postponing Rosh HaShanah in such a situation can be explained as follows: In principle, Rosh Chodesh is dependent on the sighting of the moon, not on the conjunction. As is explained in the subsequent chapters of the text, the new moon does not become visible until several hours after the conjunction between the moon and the sun. Thus, if the conjunction takes place after noon, it is impossible for the moon to be sighted on that day. Therefore, Rosh HaShanah is celebrated on the following day. (See *Rosh HaShanah* 20b and commentaries.)

There is a slight difficulty in the Rambam's statements, for based on Chapter 15, Halachah 2, it would appear that at certain times it is possible to sight the moon only five hours after conjunction.

I.e., after the eighteenth hour of the seventh day.

It should not be established on the Sabbath, because of the principle of *molad zaken*. Nor should it be established on Sunday, as stated in Halachah 1.

I.e., the night between Monday and Tuesday.

The rationale for the postponement of Rosh HaShanah in such a situation can be explained as follows: As explained in the following chapter, the maximum length of a lunar year is 355 days. As mentioned previously, 4 days, 8 hours, and 876 units is the remainder of a normal year. To calculate the conjunction of Tishrei in the following year, this figure should be added to 3 - 9 - 204 (the day and the time mentioned by the Rambam above). The result is 12:00 noon on the Sabbath.

As explained above, when the conjunction takes place at 12:00 noon or later, the celebration of Rosh HaShanah is postponed to the following day. In this instance, however, the following day is Sunday, and Rosh HaShanah never begins on that day. Thus, the holiday would have to be celebrated on Monday. If Rosh HaShanah had been celebrated on Tuesday of the previous year, there would have been a six-day difference between the days on which the holiday was celebrated in these two successive years, producing a year of 356 days, one day longer than the maximum length of an ordinary year. To avoid this, Rosh HaShanah is not celebrated on Tuesday. Since it also is never celebrated on Wednesday, it is postponed until Thursday, producing a lunar year of 354 days (*Tur, Orach Chayim* 428).

For three hours after daybreak is 15 hours after the beginning of the day.

The rationale for the postponement of Rosh HaShanah in such a situation can be explained as follows: As explained in the following chapter, the minimum length of a lunar leap year is 383 days. As mentioned previously, the remainder of a leap year is five days, twenty-one hours, and 589 units. When, in an effort to calculate the time of the conjunction of the leap year, this figure is subtracted from 2 - 15 - 589 (the day and the time mentioned by the Rambam), the result is Tuesday at noon.

As mentioned, when the conjunction takes place at 12:00 noon or later, the celebration of Rosh HaShanah is postponed to the following day. In this instance, however, the following day is Wednesday, and Rosh HaShanah never begins on that day. Thus, in the leap year, Rosh HaShanah began on Thursday. If Rosh HaShanah were celebrated on Monday in the year after the leap year, this would produce only a four-day difference between the days on which the holiday was celebrated in these two successive years, causing the length of the year to be only 382 days. To avoid this, in the year following the leap year Rosh HaShanah is celebrated on Tuesday, rather than on Monday, causing the leap year to be 383 days long (*Tur, Orach Chayim* 428).

The Rambam's statements have stirred the attention - and often the indignation - of the Ra'avad and other commentaries, because they appear to ignore the explanations given by *Rosh HaShanah* 20a why Rosh HaShanah never begins on these days. The Talmud states that if Rosh HaShanah falls on either Wednesday or Friday, Yom Kippur will fall on either Friday or Sunday, and thus there would be two consecutive days, Yom Kippur and the Sabbath, when it would be forbidden to bury the dead. In the Talmudic era, this could have caused a corpse to deteriorate, detracting from its honor and respect.

Alternatively, the Sages state that if Rosh HaShanah fell on any of these three days, there would be two successive days when it would be forbidden to pick fresh vegetables, and the people would be unable to celebrate the festivals or the Sabbath properly.

*Sukkah* 43a gives another reason why Rosh HaShanah is not held on Sunday: were this to be the case, *Hoshana Rabbah,* the seventh day of Sukkot, would fall on the Sabbath. In such an instance, restrictions were placed on the willow ritual in the Temple. (See *Hilchot Shofar, Sukkah V'Lulav* 7:21-22.) To avoid such an instance, the Sages structured the calendar so that Rosh HaShanah never falls on Sunday.

In defense of the Rambam's position, it must be noted that both earlier (Rabbenu Chanan'el) and subsequent (the *P'nei Yehoshua*) Talmudic commentaries understood the reasons given by the Talmud as being merely the external dimension of the rationale for the calendar's adjustment, while the inner meaning is associated with the actual position of the sun and the moon in the heavenly sphere.

Even according to this perspective, there is, however, a difficulty with the Rambam's statements. Although it is correct that the true positions of the sun and the moon often differ from the position determined by calculating their mean movement, the concept of postponing the celebration of Rosh HaShanah on these three days appears arbitrary and without any obvious connection to the movement of these bodies in the celestial sphere. The commentaries note that explanations why Rosh HaShanah is not celebrated on these days are found in the Kabbalah.

The instance mentioned in Halachah 4.

Which is also Rosh HaShanah.

The Rambam mentions the reason for postponing Rosh Chodesh in Halachah 7.

The first day of Rosh HaShanah is therefore celebrated frequently on Monday, Thursday, and the Sabbath, for the holiday is held on these days when the conjunction falls on the day itself or on the previous day. The first day of Rosh HaShanah is rarely celebrated on Tuesday, for the probability of the conjunction falling on that day is merely one out of seven, half that of the other days.

The principle mentioned in this halachah - and indeed, in the entire chapter - applies to Rosh Chodesh Tishrei alone, and not to the other months.

This condition is referred to as a *molad zaken*, literally, "an aged conjunction." The rationale for postponing Rosh HaShanah in such a situation can be explained as follows: In principle, Rosh Chodesh is dependent on the sighting of the moon, not on the conjunction. As is explained in the subsequent chapters of the text, the new moon does not become visible until several hours after the conjunction between the moon and the sun. Thus, if the conjunction takes place after noon, it is impossible for the moon to be sighted on that day. Therefore, Rosh HaShanah is celebrated on the following day. (See *Rosh HaShanah* 20b and commentaries.)

There is a slight difficulty in the Rambam's statements, for based on Chapter 15, Halachah 2, it would appear that at certain times it is possible to sight the moon only five hours after conjunction.

I.e., after the eighteenth hour of the seventh day.

It should not be established on the Sabbath, because of the principle of *molad zaken*. Nor should it be established on Sunday, as stated in Halachah 1.

I.e., the night between Monday and Tuesday.

The rationale for the postponement of Rosh HaShanah in such a situation can be explained as follows: As explained in the following chapter, the maximum length of a lunar year is 355 days. As mentioned previously, 4 days, 8 hours, and 876 units is the remainder of a normal year. To calculate the conjunction of Tishrei in the following year, this figure should be added to 3 - 9 - 204 (the day and the time mentioned by the Rambam above). The result is 12:00 noon on the Sabbath.

As explained above, when the conjunction takes place at 12:00 noon or later, the celebration of Rosh HaShanah is postponed to the following day. In this instance, however, the following day is Sunday, and Rosh HaShanah never begins on that day. Thus, the holiday would have to be celebrated on Monday. If Rosh HaShanah had been celebrated on Tuesday of the previous year, there would have been a six-day difference between the days on which the holiday was celebrated in these two successive years, producing a year of 356 days, one day longer than the maximum length of an ordinary year. To avoid this, Rosh HaShanah is not celebrated on Tuesday. Since it also is never celebrated on Wednesday, it is postponed until Thursday, producing a lunar year of 354 days (*Tur, Orach Chayim* 428).

For three hours after daybreak is 15 hours after the beginning of the day.

The rationale for the postponement of Rosh HaShanah in such a situation can be explained as follows: As explained in the following chapter, the minimum length of a lunar leap year is 383 days. As mentioned previously, the remainder of a leap year is five days, twenty-one hours, and 589 units. When, in an effort to calculate the time of the conjunction of the leap year, this figure is subtracted from 2 - 15 - 589 (the day and the time mentioned by the Rambam), the result is Tuesday at noon.

As mentioned, when the conjunction takes place at 12:00 noon or later, the celebration of Rosh HaShanah is postponed to the following day. In this instance, however, the following day is Wednesday, and Rosh HaShanah never begins on that day. Thus, in the leap year, Rosh HaShanah began on Thursday. If Rosh HaShanah were celebrated on Monday in the year after the leap year, this would produce only a four-day difference between the days on which the holiday was celebrated in these two successive years, causing the length of the year to be only 382 days. To avoid this, in the year following the leap year Rosh HaShanah is celebrated on Tuesday, rather than on Monday, causing the leap year to be 383 days long (*Tur, Orach Chayim* 428).

The Rambam's statements have stirred the attention - and often the indignation - of the Ra'avad and other commentaries, because they appear to ignore the explanations given by *Rosh HaShanah* 20a why Rosh HaShanah never begins on these days. The Talmud states that if Rosh HaShanah falls on either Wednesday or Friday, Yom Kippur will fall on either Friday or Sunday, and thus there would be two consecutive days, Yom Kippur and the Sabbath, when it would be forbidden to bury the dead. In the Talmudic era, this could have caused a corpse to deteriorate, detracting from its honor and respect.

Alternatively, the Sages state that if Rosh HaShanah fell on any of these three days, there would be two successive days when it would be forbidden to pick fresh vegetables, and the people would be unable to celebrate the festivals or the Sabbath properly.

*Sukkah* 43a gives another reason why Rosh HaShanah is not held on Sunday: were this to be the case, *Hoshana Rabbah,* the seventh day of Sukkot, would fall on the Sabbath. In such an instance, restrictions were placed on the willow ritual in the Temple. (See *Hilchot Shofar, Sukkah V'Lulav* 7:21-22.) To avoid such an instance, the Sages structured the calendar so that Rosh HaShanah never falls on Sunday.

In defense of the Rambam's position, it must be noted that both earlier (Rabbenu Chanan'el) and subsequent (the *P'nei Yehoshua*) Talmudic commentaries understood the reasons given by the Talmud as being merely the external dimension of the rationale for the calendar's adjustment, while the inner meaning is associated with the actual position of the sun and the moon in the heavenly sphere.

Even according to this perspective, there is, however, a difficulty with the Rambam's statements. Although it is correct that the true positions of the sun and the moon often differ from the position determined by calculating their mean movement, the concept of postponing the celebration of Rosh HaShanah on these three days appears arbitrary and without any obvious connection to the movement of these bodies in the celestial sphere. The commentaries note that explanations why Rosh HaShanah is not celebrated on these days are found in the Kabbalah.

The instance mentioned in Halachah 4.

## Kiddush HaChodesh - Chapter Eight

A lunar month is twenty-nine and one half days, and 793 units, as we have explained.1 It is impossible for Rosh Chodesh to begin in the middle of the day - i.e., that a portion of the day would be part of the previous month and a portion of the day would be part of the following month - as [implied by Numbers 11:20]: "For a month of days...." According to the Oral Tradition,2 this was interpreted [to mean], "You count the days of a month; you do not count the hours [of a month]."

אחָדְשָׁה שֶׁל לְבָנָה תִּשְׁעָה וְעֶשְׂרִים יוֹם וּמֶחֱצָה וְתשצ''ג חֲלָקִים כְּמוֹ שֶׁבֵּאַרְנוּ. וְאִי אֶפְשָׁר לוֹמַר שֶׁרֹאשׁ הַחֹדֶשׁ יִהְיֶה בְּמִקְצָת הַיּוֹם עַד שֶׁיִּהְיֶה מִקְצָת הַיּוֹם מֵחֹדֶשׁ שֶׁעָבַר וּמִקְצָתוֹ מֵהַבָּא. שֶׁנֶּאֱמַר (במדבר יא כ) "עַד חֹדֶשׁ יָמִים" מִפִּי הַשְּׁמוּעָה לָמְדוּ שֶׁיָּמִים אַתָּה מְחַשֵּׁב לְחֹדֶשׁ וְאִי אַתָּה מְחַשֵּׁב שָׁעוֹת:

Therefore, some lunar months are established as lacking [a day], and others as full. A month that is lacking has only twenty- nine days, even though a lunar month is several hours longer. A full month is thirty days, even though a lunar month is several hours shorter. In this manner, the months will be calculated according to complete days, not according to hours.

בלְפִיכָךְ עוֹשִׂין חָדְשֵׁי הַלְּבָנָה מֵהֶן חֹדֶשׁ חָסֵר וּמֵהֶם חֹדֶשׁ מָלֵא. חֹדֶשׁ חָסֵר תִּשְׁעָה וְעֶשְׂרִים יוֹם בִּלְבַד וְאַף עַל פִּי שֶׁחָדְשָׁהּ שֶׁל לְבָנָה יֶתֶר עַל זֶה בְּשָׁעוֹת. וְחֹדֶשׁ מָלֵא מִשְּׁלֹשִׁים יוֹם וְאַף עַל פִּי שֶׁחָדְשָׁהּ שֶׁל לְבָנָה פָּחוֹת מִזֶּה בְּשָׁעוֹת. כְּדֵי שֶׁלֹּא לְחַשֵּׁב שָׁעוֹת בַּחֹדֶשׁ אֶלָּא יָמִים שְׁלֵמִים:

If a lunar month were exactly twenty-nine and a half days [long], the years [would be divided evenly] into full and lacking months, and there would be exactly 354 days to a lunar year. Thus, there would be six full months and six lacking months. It is the units that exist in every month that exceed the half day - which ultimately add up to hours and days - that cause certain years to have more lacking months than full months, and other years to have more full months than lacking months.

גאִלּוּ הָיָה חָדְשָׁהּ שֶׁל לְבָנָה תִּשְׁעָה וְעֶשְׂרִים יוֹם וּמֶחֱצָה בִּלְבַד הָיוּ כָּל הַשָּׁנִים חֹדֶשׁ מָלֵא וְחֹדֶשׁ חָסֵר. וְיִהְיוּ יְמֵי שְׁנַת הַלְּבָנָה שנ''ד, שִׁשָּׁה חֳדָשִׁים חֲסֵרִים וְשִׁשָּׁה חֳדָשִׁים מְלֵאִים. אֲבָל מִפְּנֵי הַחֲלָקִים שֶׁיֵּשׁ בְּכָל חֹדֶשׁ וְחֹדֶשׁ יוֹתֵר עַל חֲצִי הַיּוֹם יִתְקַבֵּץ מֵהֶן שָׁעוֹת וְיָמִים. עַד שֶׁיִּהְיוּ מִקְצָת הַשָּׁנִים חֳדָשִׁים חֲסֵרִים יוֹתֵר עַל הַמְּלֵאִים וּבְמִקְצָת הַשָּׁנִים חֳדָשִׁים מְלֵאִים יוֹתֵר עַל הַחֲסֵרִים:

According to this reckoning, the thirtieth day of the month is always established as Rosh Chodesh. If the month is lacking, the thirtieth day will be Rosh Chodesh of the coming month.

If the month is full [the coming month will have two days that are Rosh Chodesh]. The thirtieth day will be Rosh Chodesh, since a portion of it is [fit to be] Rosh Chodesh. [Nevertheless,] it will be counted as the completion of the previous month, which was full. The thirty-first day also will be Rosh Chodesh, and the reckoning [of the days of the coming month] will start from it. It is the day established [as Rosh Chodesh].

Thus, according to this calculation, there are some months that have only one day Rosh Chodesh, and other months that have two days Rosh Chodesh.

דיוֹם שְׁלֹשִׁים לְעוֹלָם עוֹשִׂין אוֹתוֹ רֹאשׁ חֹדֶשׁ בְּחֶשְׁבּוֹן זֶה. אִם הָיָה הַחֹדֶשׁ שֶׁעָבַר חָסֵר יִהְיֶה יוֹם שְׁלֹשִׁים רֹאשׁ חֹדֶשׁ הַבָּא. וְאִם יִהְיֶה הַחֹדֶשׁ שֶׁעָבַר מָלֵא יִהְיֶה יוֹם שְׁלֹשִׁים רֹאשׁ חֹדֶשׁ הוֹאִיל וּמִקְצָתוֹ רֹאשׁ חֹדֶשׁ. וְיִהְיֶה תַּשְׁלוּם הַחֹדֶשׁ הַמָּלֵא שֶׁעָבַר. וְיִהְיֶה יוֹם אֶחָד וּשְׁלֹשִׁים רֹאשׁ הַחֹדֶשׁ הַבָּא וּמִמֶּנּוּ הוּא הַמִּנְיָן. וְהוּא יוֹם הַקְּבִיעָה. וּלְפִיכָךְ עוֹשִׂין רָאשֵׁי חֳדָשִׁים בְּחֶשְׁבּוֹן זֶה חֹדֶשׁ אֶחָד יוֹם אֶחָד בִּלְבַד וְחֹדֶשׁ אֶחָד שְׁנֵי יָמִים:

The following is the order of the full and lacking months according to [our] fixed calendar: Tishrei is always full. Tevet is always lacking. From Tevet on, there is one full month and one lacking month in sequence.

What is implied? Tevet is lacking; Shevat is full; Adar is lacking; Nisan is full; Iyar, lacking; Sivan, full; Tammuz, lacking; Av, full; Elul, lacking. In a leap year, the first Adar is full,3 and the second Adar is lacking.

הסֵדֶר הֶחֳדָשִׁים הַמְּלֵאִים וְהַחֲסֵרִים לְפִי חֶשְׁבּוֹן זֶה כָּךְ הוּא. תִּשְׁרֵי לְעוֹלָם מָלֵא. וְטֵבֵת לְעוֹלָם חָסֵר. וּמִטֵּבֵת וְאֵילָךְ אֶחָד מָלֵא וְאֶחָד חָסֵר עַל הַסֵּדֶר. כֵּיצַד. טֵבֵת חָסֵר שְׁבָט מָלֵא. אֲדָר חָסֵר נִיסָן מָלֵא. אִיָּר חָסֵר סִיוָן מָלֵא. תַּמּוּז חָסֵר אָב מָלֵא. אֱלוּל חָסֵר. וּבְשָׁנָה הַמְעֻבֶּרֶת אֲדָר רִאשׁוֹן מָלֵא וַאֲדָר שֵׁנִי חָסֵר:

Two months remain: Marcheshvan and Kislev. Sometimes they are [both] full; sometimes they are [both] lacking; and sometimes Marcheshvan is lacking and Kislev is full.

A year in which both of these months are full is called a year of complete months. A year in which both these months are lacking is called a year of lacking months. And a year in which Marcheshvan is lacking and Kislev is full is called a year whose months [proceed] in order.4

ונִשְׁאֲרוּ שְׁנֵי הֶחֳדָשִׁים שֶׁהֵן מַרְחֶשְׁוָן וְכִסְלֵו. פְּעָמִים יִהְיוּ שְׁנֵיהֶם מְלֵאִים וּפְעָמִים יִהְיוּ שְׁנֵיהֶם חֲסֵרִים וּפְעָמִים יִהְיֶה מַרְחֶשְׁוָן חָסֵר וְכִסְלֵו מָלֵא. וְשָׁנָה שֶׁיִּהְיוּ בָּהּ שְׁנֵי חֳדָשִׁים אֵלּוּ מְלֵאִים הִיא שֶׁנִּקְרְאוּ חֳדָשֶׁיהָ שְׁלֵמִים. וְשָׁנָה שֶׁיִּהְיוּ בָּהּ שְׁנֵי חֳדָשִׁים אֵלּוּ חֲסֵרִים נִקְרְאוּ חֳדָשֶׁיהָ חֲסֵרִין. וְשָׁנָה שֶׁיִּהְיוּ בָּהּ מַרְחֶשְׁוָן חָסֵר וְכִסְלֵו מָלֵא נִקְרְאוּ חֳדָשֶׁיהָ כְּסִדְרָן:

The way to know whether the months of a year will be lacking, will be complete, or will [proceed] in order [can be explained] as follows: First, determine the day on which Rosh HaShanah will fall in the year about whose months you desire to know, as explained in Chapter 7. Then determine the day on which Rosh HaShanah will fall in the year that follows.

Afterwards, count the number of days between them without including the day on which Rosh HaShanah falls in either of these years. If there are only two days between them,5 the months of the year will be lacking. If there are three days between them,6 the months of the year will proceed in order. And if there are four days between them,7 the months of the year will be complete.

זדֶּרֶךְ יְדִיעַת הַשָּׁנָה אִם חֳדָשֶׁיהָ מְלֵאִים אוֹ חֲסֵרִין אוֹ כְּסִדְרָן לְפִי חֶשְׁבּוֹן זֶה כָּךְ הוּא. תֵּדַע תְּחִלָּה יוֹם שֶׁנִּקְבַּע בּוֹ רֹאשׁ הַשָּׁנָה שֶׁתִּרְצֶה לֵידַע סִדּוּר חֳדָשֶׁיהָ כְּמוֹ שֶׁבֵּאַרְנוּ בְּפֶרֶק שְׁבִיעִי. וְתֵדַע יוֹם שֶׁיִּקָּבַע בּוֹ רֹאשׁ הַשָּׁנָה שֶׁלְּאַחֲרֶיהָ. וּתְחַשֵּׁב מִנְיַן הַיָּמִים שֶׁבֵּינֵיהֶן חוּץ מִיּוֹם הַקְּבִיעָה שֶׁל זוֹ וְשֶׁל זוֹ. אִם תִּמְצָא בֵּינֵיהֶן שְׁנֵי יָמִים יִהְיוּ חָדְשֵׁי הַשָּׁנָה חֲסֵרִין. וְאִם תִּמְצָא בֵּינֵיהֶם שְׁלֹשָׁה יָמִים יִהְיוּ כְּסִדְרָן. וְאִם תִּמְצָא בֵּינֵיהֶם אַרְבָּעָה יָמִים יִהְיוּ חָדְשֵׁי הַשָּׁנָה שְׁלֵמִים:

When does the above apply? When the year in question is an ordinary year. When, however, [the year in question] is a leap year [different rules apply]: If there are only four days between the day on which [Rosh HaShanah] is established [in the leap year] and the day on which it will be established in the following year, the months of the year will be lacking.8 If there are five days between these [two days], the months of the year will proceed in order. And if there are six days between them, the months of the year will be complete.

חבַּמֶּה דְּבָרִים אֲמוּרִים כְּשֶׁהָיְתָה הַשָּׁנָה שֶׁתִּרְצֶה לֵידַע סִדּוּר חֳדָשֶׁיהָ פְּשׁוּטָה. אֲבָל אִם הָיְתָה מְעֵבֶּרֶת. אִם תִּמְצָא בֵּין יוֹם קְבִיעָתָהּ וּבֵין יוֹם קְבִיעַת שָׁנָה שֶׁלְּאַחֲרֶיהָ אַרְבָּעָה יָמִים יִהְיוּ חָדְשֵׁי אוֹתָהּ שָׁנָה הַמְעֻבֶּרֶת חֲסֵרִים. וְאִם תִּמְצָא בֵּינֵיהֶם חֲמִשָּׁה יָמִים יִהְיוּ כְּסִדְרָן. וְאִם תִּמְצָא בֵּינֵיהֶם שִׁשָּׁה יִהְיוּ שְׁלֵמִים:

What is implied? If we desire to know the order of the months of the present year, and [we know the following]: Rosh HaShanah falls on Thursday; it is an ordinary year; and in the following year Rosh HaShanah falls on Monday, there are three days between them and the months of the year proceed in order.9

If Rosh HaShanah falls on Tuesday in the following year, the months of the year will be complete.10 If Rosh HaShanah falls on the Sabbath in the present year, and on Tuesday in the following year, the months of the year will be lacking.11 Similar concepts should be applied regarding the calculation [of the order of the months] of a leap year, as was explained.

טכֵּיצַד. הֲרֵי שֶׁרָצִינוּ לֵידַע סִדּוּר חָדְשֵׁי שָׁנָה זוֹ. וְהָיָה רֹאשׁ הַשָּׁנָה בַּחֲמִישִׁי וְהִיא פְּשׁוּטָה וְרֹאשׁ הַשָּׁנָה שֶׁלְּאַחֲרֶיהָ בְּשֵׁנִי בְּשַׁבָּת. נִמְצָא בֵּינֵיהֶן שְׁלֹשָׁה יָמִים. יָדַעְנוּ שֶׁשָּׁנָה זוֹ חֳדָשֶׁיהָ כְּסִדְרָן. וְאִלּוּ הָיָה רֹאשׁ הַשָּׁנָה שֶׁלְּאַחֲרֶיהָ בִּשְׁלִישִׁי הָיוּ חָדְשֵׁי הַשָּׁנָה זוֹ שְׁלֵמִים. וְאִלּוּ הָיָה רֹאשׁ הַשָּׁנָה בְּשָׁנָה זוֹ בְּשַׁבָּת וּבַשָּׁנָה שֶׁלְּאַחֲרֶיהָ בִּשְׁלִישִׁי בְּשַׁבָּת הָיוּ חָדְשֵׁי שָׁנָה זוֹ חֲסֵרִין. וְעַל דֶּרֶךְ זוֹ תְּחַשֵּׁב לַשָּׁנָה הַמְעֻבֶּרֶת כְּמוֹ שֶׁבֵּאַרְנוּ:

There are certain indications upon which one can rely, so that one will not err regarding the calculation of the order of the months of a year. These principles are based on the fundamental principles of the fixed calendar and the determination of the days on which Rosh HaShanah will be established and those that will cause it to be postponed, as we explained previously.

Whenever Rosh HaShanah is celebrated on a Tuesday, [the months of] the year will [proceed] in order. [This applies regardless of whether the year] is an ordinary year or a leap year.12

Whenever Rosh HaShanah is celebrated on the Sabbath or on a Monday, [the months of] the year will never [proceed] in order. [This applies regardless of whether the year] is an ordinary year or a leap year.13

[The following rules apply when] Rosh HaShanah falls on a Thursday. If the year is an ordinary year, it is impossible for its months to be lacking.14 If it is a leap year, it is impossible for its months to proceed in order.15

ייֵשׁ שָׁם סִימָנִין שֶׁתִּסְמֹךְ עֲלֵיהֶם כְּדֵי שֶׁלֹּא תִּטְעֶה בְּחֶשְׁבּוֹן סִדּוּר חָדְשֵׁי הַשָּׁנָה וְהֵן בְּנוּיִין עַל עִקְּרֵי זֶה הַחֶשְׁבּוֹן וְהַקְּבִיעוֹת וְהַדְּחִיּוֹת שֶׁבֵּאַרְנוּ דַּרְכָּם. וְאֵלּוּ הֵן. כָּל שָׁנָה שֶׁיִּהְיֶה רֹאשׁ הַשָּׁנָה בָּהּ בַּשְּׁלִישִׁי תִּהְיֶה לְעוֹלָם כְּסִדְרָן לְפִי חֶשְׁבּוֹן זֶה. בֵּין פְּשׁוּטָה בֵּין מְעֻבֶּרֶת. וְאִם יִהְיֶה רֹאשׁ הַשָּׁנָה בְּשַׁבָּת אוֹ בְּשֵׁנִי לֹא תִּהְיֶה כְּסִדְרָן לְעוֹלָם בֵּין בִּפְשׁוּטָה בֵּין בִּמְעֵבֶּרֶת. וְאִם יִהְיֶה רֹאשׁ הַשָּׁנָה בַּחֲמִישִׁי. אִם פְּשׁוּטָה הִיא אִי אֶפְשָׁר שֶׁיִּהְיוּ חֳדָשֶׁיהָ חֲסֵרִים לְפִי חֶשְׁבּוֹן זֶה. וְאִם מְעֻבֶּרֶת הִיא אִי אֶפְשָׁר שֶׁיִּהְיוּ חֳדָשֶׁיהָ כְּסִדְרָן לְפִי חֶשְׁבּוֹן זֶה:

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Chapter 6, Halachah 3.

*Megillah* 5a.

This supports the Rambam's contention that it is the first Adar that is the extra month of the year. (See the notes on Chapter 4, Halachah 1.)

For all the months of the year from Marcheshvan onward proceed in sequence, one full and one lacking.

The Rambam gives examples in Halachah 9 to illustrate this situation and those that follow. When there are two days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and three days - i.e., 353 days - long.

When there are three days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and four days - i.e., 354 days - long.

When there are four days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and five days - i.e., 355 days - long. The remainder of an ordinary lunar year is slightly more than four days, producing a year whose months proceed in order. Frequently, however, the year will contain an extra day, if, because of the reasons mentioned in the previous chapter, the celebration of Rosh HaShanah is postponed. Similarly, it may lack a day, because the celebration of Rosh HaShanah was postponed in the previous year.

In such a situation, there will be 54 weeks and five days in the year, a total of 383 days.

For there are three days - Friday, the Sabbath, and Sunday - between the days on which Rosh HaShanah is celebrated in the years in question.

For there are four days - Friday, the Sabbath, Sunday, and Monday - between the days on which Rosh HaShanah is celebrated in these successive years.

For there are only two days between them.

As mentioned, Rosh HaShanah cannot fall on Sunday, Wednesday, or Friday. Therefore, in an ordinary year, if Rosh HaShanah falls on a Tuesday, the following year it cannot fall on a Thursday, for then there would be only one day between them, producing a year of only 352 days. Nor can it fall on a Monday, for then the year would be 356 days long. Thus, the only day on which it can fall is the Sabbath, producing a year of 354 days. In such a year, the months proceed in order.

When Rosh HaShanah falls on Tuesday in a leap year, it cannot fall on Thursday or the Sabbath in the following year, for that would produce a year that is too short (380 or 382) days. Nor can it fall on Tuesday itself, for Rosh HaShanah falls on Tuesday only when the conjunction takes place not later than Tuesday, before noon. When the remainder of a leap year - 5 days, 21 hours, and 589 units - is added to noon time on Tuesday, the result is that the conjunction of the following year will take place on Sunday. Since Rosh HaShanah is never celebrated on Sunday, the holiday will be postponed until Monday. Thus, the length of the leap year will be 384 days, the length of a year whose months proceed in order.

For the months of an ordinary year to proceed in order, the year must be 354 days long. That means that if Rosh HaShanah fell on the Sabbath, it would have to fall on Wednesday in the following year, which is impossible. Similarly, if Rosh HaShanah fell on Monday, it would have to fall on Friday in the following year, which is also impossible.

For the months of a leap year to proceed in order, the year must be 384 days long. That means that if Rosh HaShanah had fallen on the Sabbath, in the following year it would have to fall on Friday, which is impossible. Similarly, if Rosh HaShanah had fallen on Monday, in the following year it would have to fall on Sunday, which is also impossible.

When the months of an ordinary year are lacking, the year has only 353 days. Thus, if Rosh HaShanah fell on Thursday, it would have to fall on Sunday in the following year, which is impossible.

When the months of a leap year are lacking, the year has 383 days. Thus, if Rosh HaShanah fell on Thursday, it would have to fall on Wednesday in the following year, which is impossible.

Chapter 6, Halachah 3.

*Megillah* 5a.

This supports the Rambam's contention that it is the first Adar that is the extra month of the year. (See the notes on Chapter 4, Halachah 1.)

For all the months of the year from Marcheshvan onward proceed in sequence, one full and one lacking.

The Rambam gives examples in Halachah 9 to illustrate this situation and those that follow. When there are two days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and three days - i.e., 353 days - long.

When there are three days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and four days - i.e., 354 days - long.

When there are four days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and five days - i.e., 355 days - long. The remainder of an ordinary lunar year is slightly more than four days, producing a year whose months proceed in order. Frequently, however, the year will contain an extra day, if, because of the reasons mentioned in the previous chapter, the celebration of Rosh HaShanah is postponed. Similarly, it may lack a day, because the celebration of Rosh HaShanah was postponed in the previous year.

In such a situation, there will be 54 weeks and five days in the year, a total of 383 days.

For there are three days - Friday, the Sabbath, and Sunday - between the days on which Rosh HaShanah is celebrated in the years in question.

For there are four days - Friday, the Sabbath, Sunday, and Monday - between the days on which Rosh HaShanah is celebrated in these successive years.

For there are only two days between them.

As mentioned, Rosh HaShanah cannot fall on Sunday, Wednesday, or Friday. Therefore, in an ordinary year, if Rosh HaShanah falls on a Tuesday, the following year it cannot fall on a Thursday, for then there would be only one day between them, producing a year of only 352 days. Nor can it fall on a Monday, for then the year would be 356 days long. Thus, the only day on which it can fall is the Sabbath, producing a year of 354 days. In such a year, the months proceed in order.

When Rosh HaShanah falls on Tuesday in a leap year, it cannot fall on Thursday or the Sabbath in the following year, for that would produce a year that is too short (380 or 382) days. Nor can it fall on Tuesday itself, for Rosh HaShanah falls on Tuesday only when the conjunction takes place not later than Tuesday, before noon. When the remainder of a leap year - 5 days, 21 hours, and 589 units - is added to noon time on Tuesday, the result is that the conjunction of the following year will take place on Sunday. Since Rosh HaShanah is never celebrated on Sunday, the holiday will be postponed until Monday. Thus, the length of the leap year will be 384 days, the length of a year whose months proceed in order.

For the months of an ordinary year to proceed in order, the year must be 354 days long. That means that if Rosh HaShanah fell on the Sabbath, it would have to fall on Wednesday in the following year, which is impossible. Similarly, if Rosh HaShanah fell on Monday, it would have to fall on Friday in the following year, which is also impossible.

For the months of a leap year to proceed in order, the year must be 384 days long. That means that if Rosh HaShanah had fallen on the Sabbath, in the following year it would have to fall on Friday, which is impossible. Similarly, if Rosh HaShanah had fallen on Monday, in the following year it would have to fall on Sunday, which is also impossible.

When the months of an ordinary year are lacking, the year has only 353 days. Thus, if Rosh HaShanah fell on Thursday, it would have to fall on Sunday in the following year, which is impossible.

When the months of a leap year are lacking, the year has 383 days. Thus, if Rosh HaShanah fell on Thursday, it would have to fall on Wednesday in the following year, which is impossible.

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