Nazir Chapter 3, Mishnah 2: Two Consecutive Nezirus and the Thirtieth Day

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Nazir Chapter 3, Mishnah 2. This mishnah builds on the principle taught in the previous mishnah: someone who takes an unspecified nezirus vow must complete his nezirus on the thirty first day, and after the fact, if he completed it on the thirtieth day, it is valid. Our mishnah expresses that very same idea, only it applies it to a case of two consecutive periods of nezirus, one after the other.

Ideally: shaving on the thirty first day and on the sixty first day

Someone who vows to be a nazir twice shaves for the first nezirus on the thirty first day, and for the second on the sixty first day. That is the ideal time. The reason, as the mishnah itself explains at its conclusion: on the thirty first day, once he has shaved and brought his offerings, the second nezirus begins on that very day. And since the second nezirus begins on that day, its thirtieth day is day sixty, and therefore the shaving and the offerings should ideally be done on the sixty first day.

When he shaved for the first nezirus on the thirtieth day (valid after the fact)

The ideal time for the second nezirus: day sixty. If he did the shaving and the offerings on the thirtieth day, which is valid after the fact as we learned in the previous mishnah, then the first day of the second nezirus was the thirtieth day of the first nezirus. It turns out that the day that would seem to be its first day is really its second day, and therefore day sixty is truly the thirty first day of the second nezirus.
After the fact: day fifty nine. If he shaved for the second nezirus on day fifty nine, it is valid, since that is the thirtieth day of the second nezirus.

The testimony of Rabbi Papus

The mishnah concludes with the testimony given by Rabbi Papus: someone who vowed two periods of nezirus and shaved for the first nezirus on the thirtieth day, which is the time that is valid after the fact, so that this day in fact became the first day of the second nezirus, should ideally shave for the second nezirus on day sixty, which is really its thirty first day. And if he shaved on day fifty nine, he has fulfilled his obligation, since that is really its thirtieth day.

In summary: the principle at work in this entire calculation is that the thirtieth day of the first nezirus does double duty and counts as the first day of the second nezirus. On the strength of this principle the times for shaving were set: ideally the thirty first day and the sixty first day; and for someone who shaved for the first nezirus on the thirtieth day, ideally day sixty, and day fifty nine after the fact.

Original maamar

אות נזיר ג:ב

מִי שֶׁנָּזַר שְׁתֵּי נְזִירִיּוֹת, מְגַלֵּחַ אֶת הָרִאשׁוֹנָה יוֹם שְׁלשִׁים וְאֶחָד, וְאֶת הַשְּׁנִיָּה יוֹם שִׁשִּׁים וְאֶחָד. וְאִם גִּלַּח אֶת הָרִאשׁוֹנָה יוֹם שְׁלשִׁים, מְגַלֵּחַ אֶת הַשְּׁנִיָּה יוֹם שִׁשִּׁים. וְאִם גִּלַּח יוֹם שִׁשִּׁים חָסֵר אֶחָד, יָצָא. וְזוֹ עֵדוּת הֵעִיד רַבִּי פַּפְּיַס עַל מִי שֶׁנָּזַר שְׁתֵּי נְזִירִיּוֹת, שֶׁאִם גִּלַּח אֶת הָרִאשׁוֹנָה שְׁלשִׁים יוֹם, מְגַלֵּחַ אֶת הַשְּׁנִיָּה יוֹם שִׁשִּׁים. וְאִם גִּלַּח לְיוֹם שִׁשִּׁים חָסֵר אֶחָד, יָצָא, שֶׁיּוֹם שְׁלשִׁים עוֹלֶה לוֹ מִן הַמִּנְיָן: One who accepted two terms of naziriteship shaves at the close of the first naziriteship on the thirty-first day, and at the close of the second term on the sixty-first day. Since his second term of naziriteship begins after shaving on the thirty-first day, the sixty-first day of the first term is the thirty-first day of his second term. And if he shaved for the first term on the thirtieth day, he shaves for the second term on the sixtieth day, which is the thirty-first day after the start of his second term of naziriteship. And if he shaved for the second term on day sixty less one, he has fulfilled his obligation, as this is the thirtieth day of his second term. And this testimony was attested to by Rabbi Pappeyas, who heard from his teachers with regard to one who vowed to observe two terms of naziriteship, that if he shaved for the first term on the thirtieth day, he shaves for the second term on the sixtieth day. And if he shaved for the second term on the day sixty less one, he has fulfilled his obligation, because the thirtieth day of the first term of naziriteship counts as part of his tally of the second term.