Commentary for Rosh Hashanah 4:3
ת"ר מת באדר ועמד אחר תחתיו באדר מונין שנה לזה ולזה מת בניסן ועמד אחר תחתיו בניסן מונין שנה לזה ולזה מת באדר ועמד אחר תחתיו בניסן מונין ראשונה לראשון ושניה לשני
Our Rabbis learnt: If [a king] died in Adar and was succeeded by another in Adar, we can designate [the rest of] the year [up to the first of Nisan] as belonging to either.<span class="x" onmousemove="('comment',' I.e., we can regard the remaining days of the year as belonging either to the last year of the late king or the first year of the new king.');"><sup>2</sup></span> If he died in Nisan and was succeeded by another in Nisan, we can date the year by either.<span class="x" onmousemove="('comment',' And similarly if the second ascended the throne in any other month of the year.');"><sup>3</sup></span> If he died in Adar and was succeeded by another in Nisan, the earlier year is dated by the first and the later by the second.