Midrasch zu Wajikra 23:4

(Fol. 25) MISHNAH: It once happened that two witnesses came and said: "We saw the moon in the eastern part of the horizon in the morning, and in the evening, in the western part of the horizon." R. Jochanan b. Nuri declared them to be false witnesses; but when they came to Yamnia, Rabban Gamaliel accepted their testimony as valid. On another occasion two other witnesses came and said: "We saw the moon on its proper day, but could not see it on the next evening of the intercalary day." R. Gamaliel accepted their testimony, but R. Dosa b. Harkinas said: "They are false witnesses; for how can they testify of a woman that she gave birth, when on the next day she appears to be pregnant?" "I approve of your opinion," remarked R. Joshua. Upon this, R. Gamaliel sent word to R. Joshua, saying: "I order thee to come to me with your staff and your money, on the Day of Atonement, — which is to come according to your computation." R. Akiba went to him (R. Joshua) and found him grieving. He then said to him: "I can prove that all which Rabban Gamaliel has done is proper, for it is said (Lev. 23, 4) These are the feasts of the Lord, holy convocations which ye shall proclaim, etc.; i.e., whether at their proper time, or not at their proper time, shall their convocations be considered as holy festivals." R. Joshua then went to R. Dosa b. Harkinas. "If we are to reinvestigate the decisions of the Beth Din of R. Gamaliel." R. Doso b. Hankinas said to him, "then we must also reinvestigate the decisions of all the tribunals of justice which have existed from the time of Moses till the present day! But it is said (Ex. 24, 9) "Moses, Nadah, Abihu, and seventy elders went up [to the Mount]. Why were not the names of the elders also specified? To teach us that every three men which are appointed in Israel to form a Beth Din (judiciary tribunal), are equal to the Beth Din of Moses." E. Joshua then took his staff and money in his hand, and went to Yamnia, to Rabban Gamaliel, on the very day on which the Day of Atonement would have been according to his computation. Then Rabban Gamaliel arose and kissed him on his forehead, saying: "Enter in peace, my teacher and my disciple! My teacher in knowledge; my disciple — since thou didst fulfil my words."

3) If the year should not have been intercalated, and they intercalated it perforce or unwittingly or mistakenly — Whence is it derived that it is (nevertheless) intercalated? From (Vayikra 23:9) ("These are the festivals of the L–rd, callings of holiness, which you shall call (them) in their times": "them" — even unwittingly; "them" — even mistakenly; "them" — even perforce.

6) I might think that just as the year is intercalated to answer some special need, so, it is intercalated because of tumah (of the populace); it is, therefore, written (Vayikra 23:5) "In the first month … it is Pesach" — Let the first month not pass without Pesach.