Jerusalem Talmud Rosh Hashanah 2:6

משנה: דְּמוּת צוּרוֹת לְבָנָה הָיוּ לוֹ לְרַבָּן גַּמְלִיאֵל בַּעֲלִיָיתוֹ בַּטַּבֻלָה וּבַכּוֹתֶל שֶׁבָּהֶן מַרְאֶה אֶת הַהֶדְיוֹטוֹת וְאוֹמֵר כָזֶה רָאִיתָ אוֹ כָזֶה. מַעֲשֶׂה שֶׁבָּאוּ שְׁנַיִם וְאָ‍מְרוּ רְאִינוּהוּ שַׁחֲרִית בַּמִּזְרָח וְעַרְבִית בַּמַּעֲרָב. אָמַר רַבִּי יוֹחָנָן עֵידֵי שֶׁקֶר הֵם. כְּשֶׁבָּאוּ לְיַבְנֶה קִיבְּלָן רַבָּן גַּמְלִיאֵל. וְעוֹד בָּאוּ שְׁנַיִם וְאָ‍מְרוּ רְאִינוּהוּ בִזְמַנּוֹ וּבְלַיְלָה בְּעִיבּוּרוֹ לֹא נִרְאָה וְקִבְּלָן רַבָּן גַּמְלִיאֵל. אָמַר רִבִּי דוֹסָא בֶּן אַרְכִּינַס עֵידֵי שֶׁקֶר הֵן הֵיאָךְ מְעִידִין עַל הָאִשָּׁה שֶׁיָּלָדָה וַהֲרֵי כְּרֵיסָהּ בֵּין שִׁנֶּיהָ. אָמַר לוֹ רִבִּי יְהוֹשֻׁעַ רוֹאֶה אֲנִי אֶת דְּבָרֶיךָ: MISHNAH: Rabban Gamliel had pictures of the moon phases on a tablet¹⁰⁶Latin tabula. and on the wall on his upper floor which he showed to the common people¹⁰⁷Who are not trained in astronomy but come to testify. Greek ̓ιδιώτης. and asked, did you see it like this or like that? It happened that two came and said, we saw it in the morning in the East and in the evening in the West¹⁰⁸Since the new moon appears from behind the sun, the entire period near a new moon it must be close to the sun, in the East in the morning and the West in the evening. R. Joḥanan ben Nuri does not dispute this fact but he holds that the time elapsed between in the disappearance of the old moon in the East and the appearance of the new moon in the West must be more than 12 hours.. Rebbi Joḥanan {ben Nuri} said, they are false witnesses. Rabban Gamliel accepted them when they came to Jabneh.
Another time two came and said, we saw it on time, and in the night of the addition¹⁰⁹The night of the 31st of the old month. it was not seen, but Rabban Gamliel accepted them. Rebbi Dosa ben Hyrkanos said, they are false witnesses. How can one testify about a woman that she gave birth and the next day she is in labor pains? Rebbi Joshua said to him, I am agreeing with your words.

הלכה: אָמַר רִבִּי שִׂמְלַאי. טַעֲמֵיהּ דְּרִבִּי יוּחָנָן בֶּן נוּרִי. כָּל חוֹדֶשׁ שֶׁנּוֹלַד קוֹדֶם לְשֵׁשׁ שָׁעוֹת אֵין כֹּחַ בָּעַיִן לִרְאוֹת אֶת הַיָּשָׁן. וְתַנֵּי כֵן. נִרְאָה יָשָׁן בַּשַׁחֲרִית לֹא נִרְאָה חָדָשׁ בֵּין הָעַרְבָּיִם. נִרְאָה חָדָשׁ בֵּין הָעַרְבָּיִם לֹא נִרְאָה יָשָׁן בַּשַׁחֲרִית. אָמַר רִבִּי חִיָיה בַּר בָּא. וְלָמָּה קִיבְּלָן רַבָּן גַּמְלִיאֵל. שֶׁכֵּן מְסוֹרֶת בְּיָדָיו מֵאֲבוֹתָיו. פְּעָמִים מְהַלֵּךְ בִּקְצָרָה. פְּעָמִים מְהַלֵּךְ בַּאֲרוּכָּה. HALAKHAH: Rebbi Simlai said, the reason of Rebbi Joḥanan ben Nuri is that for any month which starts before noontime the eye is not able to see the old moon. And it was stated thus: If the old moon was seen in the morning, the new moon is not seen in the evening¹¹⁰Cf. Babli 20b.. If the new moon was seen in the evening the old moon was not seen in the morning. Rebbi Ḥiyya bar Abba said, why did Rabban Gamliel accept them? Because he had a tradition from his forefathers that sometimes it moves in a shortcut, sometimes it moves on an extended path¹¹¹Babli 25a. The deviation of the actual from the mean month may be up to ±12 hours..