The Gemara tells us that they made a takana not to receive witnesses who saw the moon after mincha. A) Mincha k'tanah or mincha g'dolah? B) If it's mincha g'dolah - Is the moon really always or usually visible at midday (6/12 shaot zemaniyot into the day)? I often see it towards evening time but I don't recall seeing it in midafternoon.
The new moon can only be seen in the evening, immediately after sunset, and for only a few minutes (and then the new moon itself sets, just behind the sun).
The Gemara is referring to the time that the Korban Minchah was generally brought (after Minchah Gedolah). The Mishnah in Pesachim (58a) says that the Korban Minchah was slaughtered at 8 1/2 hours into the day, and offered upon the Mizbe'ach at 9 1/2 hours into the day.
Thank you for your response. This, of course, means that there was a very small "window of opportunity," for anyone to give eidut on seeing the molad - one hour. Anyone giving testimony would have have to live within an hour's walk, (or horse, camel, donkey...ride), of the Bet Din in Yerushalayim. It seems to me that the gemara's discussion of this process elsewhere discusses those who lived some distance from the bet din and how they could be carried if need be etc. Would that have been before the gezerah was made only to accept testimony at the time that the mincha was offered?
The witnesses had a full day to come to Beis Din to testify about the new moon that they saw the evening before. That is, a few minutes after sunset on the 29th of Elul, two people spot the new moon just above the western horizon. It appears for only a few minutes, and then it dips below the horizon, out of sight. Those two witnesses have all night and most of the next day to travel to Yerushalayim to give testimony about what they saw.
Once, it happened that they arrived quite late -- after the time of the Minchah-offering (the day following the night during which they saw the new moon in the evening).
This clarification should resolve your questions.
All the best,