Sanhedrin, Chapter 5, Mishnah 3. The Mishnah discusses the rule regarding a contradiction between two witnesses during the formal inquiries: what margin of error is allowed for them, and in which cases is there no room for such a margin at all.
A Contradiction in the Date:
The Mishnah begins: "Echad omer b'shnayim bachodesh v'echad omer b'shloshah bachodesh" - one witness testifies that he saw the event on the second of the month, and his counterpart testifies that he saw it on the third of the month, and nevertheless, "edusan kayemes" - their testimony stands. It must be remembered that the testimony also includes the day of the week: one says, "I saw it on Thursday, the second of Adar", and the other says, "I saw it on Thursday, the third of Adar". Despite the discrepancy between them, their testimony is accepted.
The reason for this: during the time of the Mishnah, the count of the days of the month depended on the sanctification of the month by the Beis Din, and it was not always known to everyone. It is therefore possible that both witnesses are referring to the exact same day, but one thought that the previous month was twenty-nine days long and the other thought it was thirty days long, and from this a one-day discrepancy was created in their counting. And this is the wording of the Mishnah: "Shezeh yodea b'iburo shel chodesh v'zeh eino yodea b'iburo shel chodesh" - one knew that the month was elongated, having thirty days, and the other did not know this.
It is worth noting that the Mishnah deals, as is its way, with events from the recent past. Therefore, the Gemara says that if it was an event that occurred after the middle of the month - one says on the sixteenth of the month and the other says on the seventeenth of the month - the testimony is not accepted, because by the middle of the month everyone had already clarified whether the previous month was full or lacking.
The Mishnah continues: "Echad omer b'shloshah v'echad omer b'chamishah" - here the discrepancy is two days, and it has no satisfactory explanation, and therefore the testimonies do not align. For this reason, "edusan betelah" - their testimony is void: the contradiction between the two testimonies leads to the rejection of both of them as invalid witnesses, and their testimony does not combine.
A Contradiction in the Time:
Until this point we discussed matters of the date; but what is the rule regarding a contradiction in the time? "Echad omer bishtei sha'os v'echad omer b'shalosh sha'os" - one testifies that the event occurred two hours after the start of the day, and the other testifies that it occurred three hours after its start.
During the time of the Mishnah, clocks were not used, and the time was estimated according to the height of the sun in the sky. When the sun stood at its peak height, directly overhead, this is the sixth hour, which is midday, and from then on we enter the seventh hour. In the first half of the day the sun is in the east, and in the second half it is in the west. The estimation of the time was therefore done according to the angle of the sun in the sky.
From this the Gemara assumes that a person might err by up to, but not including, two hours. If we assume that the day lasts from six in the morning until six in the evening, and we have twelve equal hours of sixty minutes, it emerges that one is saying eight in the morning and the other is saying nine in the morning - a common mistake among those who rely on the sun to determine the time.
It is worth noting: if the event occurred in the city square where a sundial is fixed, we would not permit this discrepancy, as we would expect greater accuracy. So too in our times, when clocks are available to everyone and the time is known with great accuracy. The words of the Mishnah are therefore said regarding someone who relies on the sun alone, and in this case there is room for a certain margin of error in estimating the time.
Therefore we learned: "Echad omer b'shalosh v'echad omer b'chamesh" - one says three hours into the day, meaning nine in the morning, and the other says five hours into the day, meaning eleven in the morning. A discrepancy of two full hours is too large, and according to the Tanna Kamma, "edusan betelah" - their testimony is void.
Rabbi Yehudah disagrees: "Rabbi Yehudah omer: kayemes" - according to his view, people can make a mistake of up to three hours, but not including a full three hours. Since from the third to the fifth hour there is only a discrepancy of two hours, the testimony is accepted.
Nevertheless, Rabbi Yehudah agrees: "Echad omer bechamesh ve'echad omer besheva - edusan betelah" - one says it was five hours into the day, which is like eleven in the morning, and the second says it was seven hours, which is like one in the afternoon. Even though there is only a gap of two hours, which is less than three hours, the testimony is rejected: "Shebechamesh chamah bamizrach" - in the fifth hour the sun is still in the eastern half of the sky, "uvesheva chamah bamaarav" - and from the seventh hour onward it is already in the western half, on its way to setting. This transition is sharp and clear, everyone sees it and knows it, and people do not make mistakes regarding it. Since the witnesses erred regarding this, they are no longer believed and their testimony is rejected.
The source for the requirement that the testimony be consistent:
This is the place to point out, as would have been fitting to mention in the previous Mishnah as well, that the requirement for the two testimonies to match one another - without which they are rejected - is derived from the verses. There are two verses regarding this matter, and both indicate that the testimony must be consistent. In the first source, the verse states: "Vehineh emes nachon hadavar" - that you will investigate the matter and find it to be true.
The word "emes" simply means the truth, while the word "nachon" seems superfluous once "emes" has already been stated. Rather, the essence of "nachon" relates to the concepts of "kavanah" and "kivun" (direction or alignment) - meaning straight and aligned. From this we learn that if their testimonies do not align with one another and cannot be reconciled, the condition of "emes nachon hadavar" is not met, and in such a case the Torah requires us to reject their testimony.