Rosh Hashanah, Chapter 2, Mishnah 6. This Mishnah describes the procedure for questioning the witnesses who saw the new moon, and how beis din would examine them.
"Keitzad bodkin es ha'edim" - How do they examine the witnesses?
"Zug shebba rishon bodkin oso rishon" - the pair that arrived first was first in line, and they were examined first. "Umachnisin es hagadol shebahen" - they would first bring in the older of the two witnesses, "ve'omer lo: Emor keitzad ra'isa es halevanah" - that is, tell us how you saw it. And these are the questions they would ask him:
"Lifnei hachamah o le'achar hachamah" - was the missing part of the new moon facing toward the sun or away from it, at a time when the sun was still in the sky. "After the sun" means that it was facing away from the sun.
"Latzafon o ladarom" - was it to the north of the sun or to its south.
"Kamah hayah gavoah" - how high was it above the horizon.
"Ule'ayin hayah noteh" - in which direction was the rounded part of the moon facing.
"Kamah hayah rachav" - how wide was the portion of the moon that could be seen.
The answer that invalidates the testimony:
The Mishnah teaches that one answer disqualifies the witnesses immediately: "Im amar lifnei hachamah - lo amar klum". If he testified that the missing part of the moon was facing toward the sun, there is nothing to his words. The reason is that the missing part of the moon never faces the sun; when both are seen in the sky together, it is always the round, convex side of the moon that faces the sun. It is therefore clear that the witness is lying.
Examining the second witness:
"Ve'achar kach hayu machnisin es hasheni uvodkin oso" - after examining the first, they would bring in the second witness and examine him in the same way. "Im nimtze'u divreihem mechuvanim - eidusan kayemes": if their words match and both tell the same account, their testimony stands.
The remaining pairs:
"Ushe'ar kol hazugos sho'alin osam rashei devarim" - the remaining pairs, whose testimony was no longer needed once a valid pair of witnesses had been accepted, were asked only the main points, a few central questions. And the reason for this: "Lo shehayu tzerichin lahen" - it was not because their testimony was needed, but so that they should not go away dejected, and so that they would be in the habit of coming and would always feel that it was worthwhile to come.
For a person who feels that he was not needed at all, even if he received a good meal and everything else, and it seems to him that everything would have been accomplished without him, finds it depressing and demoralizing. It is always good to feel that one has a role to fill.