After Bais Din accepted the witnesses, the head of Bais Din would say, ‘Mekudash’ [it is holy]. Then the people standing in Bais Din would say, ’Mekudash mekudash’.

It doesn’t make a difference if the new moon is coming out on the 30th or the 31th of the month, Bais Din always says ‘Mekudash’. R’ Elazar bar Tzadok says if the new moon is sighted on the 31th, Bais Din does not say, ‘Mekudash’ as that day has to be Rosh Chodesh.

[Every Jewish month has either 29 or 30 days. The new moon goes in a cycle of 29 days 18 hours and 793/1080 of an hour.]

Rosh Hashana 2:8

R’ Gamlial had a tablet and on the wall in his attic with pictures of the moon that he would show the witnesses and ask, ‘Did you see it this way or that way?’

There was a story that 2 witnesses said they saw the old moon in the morning and the new moon in the evening. R’ Yochanan ben Nuri said they were liars as it couldn’t be . When they came before R’ Gamlial, he accepted them saying that what they saw in the morning was a mistake as R’ Gamlial knew the calculation when the new moon was supposed to be seen.

Another story was that witnesses came and said, ‘We saw the moon on the 30^th day and on the 31th day we did not see the new moon’. R’ Dosa ben Hurkanos said they were liars. R’ Yehoshua said he liked their words.