Demai, Chapter 7, Mishnah 1. This Mishnah describes a case in which a person is invited to eat a Shabbos meal at the home of a friend whom he does not trust regarding tithes. Separating maaser is forbidden on Shabbos - even from demai - so how can he eat at his table? The Mishnah lays out a method that makes it possible.
A comparison with what we learned in Chapter Four:
Back in Chapter Four we described a case of someone eating on Shabbos at the home of a person who is not trusted regarding tithes, and yet he is permitted to rely on him - for the Mishnah there rules that if the host says the maaser has already been separated, we accept his word. That is unlike our Mishnah here, which describes a procedure by which the tithes can actually be separated, even though it is Shabbos. Two reasons were given for the leniency in Chapter Four:
There the case involved someone from whom he was under a vow of prohibition - the host had made a vow concerning him - and therefore it was a far more serious situation.
Alternatively, the case involved the first Shabbos of a groom who had just married, and for that reason a special leniency was granted.
The novel teaching of the Mishnah - making a stipulation on Friday:
The Mishnah teaches that if his friend invites him to eat at his home on Shabbos, and he does not trust him regarding maaser, he should recite a formula of stipulation on Friday, in which he designates in advance the location of every part of the separation:
Maaser rishon: the portion that he will separate tomorrow - one hundredth of the food he is going to eat - shall have the status of maaser, and the remainder of the tithe shall be in whatever is adjacent to it.
Terumas maaser: that portion which has already been tithed, or which he intends to separate as maaser and which he now designates in advance, shall be considered terumas maaser for the maaser. This is the portion that he does not eat, but rather actually separates.
Maaser sheni: it shall be on the northern side or the southern side of the plate from which he eats, and it shall be redeemed with the coins that he set aside for this purpose - and for that reason he is permitted to eat it.
And the maaser rishon itself: in the case of demai, he is permitted to eat it.
In summary: by means of the stipulation made on Friday, all that remains for him to do the next day on Shabbos is to separate the terumas maaser alone, and in this way he can eat from the food his friend serves him, even though he does not know for certain whether maaser was separated from it.