Before us is Mishnah 8 in chapter 7 of Maseches Demai - the final mishnah of the tractate. The mishnah deals with someone who had ten rows of wine barrels, with ten barrels in each row: one hundred barrels arranged in a neat square of ten by ten.
"Shurah hachitzonah achas ma'aser":
The owner of the barrels declared that one of the outer rows should count as ma'aser for the remaining ninety barrels - ten barrels making up an outer row. The problem is that he does not identify which row he means: since he said only "an outer row", he could be referring to any one of the four outer rows of the square.
This raises the question of how terumas ma'aser is to be separated here. Ma'aser rishon itself may be eaten by anyone, even though financially it belongs to the Levi, and it can be exchanged for something else; but terumas ma'aser may only be separated from something that is actually ma'aser. The question, then, is: where will the terumas ma'aser come from?
On this the mishnah instructs him to take two barrels that stand diagonally opposite one another - the northwest corner together with the southeast corner, or the northeast corner together with the southwest corner; what matters is that they stand on a diagonal from each other. One of these two barrels - even though we do not know which - certainly comes from the ma'aser, and can serve as terumas ma'aser.
The reason is this: since the square has four sides, taking two barrels on a diagonal guarantees that between the two of them there is certainly a barrel from one of the rows that were designated as ma'aser.
Therefore the two barrels are sold to a kohen for the price of one barrel: one of them belongs to the kohen financially, since it is the terumas ma'aser, while the other is only a doubt and payment may therefore be accepted for it. Both are potentially terumas ma'aser, since we do not know which of them came from the outer row that was designated as ma'aser.
It is worth noting that in this case the entire barrel is not considered terumas ma'aser, but only half of it, and the rest may be sold and money accepted for it, since only fifty percent of the ma'aser is being separated here.
"Shurah achas ma'aser":
What is the law when he wants to separate ma'aser for all one hundred barrels, but does not specify that it is an outer row; rather he says simply that one of the ten rows should count as ma'aser, and he does not know which one? In this case he must take a full row along the diagonal - from one corner to the corner opposite it - treat it as terumas ma'aser, and sell it to a kohen except for one barrel, which is certainly terumas ma'aser, even though we do not know which one it is. For the diagonal necessarily cuts through all ten rows, so it is guaranteed to include at least one of the barrels that came from the ten that are ma'aser.
"Chatzi shurah achas ma'aser":
What is the law when he decided to separate ma'aser from only half the barrels, and said that he would do so from half a row, without identifying which one? When we come to ask "eizohi" - which one it is, he does not know. On this the mishnah says: "notel shtei shuros l'orkan" - he takes two rows along their length, that is, two rows on the diagonal, in order to be sure that they include one of the barrels that is genuinely from the ma'aser.
"Chavis achas ma'aser":
In the last case of the mishnah, the Tiferes Yisrael explains that we are dealing with a situation in which only one of the rows among the hundred barrels - ten barrels only - is actually tevel. Consequently only one barrel is needed from which to separate ma'aser, but he does not identify which barrel it is.
He says, then: "one barrel is ma'aser" - one of the barrels here is ma'aser, without specifying which, and he does not know where the tevel is, "v'eino yodea eizohi" - and he does not know which one it is. The law is: "notel mikol chavis v'chavis" - he takes from each and every barrel; since any given barrel may be the ma'aser, he must separate ten percent from each one of them as terumas ma'aser, and all of those separations are sold to a kohen except for one of them, which is of course the value of the actual terumas ma'aser.
In summary: in this mishnah we learned four cases of designating ma'aser without precise identification, and how terumas ma'aser is separated in each: if he said "shurah hachitzonah achas ma'aser" - he takes two barrels on the diagonal; if he said "shurah achas ma'aser" - he takes a full row on the diagonal; if he said "chatzi shurah achas ma'aser" - he takes two rows along their length; and if he said "chavis achas ma'aser" - he takes from each and every barrel. In all these cases what he takes is sold to a kohen, except for the portion that is certainly terumas ma'aser.
Thank you very much for joining the study of Maseches Demai. Tomorrow we will begin, with Hashem's help, Maseches Kilayim, continuing our journey through the mishnayos, and in particular through Seder Zeraim.