Peah, Chapter 4, Mishnah 3. In the previous mishnayos we dealt with the competition that can arise among the poor while they gather the peah, and this mishnah continues with that same subject.
"Natal miktzas peah v'zarak al hash'ar":
A poor man takes part of the peah he has gathered and throws it over the rest of the peah lying in the field, in order to hide it from the other poor people so that they will not notice it. The Sages did not look favorably on this act - it is not fair, and the peah must be open to everyone. They therefore penalized him, and he has nothing of it: not only does he fail to acquire the peah he concealed by throwing, but even the peah he had already gathered and used to cover it - he does not receive. This is a penalty that the Sages imposed upon him.
"Nafal lo aleha, paras talliso aleha":
What is the law when a poor man wishes to acquire the peah lying before him, and instead of gathering it with his hands he falls upon it with his body, or spreads his tallis or garment over it? To this the mishnah says: "Ma'avirin oso heimenah" - we move him away from it, since he has not acquired it in this manner.
"V'chein b'leket v'chein b'omer hashich'chah":
The mishnah concludes by teaching that these two laws - both the attempt to conceal by throwing, and the attempt to acquire by falling on the peah or spreading a garment over it - do not apply to peah alone, but to the other gifts to the poor as well:
Leket: when a person harvests his grain and stalks fall from his hands - they are leket, and the poor may pick them up and take them for themselves (the details of these laws will be explained later on).
Omer hashich'chah: a sheaf of grain that the owner of the field forgot in his field - it too is given to the poor.
In both of these the law is the same: concealing, falling upon them and spreading a garment over them do not work to acquire them.
The Gemara's question in Maseches Bava Metzia:
The Gemara raises a difficulty from our mishnah: the Sages instituted that a person's four amos acquire on his behalf, meaning that his very presence near an object helps him acquire it. If so, when he falls on the peah or spreads his tallis over it, why does he not acquire it?
There are two answers in the Gemara:
By falling upon it he revealed his intent that he is not interested in acquiring through the method the Sages instituted - acquisition through the object's proximity to him - since he adopts a different approach and falls upon it with his body. And since he does not want the four amos to work for him, and he is attempting a different method that constitutes no acquisition at all (for there is no acquisition by falling on an object or spreading a tallis over it) - nothing helped him and he does not acquire it.
The enactment of four amos was stated only in a place that any person is permitted to enter, such as a side alley or the sides of a public thoroughfare, but it does not apply in private property. And here we are dealing with another person's field, since he is gathering in someone else's field, and therefore the four amos do not acquire for him in this situation.
In summary: in this mishnah we learned that the Sages penalized a poor man who seeks to take control of the gifts to the poor improperly: one who throws part of the peah over the rest in order to conceal it - he has nothing of it, not even what he had already gathered; and one who falls upon it or spreads his tallis over it - we move him away from it. These laws apply to leket and to the forgotten sheaf as well. We also saw the Gemara's question from the enactment of four amos, and the two answers: that he revealed his intent that he does not wish to acquire in that manner, and that four amos do not acquire in another person's field.