Pe'ah, Chapter 4, Mishnah 5. This Mishnah discusses the times during the day when the poor are permitted to gather the pe'ah. By way of introduction, one should know that the commentators explain that in order for a poor person to gather pe'ah, the owner of the field must either grant permission or be present at that time, and from this comes the halachah before us.
"Shalosh av'ayos bayom":
Three appearances of the owner during the day. Two explanations are given for the word "av'ayos":
An expression of appearing - the owner comes out and shows himself in the field three times a day, so that he can be present when the poor take the pe'ah.
An expression of be'aya - from the language of requesting and asking, meaning that these are the times at which the poor ask for the pe'ah.
In either case, the pe'ah is taken by the poor three times a day: "bashachar uvachatzos uvaminchah" - in the morning, at midday and at minchah time. The Yerushalmi explains the reason for each of these times:
In the morning - for nursing mothers, who can come and gather while their children are still asleep in the morning.
At midday - for the young children of the poor, who get up a little later, and at that hour they are able to gather.
At minchah time - for the elderly, since it takes them a long time to reach the field.
The dispute between Rabban Gamliel and Rabbi Akiva regarding the reason for these times:
Rabban Gamliel says: "Lo amru ela kedei shelo yifchosu" - the Sages established these times only as a minimum, and if the owner is willing he may add to them, since they were set for the benefit of the poor, provided that he does not give less than that.
Rabbi Akiva says: "Lo amru ela kedei shelo yosifu" - this is the maximum number, and it was set for the benefit of the owner, so that he should not have to trouble himself more than three times a day; but if he wishes to do less, he is permitted to do so.
The Rambam rules that the times are exactly three, no more and no less.
"Shel beis Nemer hayu melaktin al hachevel":
The Mishnah relates that in the field of a certain owner, of the house of Nemer, they would harvest using a rope: in every single row they would stretch out a rope in order to mark off the amount that would serve as pe'ah.
In this way, "venosnin pe'ah mikol uman v'uman" - they gave pe'ah from each and every row, so that the pe'ah was not concentrated in one spot in the field but was available in a number of places. This brought great benefit to the poor: they could find pe'ah throughout the harvest, at the end of every row, and it was accessible to them in various places in the field.
In summary: in this Mishnah we learned about the three times set for gathering pe'ah - in the morning, at midday and at minchah time - and about their reasons according to the Yerushalmi: nursing mothers, young children and the elderly. We examined the dispute between Rabban Gamliel and Rabbi Akiva as to whether these times were set as a minimum for the benefit of the poor or as a maximum for the benefit of the owner, and the Rambam's ruling that the three times are exact. Finally, we learned from the practice of the house of Nemer, who gave pe'ah from each and every row, and in doing so acted kindly toward the poor and spread the pe'ah throughout the entire field.