5:
We are now in a better position to understand the views presented in our mishnah. If a farmer has utilized all the land available to him in such a way that he has beds of cereal crops (wheat, barley etc) laid out among his olive trees Bet Shammai have the tradition that he must treat each bed as a separate field and give
Pe'ah from each bed individually. Bet Hillel, on the other hand, have an opposite tradition, that the farmer may treat all the beds as if they were but one field and give
Pe'ah once only for the whole 'field' of cereal beds.
6:
From the very careful wording of Rambam's commentary on our mishnah it seems that we must treat the term in our mishnah 'cereal crops' not just as an example of crops that may be grown in such a manner, but to refer specifically to cereal crops. (It is possible that only cereal crops were grown in such a manner, among the trees.) On the other hand, Rabbi Ovadyah of Bertinoro in his commentary on our mishnah states that our mishnah uses olive trees merely as an example and that the given rule applies to cereal crops being grown by the farmer among any kinds of tree. (This is supported by the Gemara [Pe'ah 17b] which states that in Eretz-Israel the wording of our mishnah according to Rabbi Yoĥanan was 'beds of cereal crops between olive trees', whereas apparently the original wording given by Rabbi Yehudah the President of the Sanhedrin and original editor of the Mishnah was 'beds of cereal crops between trees' in general.)
7:
From a careful reading of the elaboration of our mishnah in the Gemara [Pe'ah 17b-c] we can understand that the maĥloket [disagreement] between the two schools is not as general as one might think. The Gemara explains that Bet Shammai hold that it is not usual for farmers to grow cereal crops in orchards and therefore we must assume that the farmer himself looks upon each bed as a separate field. Bet Hillel, on the other hand, hold that it is quite usual for farmers to act in this manner and that therefore no such assumption may be made. It seems that we can explain this divergence of opinion along socio-economic lines. Bet Shammai represented the landed gentry who had large estates in the countryside: they would have enough land area to obviate the necessity of planting cereal crops in orchards; therefore if a farmer does so it must be viewed as a curiosity and he must give Pe'ah for each bed separately. Bet Hillel, however, represented the townsfolk who had to make the best use of the small allotments that they had in the agricultural areas that surrounded the towns and villages. For them the maximum utilization of the meagre amounts of land available would be the rule rather than the exception.
8:
The Gemara determines that this maĥloket is defined by the density of the trees: if there are less than a certain number of trees growing within a certain area the cereal beds would be too far apart to be considered as being 'together' whereas the opposite would be true if there are more trees within that area. The Gemara refers the view of Bet Shammai to a situation in which the density of the trees is less than ten olive trees in an area called Bet Se'ah, which is defined as being 50 cubits by 50 cubits – 2500 square cubits. This is approximately 625 square metres in modern measurement. The utilization of the land between trees so far apart could not be interpreted, they say, as caused by economic considerations. It follows then that Bet Hillel are assuming a situation in which there are more than 10 trees growing in an area of 625 square metres and the farmer is utilizing this space.
9:
Perhaps we can understand this maĥloket in terms of appearance. When the trees are near to each other the farmer may be considered as viewing the whole area as being one field and therefore the beds of cereal crops are really just one field which has been interrupted as it were by the trees. On the other hand, if the trees are further apart from each other the farmer would not see the area as one field.
10:
Bet Shammai actually admit the reasoning of Bet Hillel, because they say that if the cereal beds are so close together (as they would be in an allotment) that they are actually touching one another that the rule follows Bet Hillel.
11:
In Mishneh Torah [Matnot Aniyyim 3:8-9] Rambam codifies the halakhah as follows:
If someone sows a field which has trees growing in it, even if it is
[arranged as] beds between the trees so that the seed is not contiguous
[nevertheless] he gives
Pe'ah once for the whole field since it is obvious that it is but one field and the seed has only been separated because of the trees.
Under what circumstances is this the case? – when there were ten trees [or more] in [an area of] one Bet Se'ah; if there were less trees [in such an area] he must give Pe'ah from each bed separately…
