Eduyos Chapter 3, Mishnah 3. Here too we find disputes between Rabbi Dosa ben Harkinas and the Sages, and here too Rabbi Dosa is the lenient one. The subject of the Mishnah is the gifts given to the kohanim, and it contains two topics: Terumah - the first portion of the produce, and reishis hagez - the first of the shearings. We will take each one in turn.
Terumah waste:
Terumah is a portion of the produce that a person separates and gives to a kohen. By rabbinic law its measure is one fiftieth, two percent, under ordinary circumstances for an average person. Terumah may not be eaten by a non-kohen, and the penalty is death at the hands of Heaven - dying before one's time.
The question before us is the status of those parts of the food that the kohen himself regards as waste and immediately removes and throws away. Since as far as he is concerned they are not food, has their status as Terumah lapsed, so that a non-kohen may eat them, or are they still part of the produce that was separated as Terumah and therefore forbidden?
The Mishnah gives two examples:
"Me'ei avatiach" - literally the innards of a melon. The word "me'ayim" refers to intestines, and here to the inner part of the various melons, where the seeds are held together by a stringy, fibrous material. That part is scooped out and thrown away, and it does indeed look like intestines. True, in modern Hebrew "avatiach" means watermelon, and Rashi explains it that way as well, but the straightforward reading here refers to the other melons - cantaloupe, honeydew and the like - which contain those stringy seeds that people do not eat, and which are therefore treated as waste.
"Kenivas yarak" - the verb "kaniv" means cutting off and removing the unappealing parts in order to make the food fit to eat. "Kenivas yarak" refers to those trimmings of the vegetables. The Bartenura explains that these are leaves that have grown moldy and the like, which a person cuts off and throws away because they are repulsive to him, even though strictly speaking they could be eaten - it is simply that the kohen has no interest in them.
Regarding both of these they disagreed: "Me'ei avatiach ukenivas yarak shel Terumah - Rabbi Dosa matir vachachamim osrin" - the innards of a melon and vegetable trimmings of Terumah: Rabbi Dosa permits and the Sages forbid. Rabbi Dosa holds that a non-kohen may eat them, and the Sages forbid it. And the halachah, once again, follows the Sages: every part of the Terumah food is forbidden to a non-kohen, and he may not eat any of it.
Reishis hagez:
Reishis hagez is the gift given to the kohen from the first shearing of one's flock. A person who has a flock, sheared his sheep and obtained wool, must give a portion of that wool to a kohen. By Torah law there is no fixed amount that must be given, and the Sages established the measure as one sixtieth of the shearing.
The verse says "reishis gez tzonecha," the first of the shearing of your flock, and from its wording we learn not only that this applies specifically to sheep and not to goats and cows, but also that a significant quantity of wool is required. The question is what counts as significant and what its measure is. Rabbi Dosa tends to require a large quantity, while the Sages are satisfied with less.
Rabbi Dosa's view: two conditions are required. First, that he have at least five sheep to shear; second, that each one of the five sheep produce a quantity of wool of a maneh and a half - a maneh uferas, which is one hundred and fifty dinar. Converted into sela'im (four dinar to a sela) that comes to thirty seven and a half sela'im per sheep - for simplicity's sake, almost half a kilogram, a little more than a pound. Altogether that is about two and a half kilograms, more than five pounds of wool, from five different sheep.
The Sages' view: "Chameish rechelos gozezos kol shehen" - five sheep that produce a shearing of any amount. It is enough that he has five sheep, whatever the quantity. Of course, "any amount" is not meant literally, since we have a tradition that the total shearing of the five sheep must come to at least sixty sela'im in weight. In other words, it makes no difference how much each individual sheep produces, as long as together they yield sixty sela'im - about one kilogram, roughly two pounds. That is not a large quantity; a single sheep nowadays produces twice that much.
The halachah, once again, follows the Sages: the obligation of reishis hagez applies as long as a person has five sheep, provided that their total shearing amounts to sixty sela'im - about one kilogram of wool in all.
In summary: This Mishnah contains two disputes between Rabbi Dosa ben Harkinas and the Sages regarding the laws of the gifts given to kohanim. In the first - the pulp of a melon and the trimmings of vegetables of Terumah, which the kohen treats as waste: Rabbi Dosa permits them to a non-kohen and the Sages forbid them, and the halachah follows the Sages. In the second - the minimum amount that obligates one in the first shearing of the flock: Rabbi Dosa requires five sheep, each of which yields a maneh and a peras of wool, while the Sages are satisfied with five sheep "of any amount whatsoever," provided that the total of their shearing is sixty sela'im, and the halachah follows the Sages.